Bsgamma Class Reference

A class for the \(\bar{B} \to X_s\gamma\) decay. More...

#include <bsgamma.h>

Inheritance diagram for Bsgamma:

Detailed Description

A class for the \(\bar{B} \to X_s\gamma\) decay.

Author

HEPfit Collaboration

Copyright

GNU General Public License

This class is used to build all the functions needed in order to compute the observables relative to the \(\bar{B} \to X_s\gamma\) decay, following the prescriptions of [Misiak:2006zs] and [Misiak:2015xwa].

Model parameters

The model parameters of bsgamma are summarized below:

Label	LaTeX symbol	Description
BLNPcorr	\(N_{b\to s\gamma}\)	The non perturbative uncertainty associated to the \(b\to s\gamma\) BR.
mukin	\(\mu^{\rm kin}\)	The mass scale for the b quark in the kinetic scheme.
BRsem	\(\mathrm{BR}(B\to X_ce\nu)\)	The branching ratio of \(B\to X_c e\nu\).
Mbkin	\(m_b^{\rm kin}\)	The b quark mass in the kinetic scheme.
Mcatmuc	\(m_c(\mu_c)\)	The c quark at \(\mu_c\).
mupi2, rhoD3, muG2, rhoLS3	\(\mu_{\pi}^{2}, \rho_{D}^{3}, \mu_{G}^{2}, \rho_{LS}^{3}\)	The B meson expectation values for the relevant dim. 5 and 6 operators.
mu_b_bsgamma, mu_c_bsgamma	\(\mu_b, \mu_c\)	The renormalization scales \(\mu_b\) and \(\mu_c\).

In general, the decay rate can be expressed as

\[ \Gamma(\bar{B} \to X_s^p \gamma)_{{E_\gamma > E_0}} = \frac{\left|V_{ts}^\star V_{tb}\right|^2 G_F^2 m_b^5 \alpha_{\rm em}}{32\pi^4} \sum_{i,j=1}^8 C_i(\mu_b)C_j(\mu_b) G_{ij}(E_0,\mu_b)\,. \]

Given the factor \(m_b^5\) present in the normalization, this formulation is not really usefull in a phenomenological analysis; in order to reduce this uncertainty, one can write the branching fraction dividing by the theoretical semileptonic decay rate and multiplying by the experimental semileptonic branching ratio:

\[ {\rm BR}[\bar{B} \to X_s \gamma]_{E_{\gamma} > E_0} = {\rm BR}[\bar{B} \to X_{c\,} e \bar{\nu}]_{\rm exp} \left( \frac{\Gamma[\bar{B} \to X_u e \bar{\nu}]}{\Gamma[\bar{B} \to X_{c\,} e \bar{\nu}]} \right)_{\rm th} \left( \frac{\Gamma(\bar{B} \to X_s^p \gamma)_{{E_\gamma > E_0}}}{\Gamma[\bar{B} \to X_u e \bar{\nu}]} \right)_{\rm th}\\ = {\rm BR}[\bar{B} \to X_c e \bar{\nu}]_{\rm exp} \left| \frac{ V^*_{ts} V_{tb}}{V_{cb}} \right|^2 \frac{6 \alpha_{\rm em}}{\pi\;C} \left[ P(E_0) + N(E_0) \right]\,, \]

where \(C\), taken from the fit in [Alberti:2014yda] , is the ratio

\[ C = \left| \frac{V_{ub}}{V_{cb}} \right|^2 \frac{\Gamma[\bar{B} \to X_c e \bar{\nu}]}{\Gamma[\bar{B} \to X_u e \bar{\nu}]} \,, \]

\(P(E_0)\) is given by the perturbative ratio

\[ \frac{\Gamma[ b \to X_s \gamma]_{E_{\gamma} > E_0}}{|V_{cb}/V_{ub}|^2 \; \Gamma[ b \to X_u e \bar{\nu}]} = \left| \frac{ V^*_{ts} V_{tb}}{V_{cb}} \right|^2 \frac{6 \alpha_{\rm em}}{\pi} \; P(E_0)\,, \]

and \(N(E_0)\) denotes the non-perturbative correction [Benzke:2010js] , which appears when \(b\) is replaced by \(\bar{B}\) in the previous equation.

The quantity \(P(E_0)\) depends quadratically on the Wilson coefficients, and can be perturbatively expand at NLO in the following form ( \(\tilde{\alpha}_s(\mu) \equiv \frac{ \alpha_s^{(5)}(\mu)}{4\pi}\)):

\[ P(E_0) = P^{(0)}(\mu_b) + \tilde{\alpha}_s(\mu_b)\Big[ P^{(1)}_1(\mu_b) + P^{(1)}_2(\mu_b)\Big] + O\Big(\tilde{\alpha}_s^2(\mu_b)\Big)\,. \]

Here, \(P^{(0)}\) and \(P_1^{(k)}\) mainly originate from the tree-level matrix element of \(Q_7\) [Misiak:2006ab], while a small contribution stems also from the penguin operators [Kaminski:2012eb] :

\[ P^{(0)} = \Big(C_7^{\rm (0) eff}(\mu_b)\Big)^2 + P^{(0)}_{\rm 4-body}\,,\\ P_1^{(1)} = 2C_7^{\rm (0) eff}(\mu_b)C_7^{\rm (1) eff}(\mu_b)\,.\\ \]

\(P_2^{(1)}\) depends on the LO Wilson coefficients \(C_i^{\rm (0)eff}\) throught the following relation [Misiak:2006ab] :

\[ P_2^{(1)} = \sum_{i,j=1}^8C_i^{\rm (0)eff}C_j^{\rm (0)eff}K_{ij}^{(1)}\,. \]

The \(K_{ij}^{(1)}\) functions are defined in the following way:

\[ K_{i7}^{(1)} = \mathrm{Re} r_i^{(1)} - \frac{1}{2}\gamma_{i7}^{\rm (0) eff}L_b + 2\phi_{i7}^{(1)}(\delta)\,, \qquad {\rm for}\:\:i\leq 6,\\ K_{77}^{(1)} = -\frac{182}{9} + \frac{8}{9}\pi^2 - \gamma_{77}^{\rm (0) eff}L_b + 4\phi_{77}^{(1)}(\delta)\,,\\ K_{78}^{(1)} = \frac{44}{9} - \frac{8}{27}\pi^2 - \frac{1}{2}\gamma_{87}^{\rm (0) eff}L_b + 2\phi_{78}^{(1)}(\delta)\,,\\ K_{ij}^{(1)} = 2(1+\delta_{ij})\phi_{ij}^{(1)}(\delta)\,, \qquad {\rm for}\:\:i,j \neq 7\,, \]

where we have defined the quantities

\[ L_b= \ln{\bigg(\frac{\mu_b}{ m_b^{kin}}\bigg)^2}, \qquad \delta = 1 - \frac{2E_0}{ m_b^{kin}}\,, \]

and all the relevant ingredients can be collected in [Buras:2002tp], [Gambino:2001ew], [Pott:1995if], [Huber:2014nna] .

The class is organized as follows: after the Wilson coefficients are computed in computeCoeff() and the cache is checked in checkCache(), the parameters are updated in updateParameters() and the ratio \(C\) is computed in C_sem().

The perturbative part of the Branching Ratio is computed order by order:

• at Leading Order it is computed in P0(), in which are taken into account both the leading term due to \(C_7\) and the subleading term due to the 4-body contribution, computed in P0_4body() ;

• at Next to Leading Order it is computed in P11() and P21(), where the latter is build from the Kij_1() function, which make use of the functions Phi11_1(), Phi12_1(), Phi13_1(), Phi14_1(), Phi15_1(), Phi16_1(), Phi17_1(), Phi18_1(), Phi22_1(), Phi23_1(), Phi24_1(), Phi25_1(), Phi26_1(), Phi27_1(), Phi28_1(), Phi33_1(), Phi34_1(), Phi35_1(), Phi36_1(), Phi37_1(), Phi38_1(), Phi44_1(), Phi45_1(), Phi46_1(), Phi47_1(), Phi48_1(), Phi55_1(), Phi56_1(), Phi57_1(), Phi58_1(), Phi66_1(), Phi67_1(), Phi68_1(), Phi77_1(), Phi78_1() and Phi88_1() . The subleading terms due to the 4-body contributions are currently hard-coded in Phi23_1_4body(), Phi24_1_4body(), Phi25_1_4body() and Phi26_1_4body(), and switched off due to setting the marco FOUR_BODY to false.

The \(V_{ub}\) corrections at LO are automatically taken into account in P0_4body() , while at NLO they are computed in the function Vub_NLO(), which considers contributions from 2-body, 3-body and 4-body decays, with the former switched off due to setting the marco FOUR_BODY to false.

All the perturbative corrections are eventually added in the function P(). The non-perturbative corrections are computed in the function N(). The observables are finally computed in the computeThValue() function.

Definition at line 166 of file bsgamma.h.

Public Member Functions
gslpp::complex	a (double z)
	The funcion \( a(z) \) as defined in [Buras:2002tp] . More...
gslpp::complex	b (double z)
	The funcion \( b(z) \) as defined in [Buras:2002tp] . More...
	Bsgamma (const StandardModel &SM_i, int obsFlag)
	Constructor. More...
	Bsgamma (const StandardModel &SM_i, QCD::quark quark_i, int obsFlag)
	Constructor. More...
double	C_sem ()
	The ratio \(C = | \frac{V_{ub}}{V_{cb}} |^2 \frac{\Gamma[\bar{B} \to X_c e \bar{\nu}]}{\Gamma[\bar{B} \to X_u e \bar{\nu}]} \) as defined in [Gambino:2013rza] , but with coefficients slightly modified due to different imput parameters (obtained by private conversation with Paolo Gambino). More...
void	computeCoeff (double mu)
	Compute the Wilson Coefficient. More...
double	computeThValue ()
	Computes the Branching Ratio for the \(b \to q \gamma\) decay. More...
double	delddel_Phi22_1 (double E0)
	Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines. More...
double	delddel_Phi28_1 (double z, double E0)
	Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines. More...
double	delddel_Phi88_1 (double E0)
	Derivative of the function Phi88_1() used to compute effects of massive quark loops on gluon lines. More...
double	delta (double E0)
	The cutoff energy function \( \delta = 1 - \frac{2 E_0}{M_b^{\rm kin}} \). More...
double	Delta (double r)
	The \(\Delta(r)\) function from Z. Phys. C 48, 673 (1990). More...
double	dY1 (double E0)
	The \( \delta Y^{(1)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
double	EW_NLO (double mu)
	The NLO electroweak correction to the BR as defined in [Gambino:2001au] . More...
double	f (double r)
	The \(f(\rho)\) function from hep-ph/0611123. More...
double	F_1 (double z)
	The \( F_{1}(z,1) \) interpolated function from arXiv:1503.01791. More...
double	F_2 (double z)
	The \( F_{2}(z,1) \) interpolated function from arXiv:1503.01791. More...
double	f_b (double z)
	The \( f_{b}(z) \) function from arXiv:1503.01791. More...
double	f_c (double z)
	The \( f_{c}(z) \) function from arXiv:1503.01791. More...
double	f_NLO_1 (double z)
	The \( f_{\rm NLO}(z,1) \) function from arXiv:1503.01791. More...
double	f_q (double z, double E0)
	The \( f_{q}(z,1) \) function from arXiv:1503.01791. More...
double	f_u (double r)
	The \(f_u\) function obtained after multiplying the fitted function \(U_C\) of arXiv:0803.0960 for \(C_FT_R\) and subtracting the \(r \to 0\) limit. More...
double	ff7_dMP (double E0)
	The 4-body NLO correction due to \(Q_7\) and d, \(ff^7_{d,MP}\), from [Huber:2014nna] . More...
double	ff7_sMP (double E0)
	The 4-body NLO correction due to \(Q_7\) and s, \(ff^7_{s,MP}\), from [Huber:2014nna] . More...
double	ff8_dMP (double E0)
	The 4-body NLO correction due to \(Q_8\) and d, \(ff^8_{d,MP}\), from [Huber:2014nna] . More...
double	ff8_sMP (double E0)
	The 4-body NLO correction due to \(Q_8\) and s, \(ff^8_{s,MP}\), from [Huber:2014nna] . More...
gslpp::complex	Gamma_t (double t)
	The function \( \Gamma \) as defined in [Gambino:2001ew] . More...
double	getKb_abs2_1mt (double t)
	The function \(|k_b(t)|^2(1 - t)\). More...
double	getKb_abs2_1mt2 (double t)
	The function \(|k_b(t)|^2(1 - t)^2\). More...
double	getKb_abs2_t2_1mt (double t)
	The function \(|k_b(t)|^2t^2(1 - t)\). More...
double	getKb_abs2_t2_1mt2 (double t)
	The function \(|k_b(t)|^2t^2(1 - t)^2\). More...
double	getKb_abs2_t_1mt (double t)
	The function \(|k_b(t)|^2t(1 - t)\). More...
double	getKb_abs2_t_1mt2 (double t)
	The function \(|k_b(t)|^2t(1 - t)^2\). More...
double	getKb_re_1mt (double t)
	The function \(Re(k_b(t))(1-t)\). More...
double	getKb_re_1mt2 (double t)
	The function \(Re(k_b(t))(1-t)^2\). More...
double	getKb_re_t (double t)
	The function \(Re(k_b(t))t\). More...
double	getKb_re_t2_1mt (double t)
	The function \(Re(k_b(t))t^2(1-t)\). More...
double	getKb_re_t2_1mt2 (double t)
	The function \(Re(k_b(t))t^2(1-t)^2\). More...
double	getKb_re_t_1mt (double t)
	The function \(Re(k_b(t))t(1-t)\). More...
double	getKb_re_t_1mt2 (double t)
	The function \(Re(k_b(t))t(1-t)^2\). More...
double	getKc_abs2_1mt (double t)
	The function \(|k_c(t)|^2(1 - t)\). More...
double	getKc_abs2_1mt2 (double t)
	The function \(t|k_c(t)|^2(1 - t)^2\). More...
double	getKc_abs2_t (double t)
	The function \(|k_c(t)|^2 t\). More...
double	getKc_abs2_t_1mt (double t)
	The function \(|k_c(t)|^2t(1 - t)\). More...
double	getKc_im_1mt (double t)
	The function \(Im(k_c(t))(1-t)\). More...
double	getKc_im_1mt2 (double t)
	The function \(Im(k_c(t))(1-t)^2\). More...
double	getKc_im_Kb_1mt (double t)
	The function \(Re(k_b(t))Im(k_c(t))(1-t)\). More...
double	getKc_im_Kb_1mt2 (double t)
	The function \(Re(k_b(t))Im(k_c(t))(1-t)^2\). More...
double	getKc_im_Kb_t_1mt (double t)
	The function \(Re(k_b(t))Im(k_c(t)t(1-t)\). More...
double	getKc_im_Kb_t_1mt2 (double t)
	The function \(Re(k_b(t))Im(k_c(t)t(1-t)^2\). More...
double	getKc_im_t (double t)
	The function \(Im(k_c(t))t\). More...
double	getKc_im_t_1mt (double t)
	The function \(Im(k_c(t))t(1-t)\). More...
double	getKc_im_t_1mt2 (double t)
	The function \(Im(k_c(t))t(1-t)^2\). More...
double	getKc_re_1mt (double t)
	The function \(Re(k_c(t))(1-t)\). More...
double	getKc_re_1mt2 (double t)
	The function \(Re(k_c(t))(1-t)^2\). More...
double	getKc_re_Kb_1mt (double t)
	The function \(Re(k_b(t))Re(k_c(t))(1-t)\). More...
double	getKc_re_Kb_1mt2 (double t)
	The function \(Re(k_b(t))Re(k_c(t))(1-t)^2\). More...
double	getKc_re_Kb_t_1mt (double t)
	The function \(Re(k_b(t))Re(k_c(t)t(1-t)\). More...
double	getKc_re_Kb_t_1mt2 (double t)
	The function \(Re(k_b(t))Re(k_c(t)t(1-t)^2\). More...
double	getKc_re_t (double t)
	The function \(Re(k_c(t))t\). More...
double	getKc_re_t_1mt (double t)
	The function \(Re(k_c(t))t(1-t)\). More...
double	getKc_re_t_1mt2 (double t)
	The function \(Re(k_c(t))t(1-t)^2\). More...
double	h27_2 (double z, double E0)
	The \( h_{27}^{(2)}(z,\delta) \) function from arXiv:1009.5685 and arXiv:1503.01791. More...
double	Int_b1 (double E0)
	Integral of the functions getKb_re_1mt() and getKb_re_1mt2(). More...
double	Int_b2 (double E0)
	Integral of the functions getKb_re_t_1mt() and getKb_re_t_1mt2(). More...
double	Int_b3 (double E0)
	Integral of the functions getKb_re_t() and getKb_re_t_1mt(). More...
double	Int_b4 (double E0)
	Integral of the functions getKb_re_t2_1mt() and getKb_re_t2_1mt2(). More...
double	Int_bb1 (double E0)
	Integral of the functions getKb_abs2_1mt() and getKb_abs2_1mt2(). More...
double	Int_bb2 (double E0)
	Integral of the functions getKb_abs2_t_1mt() and getKb_abs2_t_1mt2(). More...
double	Int_bb4 (double E0)
	Integral of the functions getKb_abs2_t2_1mt() and getKb_abs2_t2_1mt2(). More...
gslpp::complex	Int_bc1 (double E0)
	Integral of the functions getKc_re_Kb_1mt(), getKc_im_Kb_1mt() and getKc_re_Kb_1mt2(), getKc_im_Kb_1mt2(). More...
gslpp::complex	Int_bc2 (double E0)
	Integral of the functions getKc_re_Kb_t_1mt(), getKc_im_Kb_t_1mt() and getKc_re_Kb_t_1mt2(), getKc_im_Kb_t_1mt2(). More...
gslpp::complex	Int_c1 (double E0)
	Integral of the functions getKc_re_1mt(), getKc_im_1mt() and getKc_re_1mt2(), getKc_im_1mt2(). More...
gslpp::complex	Int_c2 (double E0)
	Integral of the functions getKc_re_t_1mt(), getKc_im_t_1mt() and getKc_re_t_1mt2(), getKc_im_t_1mt2(). More...
gslpp::complex	Int_c3 (double E0)
	Integral of the functions getKc_re_t(), getKc_im_t() and getKc_re_t_1mt(), getKc_im_t_1mt(). More...
double	Int_cc (double E0)
	Integral of the functions getKc_abs2_t() and getKc_abs2_t_1mt(). More...
double	Int_cc1 (double E0)
	Integral of the functions getKc_abs2_1mt() and getKc_abs2_1mt^(). More...
double	Int_cc1_part1 (double E0)
	Integral of the functions getKc_abs2_1mt(). More...
double	Int_Phi77_2rem (double E0)
	The integral of omega77() More...
double	K77_2_z1 (double E0, double mu)
	The \( K_{77}^{(2),z=1} \) function computed in the limit \( m_b = m_c \). More...
gslpp::complex	kappa (double Mq, double t)
	The function \( k \) as defined in [Pott:1995if] . More...
gslpp::complex	Kij_1 (int i, int j, double E0, double mu)
	The \( K_{ij}^{(1)} \) function from [Misiak:2006ab] . More...
double	Kij_2 (int i, int j, double E0, double mu_b, double mu_c)
	The \( K_{ij}^{(2)} \) function from arXiv:1503.01791. More...
double	mddel_f_NLO (double z, double E0)
	The \( (1. - \delta)\frac{d}{d\delta}f_{\rm NLO}(z,\delta) \) function from arXiv:1503.01791. More...
double	N (double E0, double mu)
	The non perturbative part of the \(BR\) as defined in [Benzke:2010js] , \(N\). More...
double	N_27 ()
	The non perturbative part of the \(BR\) due to \(Q_2-Q_7\) interference as defined in [Gambino:2001ew] , \(N_{27}\). More...
double	N_77 (double E0, double mu)
	The non perturbative part of the \(BR\) due to \(Q_7-Q_7\) interference as defined in arXiv:0911.2175, \(N_{77}\). More...
double	omega (double E0)
	The cutoff energy function \( \omega \) as defined in [Kaminski:2012eb] . More...
double	omega77 (double z)
	The \( \omega_{77} \) function, linear combination of the functions \( F^{(2,a)} \), \( F^{(2,na)} \) and \( F^{(2,nf)} \) from hep-ph/0505097. More...
double	P (double E0, double mu_b, double mu_c, orders order)
	The perturbative part of the \(BR\) as defined in [Misiak:2006ab] , \(P\). More...
double	P0 (double E0)
	The perturbative part \( P^{(0)} \) of the BR as defined in [Misiak:2006ab] . More...
double	P0_4body (double E0, double t)
	The 4-body LO contribution as defined in [Kaminski:2012eb] . More...
double	P11 ()
	The perturbative part \( P_1^{(1)} \) of the BR as defined in [Misiak:2006ab] . More...
double	P12 ()
	The perturbative part \( P_1^{(2)} \) of the BR as defined in [Misiak:2006ab] . More...
double	P21 (double E0, double mu)
	The perturbative part \( P_2^{(1)} \) of the BR as defined in [Misiak:2006ab] . More...
double	P21_CPodd (double E0, double mu)
	The CP odd part of the perturbative part \( P_2^{(1)} \) of the BR as defined in [Misiak:2006ab] . More...
double	P22 (double E0, double mu_b, double mu_c)
	The perturbative part \( P_2^{(2)} \) of the BR as defined in [Misiak:2006ab] . More...
double	P32 (double E0, double mu)
	The perturbative part \( P_3^{(2)} \) of the BR as defined in [Misiak:2006ab] . More...
double	Phi11_1 (double E0)
	The \( \Phi_{11}^{(1)} \) function from [Gambino:2001ew] . More...
double	Phi12_1 (double E0)
	The \( \Phi_{12}^{(1)} \) function from [Gambino:2001ew] . More...
gslpp::complex	Phi13_1 (double E0)
	The \( \Phi_{13}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
gslpp::complex	Phi14_1 (double E0)
	The \( \Phi_{14}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
gslpp::complex	Phi15_1 (double E0)
	The \( \Phi_{15}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
gslpp::complex	Phi16_1 (double E0)
	The \( \Phi_{16}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
gslpp::complex	Phi17_1 (double E0, double z)
	The \( \Phi_{17}^{(1)} \) function from [Gambino:2001ew] . More...
gslpp::complex	Phi18_1 (double E0, double z)
	The \( \Phi_{18}^{(1)} \) function from [Gambino:2001ew] . More...
double	Phi22_1 (double E0)
	The \( \Phi_{22}^{(1)} \) function from [Gambino:2001ew] . More...
double	Phi22_2beta0 (double E0, double mu)
	The \( \Phi_{22}^{(2)\beta_0} \) function from arXiv:1009.5685. More...
gslpp::complex	Phi23_1 (double E0)
	The \( \Phi_{23}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi23_1_4body (double E0)
	The \( \Phi_{23}^{(1),{\rm 4-body}} \) function obtained from [Huber:2014nna] . More...
gslpp::complex	Phi24_1 (double E0)
	The \( \Phi_{24}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi24_1_4body (double E0)
	The \( \Phi_{24}^{(1),{\rm 4-body}} \) function obtained from [Huber:2014nna] . More...
gslpp::complex	Phi25_1 (double E0)
	The \( \Phi_{25}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi25_1_4body (double E0)
	The \( \Phi_{25}^{(1),{\rm 4-body}} \) function obtained from [Huber:2014nna] . More...
gslpp::complex	Phi26_1 (double E0)
	The \( \Phi_{26}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi26_1_4body (double E0)
	The \( \Phi_{26}^{(1),{\rm 4-body}} \) function obtained from [Huber:2014nna] . More...
gslpp::complex	Phi27_1 (double E0, double z)
	The \( \Re \Phi_{27}^{(1)} \) function from [Gambino:2001ew] . More...
gslpp::complex	Phi28_1 (double E0, double z)
	The \( \Phi_{28}^{(1)} \) function from [Gambino:2001ew] . More...
double	Phi28_2beta0 (double E0, double mu)
	The \( \Phi_{28}^{(2)\beta_0} \) function from arXiv:1009.5685. More...
double	Phi33_1 (double E0)
	The \( \Phi_{33}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
double	Phi34_1 (double E0)
	The \( \Phi_{34}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
double	Phi35_1 (double E0)
	The \( \Phi_{35}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
gslpp::complex	Phi36_1 (double E0)
	The \( \Phi_{36}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi37_1 (double E0)
	The \( \Phi_{37}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi38_1 (double E0)
	The \( \Phi_{38}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi44_1 (double E0)
	The \( \Phi_{44}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
double	Phi45_1 (double E0)
	The \( \Phi_{45}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
gslpp::complex	Phi46_1 (double E0)
	The \( \Phi_{46}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi47_1 (double E0)
	The \( \Phi_{47}^{(1)} \) function from [Gambino:2001ew] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi48_1 (double E0)
	The \( \Phi_{48}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi55_1 (double E0)
	The \( \Phi_{55}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
gslpp::complex	Phi56_1 (double E0)
	The \( \Phi_{56}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi57_1 (double E0)
	The \( \Phi_{57}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi58_1 (double E0)
	The \( \Phi_{58}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
gslpp::complex	Phi66_1 (double E0)
	The \( \Phi_{66}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] . More...
gslpp::complex	Phi67_1 (double E0)
	The \( \Phi_{67}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
gslpp::complex	Phi68_1 (double E0)
	The \( \Phi_{68}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] . More...
double	Phi77_1 (double E0)
	The \( \Phi_{77}^{(1)} \) function from [Gambino:2001ew] . More...
double	Phi77_2beta0 (double E0, double mu)
	The \( \Phi_{77}^{(2)\beta_0} \) function from [Misiak:2006ab] .. More...
double	Phi77_2rem (double E0)
	The part of the \( K_{77}^{(2)} \) function with no \( \beta_0 \) dependance, as defined in [Misiak:2006ab] . More...
double	Phi78_1 (double E0)
	The \( \Phi_{78}^{(1)} \) function from [Gambino:2001ew] . More...
double	Phi88_1 (double E0)
	The \( \Phi_{88}^{(1)} \) function from [Gambino:2001ew] . More...
double	Phi88_2beta0 (double E0, double mu)
	The \( \Phi_{88}^{(2)\beta_0} \) function from arXiv:1009.5685. More...
gslpp::complex	r1 (int i, double z)
	The funcion \( r_i^{(1)}(z) \) as defined in [Buras:2002tp] . More...
gslpp::complex	r1_ew (int i, double z)
	The funcion \( r_{i,ew}^{(1)}(z) \) as defined in [Gambino:2001au] . More...
double	Rer22 (double z)
	The \( Re r_2^{(2)} \) function from [Misiak:2006ab] . More...
double	rho (double E0)
	The cutoff energy function \( \rho \) as defined in [Kaminski:2012eb] . More...
double	T1 (double E0, double t)
	The cutoff energy function \( T_1 \) as defined in [Kaminski:2012eb] . More...
double	T2 (double E0, double t)
	The cutoff energy function \( T_2 \) as defined in [Kaminski:2012eb] . More...
double	T3 (double E0, double t)
	The cutoff energy function \( T_3 \) as defined in [Kaminski:2012eb] . More...
void	updateParameters ()
	The update parameter method for bsgamma. More...
double	Vub_NLO (double E0)
	The total NLO Vub part of the \(BR\), \(Vub^{NLO}\). More...
double	Vub_NLO_2body ()
	The 2 body NLO Vub part of the \(BR\) as defined in [Gambino:2001ew] , \(Vub^{NLO}_{2b}\). More...
double	Vub_NLO_2body_CPodd ()
	The CP odd part of the 2 body NLO Vub part of the \(BR\) as defined in [Gambino:2001ew] , \(Vub^{NLO}_{2b,CPodd}\). More...
double	Vub_NLO_3body_A (double E0)
	The first piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,A,CPodd}\). More...
double	Vub_NLO_3body_A_CPodd (double E0)
	The CP odd part of the first piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,A}\). More...
double	Vub_NLO_3body_B (double E0)
	The second piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,B,CPodd}\). More...
double	Vub_NLO_3body_B_CPodd (double E0)
	The CP odd part of the second piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,B}\). More...
double	Vub_NLO_4body (double E0)
	The 4 body NLO Vub part of the \(BR\) obtained from [Huber:2014nna] , \(Vub^{NLO}_{4b,CPodd}\). More...
double	Vub_NLO_4body_CPodd (double E0)
	The CP odd part of the 4 body NLO Vub part of the \(BR\) obtained from [Huber:2014nna] , \(Vub^{NLO}_{4b}\). More...
double	Vub_NLO_CPodd (double E0)
	The CP odd part of the total NLO Vub part of the \(BR\), \(Vub^{NLO}_{CPodd}\). More...
double	Vub_NNLO (double E0)
	The NNLO Vub part of the \(BR\) as defined in xxxxxxxxx, \(Vub^{NLO}\). More...
double	Y1 (double E0, double mu)
	The \( Y^{(1)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
double	Y2 (double E0, double mu)
	The \( Y^{(2)}(z_0,\mu) \) function from arXiv:0805.3911v2 and arXiv:1005.5587v1. More...
double	Y2CA (double E0, double mu)
	The \( Y^{(2,CA)}(z_0,\mu) \) function from arXiv:1005.5587v1. More...
double	Y2CF (double E0, double mu)
	The \( Y^{(2,CF)}(z_0,\mu) \) function from arXiv:1005.5587v1. More...
double	Y2NH (double E0, double mu)
	The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
double	Y2NL (double E0, double mu)
	The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
double	Y2NV (double E0, double mu)
	The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
double	Y2NV_PHI1 (double rho)
	The \( \Phi_1(\rho) \) function from arXiv:0805.3911v2. More...
double	Y2NV_PHI2 (double rho)
	The \( \Phi_2(\rho) \) function from arXiv:0805.3911v2. More...
double	Y2NV_PHI3 (double rho)
	The \( \Phi_3(\rho) \) function from arXiv:0805.3911v2. More...
double	Y2NV_PHI4 (double rho)
	The \( \Phi_4(\rho) \) function from arXiv:0805.3911v2. More...
double	zdz_f_NLO (double z, double E0)
	The \( z \frac{d}{dz}f_{\rm NLO}(z,\delta) \) function from arXiv:1503.01791. More...
double	zdz_Phi22_1 (double E0)
	Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines. More...
double	zdz_Phi28_1 (double z, double E0)
	Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines. More...
double	zeta ()
	The squared ratio between \(m_c\) and \(m_b^{\rm kin}\), \( z \). More...
Public Member Functions inherited from ThObservable
double	getBinMax ()
	A get method to get the maximum value of the bin. More...
double	getBinMin ()
	A get method to get the minimum value of the bin. More...
const StandardModel &	getModel ()
	A get method to get the model. More...
const std::vector< std::string >	getParametersForObservable ()
	A get method to get the parameters for the specific observable. More...
void	setBinMax (double max)
	A set method to set the maximum value of the bin. More...
void	setBinMin (double min)
	A set method to set the minimum value of the bin. More...
void	setParametersForObservable (std::vector< std::string > parametersForObservable_i)
	A set method to get the parameters for the specific observable. More...
	ThObservable (const StandardModel &SM_i)
	Constructor. More...
	ThObservable (const ThObservable &orig)
	The copy constructor. More...
virtual	~ThObservable ()
	The default destructor. More...

Private Member Functions
void	checkCache ()
	The caching method for bsgamma. More...

Private Attributes
double	ale
double	AleatMztilde
gslpp::vector< gslpp::complex > **	allcoeff
gslpp::vector< gslpp::complex > **	allcoeffprime
double	Alstilde
double	alsUps
double	avaINT
double	BLNPcorr
double	BRsl
double	C
gslpp::complex	C1_0
gslpp::complex	C1_1
gslpp::complex	C2_0
gslpp::complex	C2_1
gslpp::complex	C3_0
gslpp::complex	C3_1
gslpp::complex	C4_0
gslpp::complex	C4_1
gslpp::complex	C5_0
gslpp::complex	C5_1
gslpp::complex	C6_0
gslpp::complex	C6_1
gslpp::complex	C7_0
gslpp::complex	C7_1
gslpp::complex	C7_1ew
gslpp::complex	C7_2
gslpp::complex	C7p_0
gslpp::complex	C7p_1
gslpp::complex	C8_0
gslpp::complex	C8_1
gslpp::complex	C_7_NP
gslpp::complex	C_7p_NP
double	CacheIntb1
double	CacheIntb2
double	CacheIntb3
double	CacheIntb4
double	CacheIntbb1
double	CacheIntbb2
double	CacheIntbb4
gslpp::complex	CacheIntbc1
gslpp::complex	CacheIntbc2
gslpp::complex	CacheIntc1
gslpp::complex	CacheIntc2
gslpp::complex	CacheIntc3
double	CacheIntcc
double	CacheIntcc1
double	CacheIntcc1p1
double	CacheIntPhi772r
double	CKMratio
gslpp::complex	CKMu
double	CKMusq
bool	EWflag
bool	FOUR_BODY
ROOT::Math::GSLIntegrator	ig
unsigned int	Intb1Cached
unsigned int	Intb2Cached
unsigned int	Intb3Cached
unsigned int	Intb4Cached
double	Intb_cache
unsigned int	Intb_updated
unsigned int	Intbb1Cached
unsigned int	Intbb2Cached
unsigned int	Intbb4Cached
unsigned int	Intbc1Cached
unsigned int	Intbc2Cached
gslpp::vector< double >	Intbc_cache
unsigned int	Intbc_updated
unsigned int	Intc1Cached
unsigned int	Intc1imCached
unsigned int	Intc2Cached
unsigned int	Intc3Cached
unsigned int	Intcc1Cached
unsigned int	Intcc1p1Cached
unsigned int	IntccCached
unsigned int	IntPhi772rCached
double	Mb
double	Mb_kin
double	Mc
double	Ms
double	mu_b
double	mu_c
double	mu_G2
double	mu_kin
double	mu_pi2
double	Mz
int	obs
double	overall
QCD::quark	quark
double	rho_D3
double	rho_LS3
bool	SMEFT_NP_btos = false
bool	SUM
gslpp::complex	V_cb
gslpp::complex	V_tb
gslpp::complex	V_ub
bool	WET_NP_btos = false
ROOT::Math::Functor1D	wf

Additional Inherited Members
Protected Attributes inherited from ThObservable
double	max
	the bin maximum. More...
double	min
	The bin minimum. More...
std::vector< std::string >	parametersForObservable
	a vector of parameter namesfor the specific observable More...
const StandardModel &	SM
	A reference to an object of StandardMode class. More...

Constructor & Destructor Documentation

Bsgamma() [1/2]

Bsgamma::Bsgamma	(	const StandardModel &	SM_i,
		QCD::quark	quark_i,
		int	obsFlag
	)

Constructor.

Parameters

[in]	SM_i	a reference to an object of type StandardModel
[in]	quark_i	final quark type of the decay
[in]	obsFlag	flag to choose which observable to compute

Definition at line 23 of file bsgamma.cpp.

: ThObservable(SM_i),
Intbc_cache(2, 0.), ig(ROOT::Math::Integration::kADAPTIVESINGULAR, ROOT::Math::Integration::kGAUSS51), wf()
{    
    if (obsFlag > 0 and obsFlag < 3) obs = obsFlag;
    else throw std::runtime_error("obsFlag in bsgamma can only be 1 (BR) or 2 (ACP)");
    
    quark = quark_i;
    
    SUM = false;
    EWflag = true;
    FOUR_BODY = false;
    WET_NP_btos = false;
    SMEFT_NP_btos = false;
    
    setParametersForObservable(make_vector<std::string>() << "mukin" << "BRsem" << "Mbkin" << "Mcatmuc" << "mupi2" 
                                                          << "rhoD3" << "muG2" << "rhoLS3" << "BLNPcorr" << "mu_b_bsgamma" << "mu_c_bsgamma");
    
    Intb1Cached = 0;
    Intb2Cached = 0;
    Intb3Cached = 0;
    Intb4Cached = 0;
    Intbb1Cached = 0;
    Intbb2Cached = 0;
    Intbb4Cached = 0;
    Intbc1Cached = 0;
    Intbc2Cached = 0;
    Intc1Cached = 0;
    Intc2Cached = 0;
    Intc3Cached = 0;
    Intcc1Cached = 0;
    IntPhi772rCached = 0;
 
}

Bsgamma() [2/2]

Bsgamma::Bsgamma	(	const StandardModel &	SM_i,
		int	obsFlag
	)

Constructor.

Parameters

[in]	SM_i	a reference to an object of type StandardModel
[in]	obsFlag	flag to choose which observable to compute

Definition at line 58 of file bsgamma.cpp.

: ThObservable(SM_i),
Intbc_cache(2, 0.), ig(ROOT::Math::Integration::kADAPTIVESINGULAR, ROOT::Math::Integration::kGAUSS51), wf()
{
    if (obsFlag > 0 and obsFlag < 3) obs = obsFlag;
    else throw std::runtime_error("obsFlag in bsgamma can only be 1 (BR) or 2 (ACP)");
    
    SUM = true;
    EWflag = true;
    FOUR_BODY = false;
    
    Intb1Cached = 0;
    Intb2Cached = 0;
    Intb3Cached = 0;
    Intb4Cached = 0;
    Intbb1Cached = 0;
    Intbb2Cached = 0;
    Intbb4Cached = 0;
    Intbc1Cached = 0;
    Intbc2Cached = 0;
    Intc1Cached = 0;
    Intc2Cached = 0;
    Intc3Cached = 0;
    Intcc1Cached = 0;
    IntPhi772rCached = 0;
 
}

Member Function Documentation

a()

gslpp::complex Bsgamma::a

(

double

z

)

The funcion \( a(z) \) as defined in [Buras:2002tp] .

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( a(z) \)

Definition at line 232 of file bsgamma.cpp.

{
    double zeta3 = gsl_sf_zeta_int(3);
    
    double z2=z*z;
    double z3=z2*z;
    double z4=z3*z;
    double z5=z4*z;
    double z6=z5*z;
    
    double L=log(z);
    double L2=L*L;
    double L3=L2*L;
    
    double pi2=M_PI*M_PI;
    
    if (z == 1.) return 4.0859 + 4./9. * M_PI * gslpp::complex::i();
    else return 16./9. * ( ( 5./2. - pi2/3. - 3.*zeta3 
            + ( 5./2. - 3./4.*pi2 )*L + L2/4. + L3/12. )*z 
            + ( 7./4. + 2./3.*pi2 - pi2*L/2. - L2/4. + L3/12. )*z2 
            + ( -7./6. - pi2/4. + 2*L - 3./4.*L2 )*z3 
            + ( 457./216. - 5./18*pi2 - L/72. - 5./6.*L2 )*z4 
            + ( 35101./8640. - 35./72.*pi2 - 185./144.*L - 35./24.*L2 )*z5
            + ( 67801./8000. - 21./20.*pi2 - 3303./800.*L - 63./20.*L2 )*z6 + 
            gslpp::complex::i()*M_PI*( ( 2. - pi2/6. + L/2. + L2/2. )*z 
            + ( 1./2. - pi2/6. - L + L2/2. )*z2
            + z3 + 5./9.*z4 + 49./72.*z5 + 231./200.*z6) );
}

b()

gslpp::complex Bsgamma::b

(

double

z

)

The funcion \( b(z) \) as defined in [Buras:2002tp] .

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( b(z) \)

Definition at line 261 of file bsgamma.cpp.

{
    double z2=z*z;
    double z3=z2*z;
    double z4=z3*z;
    double z5=z4*z;
    double z6=z5*z;
    
    double L=log(z);
    double L2=L*L;
    
    double pi2=M_PI*M_PI;
    
    if (z == 1.) return 0.0316 + 4./81. * M_PI * gslpp::complex::i();
    else return -8./9. * ( ( -3. + pi2/6. - L )*z - 2./3.*pi2*pow(z,3./2.) 
            + ( 1./2. + pi2 -2.*L - L2/2. )*z2 
            + ( -25./12. - pi2/9. - 19./18.*L + 2.*L2 )*z3 
            + ( -1376./225. + 137./30.*L + 2.*L2 + 2./3.*pi2 )*z4 
            + ( -131317./11760. + 887./84.*L + 5.*L2 + 5./3.*pi2 )*z5 
            + ( -2807617./97200. + 16597./540.*L + 14.*L2 + 14./3.*pi2 )*z6 + 
            gslpp::complex::i()*M_PI*( -z + ( 1 - 2.*L )*z2 
            + ( -10./9. + 4./3.*L )*z3 + z4 + 2./3.*z5 + 7./9.*z6) );
}

C_sem()

double Bsgamma::C_sem

(

)

The ratio \(C = | \frac{V_{ub}}{V_{cb}} |^2 \frac{\Gamma[\bar{B} \to X_c e \bar{\nu}]}{\Gamma[\bar{B} \to X_u e \bar{\nu}]} \) as defined in [Gambino:2013rza] , but with coefficients slightly modified due to different imput parameters (obtained by private conversation with Paolo Gambino).

Returns

\(C\)

Definition at line 2402 of file bsgamma.cpp.

{
    double z=zeta();
    return (1. - 8. * z + 8. * z*z*z - z*z*z*z - 12. * z*z * log(z)) * ( 0.903 
            - 0.588 * (SM.Alstilde5(4.6)*4*M_PI - 0.22) + 0.0650 * (Mb_kin - 4.55) 
            - 0.1080 * (Mc - 1.05) - 0.0122  * mu_G2 - 0.199 * rho_D3 + 0.004 * rho_LS3);
}

checkCache()

void Bsgamma::checkCache ( )

private

The caching method for bsgamma.

Definition at line 86 of file bsgamma.cpp.

{
    if (Mb_kin == Intb_cache)
        Intb_updated = 1;
    else {
        Intb_cache = Mb_kin;
        Intb_updated = 0;
    }
    
    if (Mb_kin == Intbc_cache(0) && Mc == Intbc_cache(1)) 
        Intbc_updated = 1;
    else {
        Intbc_cache(0) = Mb_kin;
        Intbc_cache(1) = Mc;
        Intbc_updated = 0;
    }
}

computeCoeff()

void Bsgamma::computeCoeff

(

double

mu

)

Compute the Wilson Coefficient.

Parameters

[in]

mu

low scale of the decay

Definition at line 1978 of file bsgamma.cpp.

{
    
    /*allcoeff = SM.getMyFlavour()->ComputeCoeffsgamma(160.);
    
    C1_0 = (*(allcoeff[LO]))(0);
    C2_0 = (*(allcoeff[LO]))(1);
    C3_0 = (*(allcoeff[LO]))(2);
    C4_0 = (*(allcoeff[LO]))(3);
    C5_0 = (*(allcoeff[LO]))(4);
    C6_0 = (*(allcoeff[LO]))(5);
    C7_0 = (*(allcoeff[LO]))(6);
    C8_0 = (*(allcoeff[LO]))(7);
    
    C1_1 = (*(allcoeff[NLO]))(0)/Alstilde;
    C2_1 = (*(allcoeff[NLO]))(1)/Alstilde;
    C3_1 = (*(allcoeff[NLO]))(2)/Alstilde;
    C4_1 = (*(allcoeff[NLO]))(3)/Alstilde;
    C5_1 = (*(allcoeff[NLO]))(4)/Alstilde;
    C6_1 = (*(allcoeff[NLO]))(5)/Alstilde;
    C7_1 = (*(allcoeff[NLO]))(6)/Alstilde;
    C8_1 = (*(allcoeff[NLO]))(7)/Alstilde;
    
    std::cout << "C_0(MuW): (" << C1_0.real() << "," << C2_0.real() << "," 
            << C3_0.real() << "," << C4_0.real() << "," << C5_0.real() << "," 
            << C6_0.real() << "," << C7_0.real() << "," << C8_0.real() << ")" << std::endl;
    std::cout << "C_1(MuW): (" << C1_1.real() << "," << C2_1.real() << "," 
            << C3_1.real() << "," << C4_1.real() << "," << C5_1.real() << "," 
            << C6_1.real() << "," << C7_1.real() << "," << C8_1.real() << ")" << std::endl << std::endl;*/
    
    allcoeff = SM.getFlavour().ComputeCoeffsgamma(mu);
    allcoeffprime = SM.getFlavour().ComputeCoeffprimesgamma(mu);
    
    C1_0 = (*(allcoeff[LO]))(0);
    C2_0 = (*(allcoeff[LO]))(1);
    C3_0 = (*(allcoeff[LO]))(2);
    C4_0 = (*(allcoeff[LO]))(3);
    C5_0 = (*(allcoeff[LO]))(4);
    C6_0 = (*(allcoeff[LO]))(5);
    C7_0 = (*(allcoeff[LO]))(6)  + C_7_NP;
    C8_0 = (*(allcoeff[LO]))(7);
    
    C1_1 = (*(allcoeff[NLO]))(0)/Alstilde;
    C2_1 = (*(allcoeff[NLO]))(1)/Alstilde;
    C3_1 = (*(allcoeff[NLO]))(2)/Alstilde;
    C4_1 = (*(allcoeff[NLO]))(3)/Alstilde;
    C5_1 = (*(allcoeff[NLO]))(4)/Alstilde;
    C6_1 = (*(allcoeff[NLO]))(5)/Alstilde;
    C7_1 = (*(allcoeff[NLO]))(6)/Alstilde;
    C8_1 = (*(allcoeff[NLO]))(7)/Alstilde;
 
    C7_2 = (*(allcoeff[NNLO]))(6)/Alstilde/Alstilde;
 
    C7p_0 = (*(allcoeffprime[LO]))(6) + Ms/Mb*((*(allcoeff[LO]))(6)) + C_7p_NP;
    C7p_1 = ((*(allcoeffprime[NLO]))(6) + Ms/Mb*((*(allcoeff[NLO]))(6)))/Alstilde; /*Implement the other WCs*/
 
    /*std::cout << "C_0(mu): (" << C1_0.real() << "," << C2_0.real() << "," 
            << C3_0.real() << "," << C4_0.real() << "," << C5_0.real() << "," 
            << C6_0.real() << "," << C7_0.real() << "," << C8_0.real() << ")" << std::endl;
    std::cout << "C_1(mu): (" << C1_1.real() << "," << C2_1.real() << "," 
            << C3_1.real() << "," << C4_1.real() << "," << C5_1.real() << "," 
            << C6_1.real() << "," << C7_1.real() << "," << C8_1.real() << ")" << std::endl << std::endl;
    std::cout << "C_2^7(mu): " << C7_2.real() << std::endl << std::endl;*/
    
    C7_1ew = 4.868;
    
}

computeThValue()

double Bsgamma::computeThValue ( )

virtual

Computes the Branching Ratio for the \(b \to q \gamma\) decay.

Returns

\(BR\)

Implements ThObservable.

Definition at line 2506 of file bsgamma.cpp.

{
    double E0 = getBinMin();
    
    updateParameters();
    
    if (obs == 1)
        return overall *  ( P(E0, mu_b, mu_c, NNLO) + N(E0, mu_b) );
    if (obs == 2)
        return (Alstilde * P21_CPodd(E0, mu_b) + Vub_NLO_CPodd(E0) ) / (P(E0, mu_b, mu_c, NNLO) + N(E0, mu_b) );
    
    throw std::runtime_error("Bsgamma::computeThValue(): Observable type not defined. Can be only 1 or 2");
}

delddel_Phi22_1()

double Bsgamma::delddel_Phi22_1

(

double

E0

)

Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines.

Parameters

[in]

E0

energy cutoff

Returns

\( 4(1-\delta(E_0)) \frac{d\Phi_{22}^{(1)}}{d\,\delta} \)

Definition at line 1713 of file bsgamma.cpp.

{
    double d = delta(E0);
    
    return 4. * (1. - d)/d * 16./27. * Int_cc1_part1(E0);
}

delddel_Phi28_1()

double Bsgamma::delddel_Phi28_1	(	double	z,
		double	E0
	)

Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines.

Parameters

[in]

E0

energy cutoff

Returns

\( 2(1-\delta(E_0)) \frac{d\Phi_{28}^{(1)}}{d\,\delta} \)

Definition at line 1725 of file bsgamma.cpp.

{
    double d = delta(E0);
    double Sq = sqrt( (1. - d) * (1. - d - 4.*z) );
    double Log = log( ( sqrt(1. - d) + sqrt(1. - d - 4.*z) ) / 2. / sqrt(z) );
    double Log2 = Log*Log;
    
    return 4. / (27. * Sq * (1 - d - 4. * z)) * Sq * Sq *
            (-8. * (-1. + d) * Log * z * (-1. + d + 4. * z) + 
            Sq * (1. + d*d + (4. + 8. * Log2 - 2. * M_PI*M_PI) * z + 
            4. * (-4. * Log2 + M_PI*M_PI) * z * z - 
            2. * d * (1. + (2. + 4. * Log2 - M_PI*M_PI) * z)));
}

delddel_Phi88_1()

double Bsgamma::delddel_Phi88_1

(

double

E0

)

Derivative of the function Phi88_1() used to compute effects of massive quark loops on gluon lines.

Parameters

[in]

E0

energy cutoff

Returns

\( 4(1-\delta(E_0)) \frac{d\Phi_{88}^{(1)}}{d\,\delta} \)

Definition at line 1758 of file bsgamma.cpp.

{
    double d = delta(E0);
    double Ld = log(d);
    
    return 4./27. * (1. - d) * (5. - 8./(1. - d) + 5. * d - 2. * d * d - 
            2. * (2. - 4./(1. - d) + 2. * d) * log(Mb_kin/Ms) + (4. * Ld)/(1. - d)
            - d * Ld - (2. + d) * Ld);
}

delta()

double Bsgamma::delta

(

double

E0

)

The cutoff energy function \( \delta = 1 - \frac{2 E_0}{M_b^{\rm kin}} \).

Parameters

[in]

E0

cutoff energy

Returns

\( \delta(E0) \)

Definition at line 104 of file bsgamma.cpp.

{
    return 1. - 2.*E0/Mb_kin;
}

Delta()

double Bsgamma::Delta

(

double

r

)

The \(\Delta(r)\) function from Z. Phys. C 48, 673 (1990).

Parameters

[in]

r

ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\(\Delta(r)\)

Definition at line 1788 of file bsgamma.cpp.

{
    double r2 = r*r;
    double r3 = r2*r;
    double Lmr = log(1. - r);
    double Lpr = log(1. + r);
    double Lr = log(r);
    double Lr2 = Lr*Lr;
    
    if (r==1.) 
        return -3./8. + 1./8. * M_PI*M_PI;
    else
        return 1./4. * (1. - r) * (1. - r3) * ( gsl_sf_dilog(r) + Lr * Lmr - 1./2. * Lr2 - 1./3. * M_PI*M_PI ) 
                - 1./4. * (1. + r) * (1. + r3) * ( gsl_sf_dilog(-1./r) - Lr * Lpr + Lr2 ) 
                + 1./4. * Lr2 - 1./4. * r2 * Lr - 3./8. * r2 + 1./24. * M_PI*M_PI;
}

dY1()

double Bsgamma::dY1

(

double

E0

)

The \( \delta Y^{(1)}(z_0,\mu) \) function from arXiv:0805.3911v2.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( \delta Y^{(1)}(z_0,\mu) \)

Definition at line 1349 of file bsgamma.cpp.

{
    double z0 = 1. - delta(E0);
    double Li2 = gsl_sf_dilog(z0);
    
    return + 2./9. * z0*(z0*z0 + 24.)- 8./3. * (z0 - 1.)*log(1. - z0) - 8./3. * Li2;
}

EW_NLO()

double Bsgamma::EW_NLO

(

double

mu

)

The NLO electroweak correction to the BR as defined in [Gambino:2001au] .

Parameters

[in]

mu

low scale of the decay

Returns

\( P_3^{(2)} \)

Definition at line 2158 of file bsgamma.cpp.

{
    
    if(EWflag) {
        double ew_nlo = 0.;
        double ga_eff_ew_7[7] = {-832./729., -208./243., -20./243., -176./729., -22712./243., -6272./729., 16./9.};
        double Lb = log(mu/Mb_kin);
        double Lz = 2. * log(Mz/mu);
        gslpp::complex C[7] = {C1_0, C2_0, C3_0, C4_0, C5_0, C6_0, C7_0};
        gslpp::complex r[7] = {0.};
        
        r[0] = r1_ew(1,zeta()) - ga_eff_ew_7[0] * Lb;
        r[1] = r1_ew(2,zeta()) - ga_eff_ew_7[1] * Lb;
        r[2] = r1_ew(3,zeta()) - ga_eff_ew_7[2] * Lb;
        r[3] = r1_ew(4,zeta()) - ga_eff_ew_7[3] * Lb;
        r[4] = r1_ew(5,zeta()) - ga_eff_ew_7[4] * Lb;
        r[5] = r1_ew(6,zeta()) - ga_eff_ew_7[5] * Lb;
        r[6] = r1_ew(7,zeta()) - ga_eff_ew_7[6] * Lb;
    
        for(int i=0;i<7;i++){
            ew_nlo += 2. * (C7_0.real()*C[i].real() + C7_0.imag()*C[i].imag()) * r[i].real()
                - 2. * (C7_0.real()*C[i].imag() - C7_0.imag()*C[i].real()) * r[i].imag();
        }
        
        ew_nlo += 2. * (C7_0.real() * (-2. * C7_0 * Lz + C7_1ew).real() 
                + C7_0.imag() * (-2. * C7_0 * Lz + C7_1ew).imag());
        
        return ew_nlo;
    }
    
    else return 0.;
}

f()

double Bsgamma::f

(

double

r

)

The \(f(\rho)\) function from hep-ph/0611123.

Parameters

[in]

r

ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\(f(\rho)\)

Definition at line 1768 of file bsgamma.cpp.

{
    double r2 = r*r;
    double r3 = r2*r;
    double r4 = r3*r;
    double Lr = log(r);
    double zeta3 = gsl_sf_zeta_int(3);
    Polylogarithms Poly;
    
    if (r==1.) 
        return 7126./81. - 356./27. * M_PI*M_PI - 16./3. * zeta3;
    else
        return - 16./3. * Poly.Li3(r2) 
                + 8. * r * (35./9. * r2 + 9.) * ( gsl_sf_dilog(r) - atanh(r) * Lr - 1./4. * M_PI*M_PI) 
                + 2. * (8./3. * Lr - 6. * r4 - 35./9. * r3 - 9. * r - 62./9. ) * gsl_sf_dilog(r2) 
                - 8. * (3. * r4 + 31./9.) * log(1. - r2) * Lr + 32./9. * Lr*Lr*Lr 
                + 8. * (3. * r4 + 25./9.) * Lr*Lr + 64./9. * r2 * Lr 
                + 4. * M_PI*M_PI * r4 + 172./9. * r2 + 5578./81.;
}

F_1()

double Bsgamma::F_1

(

double

z

)

The \( F_{1}(z,1) \) interpolated function from arXiv:1503.01791.

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( F_{1}(z,1) \)

Definition at line 1699 of file bsgamma.cpp.

{
    return - 23.74697061848885 + 35./12. * f_q(z,0.) 
            + (2129./936. - 9./52. * M_PI*M_PI) * f_NLO_1(z)
            - 0.8444138663102 * zdz_f_NLO(z,0.);
}

F_2()

double Bsgamma::F_2

(

double

z

)

The \( F_{2}(z,1) \) interpolated function from arXiv:1503.01791.

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( F_{2}(z,1) \)

Definition at line 1706 of file bsgamma.cpp.

{
    return - 3.006537367876035 - 592./81. * f_q(z,0.) 
            - 10.344289655256379 * f_NLO_1(z)
            - 9.550817514525745 * zdz_f_NLO(z,0.);
}

f_b()

double Bsgamma::f_b

(

double

z

)

The \( f_{b}(z) \) function from arXiv:1503.01791.

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( f_{b}(z) \)

Definition at line 1689 of file bsgamma.cpp.

{
    return -1.836 + 2.608 * z + 0.8271 * z * z - 2.441 * z * log(z);
}

f_c()

double Bsgamma::f_c

(

double

z

)

The \( f_{c}(z) \) function from arXiv:1503.01791.

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( f_{c}(z) \)

Definition at line 1694 of file bsgamma.cpp.

{
    return 9.099 + 13.20 * z - 19.68 * z * z + 25.71 * z * log(z);
}

f_NLO_1()

double Bsgamma::f_NLO_1

(

double

z

)

The \( f_{\rm NLO}(z,1) \) function from arXiv:1503.01791.

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( f_{\rm NLO}(z,1) \)

Definition at line 1529 of file bsgamma.cpp.

{
    return r1(2,z).real() + 2.*Phi27_1(0.,z).real();
}

f_q()

double Bsgamma::f_q	(	double	z,
		double	E0
	)

The \( f_{q}(z,1) \) function from arXiv:1503.01791.

Parameters

[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)
[in]	E0	energy cutoff

Returns

\( f_{q}(z,1) \)

Definition at line 1684 of file bsgamma.cpp.

{
    return Rer22(z) - 4./3. * h27_2(z,E0);
}

f_u()

double Bsgamma::f_u

(

double

r

)

The \(f_u\) function obtained after multiplying the fitted function \(U_C\) of arXiv:0803.0960 for \(C_FT_R\) and subtracting the \(r \to 0\) limit.

Parameters

[in]

r

ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\(f_u\)

Definition at line 1805 of file bsgamma.cpp.

{
    double r2 = r*r;
    double r3 = r2*r;
    double r4 = r3*r;
    double r5 = r4*r;
    double r6 = r5*r;
    double r7 = r6*r;
    double Lr = log(r);
    double Lr2 = Lr*Lr;
    double Pi2 = M_PI*M_PI;
    double zeta3 = gsl_sf_zeta(3.);
    
    if (r==1.) 
        return 6335./288. - 1./2. * M_PI*M_PI - 16. * zeta3;
    else
        return -5./6. * Pi2 * r + ( 14. + 16./9. * Pi2) * r2 
                + (64./9. * Lr + 128./9. * log(2.) - 95./54.) * Pi2 * r3 
                + (-16./3. * Lr2 + 365./9. * Lr + 4. * Pi2 * Lr 
                - 4375./54. - 25./9. * Pi2 + 32. * zeta3) * r4 
                - 224./45. * Pi2 * r5 + (-128./27. * Lr2 + 16./15. * Lr 
                + 15608./2025. + 128./81. * Pi2) * r6 - 16./7. * Pi2 * r7;
}

ff7_dMP()

double Bsgamma::ff7_dMP

(

double

E0

)

The 4-body NLO correction due to \(Q_7\) and d, \(ff^7_{d,MP}\), from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\(ff^7_{d,MP}\)

Definition at line 770 of file bsgamma.cpp.

{
    if (FOUR_BODY){
        double d=delta(E0);
        double d2=d*d;
        double d3=d2*d;
 
        return 4. * d * (18. - 33.*d + 2.*d2 + 13.*d3 - 6.* d2 * (2. + d) * log(d)) 
                / (81. * (d - 1.));   
    }
    else 
        return 0.;
}

ff7_sMP()

double Bsgamma::ff7_sMP

(

double

E0

)

The 4-body NLO correction due to \(Q_7\) and s, \(ff^7_{s,MP}\), from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\(ff^7_{s,MP}\)

Definition at line 784 of file bsgamma.cpp.

{
    if (FOUR_BODY){
        double d=delta(E0);
        double d2=d*d;
        double d3=d2*d;
 
        return (-2. * d * (72. + 39.*d - 76.*d2 - 35.*d3 
                + 6.*d*(18. + 13.*d + 2.*d2)*log(d))) / (243.*(d - 1.));
    }
    else 
        return 0.;
}

ff8_dMP()

double Bsgamma::ff8_dMP

(

double

E0

)

The 4-body NLO correction due to \(Q_8\) and d, \(ff^8_{d,MP}\), from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\(ff^8_{d,MP}\)

Definition at line 798 of file bsgamma.cpp.

{
    if (FOUR_BODY){
        double d=delta(E0);
        double d2=d*d;
        double d3=d2*d;
        double ld = log(d);
        double l1d = log(1. - d);
        double Li2 = gsl_sf_dilog(d);
 
        return -136./27. * d - 724./81. * d2 + 20./27. * d3 
                + (-8./9. + 16./9. * d - 8./9. * d2) * l1d* l1d 
                + (32./27. * d + 76./27. * d2 - 16./81. * d3) * ld 
                + (-104./27. - 80./9. * d + 40./9. * d2 + (32./27. 
                + 32./9. * d - 16./9. * d2) * ld) * l1d 
                + (-64./27. * d - 152./27. * d2 + 32./81. * d3 
                + (-64./27. - 64./9. * d + 32./9. * d2) * l1d) * log(Ms/Mb_kin) 
                + (32./27. + 32./9. * d - 16./9. * d2) * Li2;
    }
    else 
        return 0.;
}

ff8_sMP()

double Bsgamma::ff8_sMP

(

double

E0

)

The 4-body NLO correction due to \(Q_8\) and s, \(ff^8_{s,MP}\), from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\(ff^8_{s,MP}\)

Definition at line 821 of file bsgamma.cpp.

{
    if (FOUR_BODY){
        double d=delta(E0);
        double d2=d*d;
        double d3=d2*d;
        double ld = log(d);
        double l1d = log(1. - d);
        double Li2 = gsl_sf_dilog(d);
 
        return -340./243. * d - 104./81. * d2 + 16./729. * d3 
                + (-4./27. + 8./27. * d - 4./27. * d2) * l1d* l1d 
                + (8./27. * d + 4./9. * d2) * ld 
                + (-16./27. * d - 8./9. * d2) * log(Ms/Mb_kin)
                + (-268./243. - 40./27. * d + 20./27. * d2 + (8./27. 
                + 16./27. * d - 8./27. * d2) * ld
                + (-16./27. - 32./27. * d + 16./27. * d2) * log(Ms/Mb_kin)) * l1d 
                + (8./27. + 16./27. * d - 8./27. * d2) * Li2;
    }
    else 
        return 0.;
}

Gamma_t()

gslpp::complex Bsgamma::Gamma_t

(

double

t

)

The function \( \Gamma \) as defined in [Gambino:2001ew] .

Parameters

[in]

t

dummy variable to be integrated out

Returns

\( \Gamma \)

Definition at line 344 of file bsgamma.cpp.

{
    if (t<4) return -2. * atan( sqrt(t/(4.-t)) ) * atan( sqrt(t/(4.-t)) );
    else return -M_PI*M_PI/2. + 2.*log( ( sqrt(t) + sqrt(t-4.) ) / 2. )*log( ( sqrt(t) + sqrt(t-4.) ) / 2. )
            - 2.*gslpp::complex::i()*M_PI*log( ( sqrt(t) + sqrt(t-4.) ) / 2. );
}

getKb_abs2_1mt()

double Bsgamma::getKb_abs2_1mt ( double  t )

inline

The function \(|k_b(t)|^2(1 - t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_b(t)|^2(1 - t)\)

Definition at line 462 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * (1. - t);
    };

getKb_abs2_1mt2()

double Bsgamma::getKb_abs2_1mt2 ( double  t )

inline

The function \(|k_b(t)|^2(1 - t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_b(t)|^2(1 - t)^2\)

Definition at line 473 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * (1. - t) * (1. - t);
    };

getKb_abs2_t2_1mt()

double Bsgamma::getKb_abs2_t2_1mt ( double  t )

inline

The function \(|k_b(t)|^2t^2(1 - t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_b(t)|^2t^2(1 - t)\)

Definition at line 506 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * t * t * (1. - t);
    };

getKb_abs2_t2_1mt2()

double Bsgamma::getKb_abs2_t2_1mt2 ( double  t )

inline

The function \(|k_b(t)|^2t^2(1 - t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_b(t)|^2t^2(1 - t)^2\)

Definition at line 517 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * t * t * (1. - t) * (1. - t);
    };

getKb_abs2_t_1mt()

double Bsgamma::getKb_abs2_t_1mt ( double  t )

inline

The function \(|k_b(t)|^2t(1 - t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_b(t)|^2t(1 - t)\)

Definition at line 484 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * t * (1. - t);
    };

getKb_abs2_t_1mt2()

double Bsgamma::getKb_abs2_t_1mt2 ( double  t )

inline

The function \(|k_b(t)|^2t(1 - t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_b(t)|^2t(1 - t)^2\)

Definition at line 495 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * t * (1. - t) * (1. - t);
    };

getKb_re_1mt()

double Bsgamma::getKb_re_1mt ( double  t )

inline

The function \(Re(k_b(t))(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))(1-t)\)

Definition at line 583 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * (1. - t);
    };

getKb_re_1mt2()

double Bsgamma::getKb_re_1mt2 ( double  t )

inline

The function \(Re(k_b(t))(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))(1-t)^2\)

Definition at line 594 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * (1. - t) * (1. - t);
    };

getKb_re_t()

double Bsgamma::getKb_re_t ( double  t )

inline

The function \(Re(k_b(t))t\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))t\)

Definition at line 528 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t ;
    };

getKb_re_t2_1mt()

double Bsgamma::getKb_re_t2_1mt ( double  t )

inline

The function \(Re(k_b(t))t^2(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))t^2(1-t)\)

Definition at line 550 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t * t * (1. - t);
    };

getKb_re_t2_1mt2()

double Bsgamma::getKb_re_t2_1mt2 ( double  t )

inline

The function \(Re(k_b(t))t^2(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))t^2(1-t)^2\)

Definition at line 561 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t * t * (1. - t) * (1. - t);
    };

getKb_re_t_1mt()

double Bsgamma::getKb_re_t_1mt ( double  t )

inline

The function \(Re(k_b(t))t(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))t(1-t)\)

Definition at line 539 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t * (1. - t);
    };

getKb_re_t_1mt2()

double Bsgamma::getKb_re_t_1mt2 ( double  t )

inline

The function \(Re(k_b(t))t(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))t(1-t)^2\)

Definition at line 572 of file bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t * (1. - t) * (1. - t);
    };

getKc_abs2_1mt()

double Bsgamma::getKc_abs2_1mt ( double  t )

inline

The function \(|k_c(t)|^2(1 - t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_c(t)|^2(1 - t)\)

Definition at line 319 of file bsgamma.h.

    {
        return kappa(Mc,t).abs2() * (1. - t);
    };

getKc_abs2_1mt2()

double Bsgamma::getKc_abs2_1mt2 ( double  t )

inline

The function \(t|k_c(t)|^2(1 - t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_c(t)|^2(1 - t)^2\)

Definition at line 341 of file bsgamma.h.

    {
        return kappa(Mc,t).abs2() * (1. - t) * (1. - t);
    };

getKc_abs2_t()

double Bsgamma::getKc_abs2_t ( double  t )

inline

The function \(|k_c(t)|^2 t\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_c(t)|^2t\)

Definition at line 308 of file bsgamma.h.

    {
        return kappa(Mc,t).abs2() * t;
    };

getKc_abs2_t_1mt()

double Bsgamma::getKc_abs2_t_1mt ( double  t )

inline

The function \(|k_c(t)|^2t(1 - t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(|k_c(t)|^2t(1 - t)\)

Definition at line 330 of file bsgamma.h.

    {
        return kappa(Mc,t).abs2() * t * (1. - t);
    };

getKc_im_1mt()

double Bsgamma::getKc_im_1mt ( double  t )

inline

The function \(Im(k_c(t))(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Im(k_c(t))(1-t)\)

Definition at line 429 of file bsgamma.h.

    {
        return kappa(Mc,t).imag() * (1. - t);
    };

getKc_im_1mt2()

double Bsgamma::getKc_im_1mt2 ( double  t )

inline

The function \(Im(k_c(t))(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Im(k_c(t))(1-t)^2\)

Definition at line 451 of file bsgamma.h.

    {
        return kappa(Mc,t).imag() * (1. - t) * (1. - t);
    };

getKc_im_Kb_1mt()

double Bsgamma::getKc_im_Kb_1mt ( double  t )

inline

The function \(Re(k_b(t))Im(k_c(t))(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))Im(k_c(t))(1-t)\)

Definition at line 616 of file bsgamma.h.

    {
        return kappa(Mc,t).imag() * kappa(Mb_kin,t).real() * (1. - t);
    };

getKc_im_Kb_1mt2()

double Bsgamma::getKc_im_Kb_1mt2 ( double  t )

inline

The function \(Re(k_b(t))Im(k_c(t))(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))Im(k_c(t))(1-t)^2\)

Definition at line 638 of file bsgamma.h.

    {
        return kappa(Mc,t).imag() * kappa(Mb_kin,t).real() * (1. - t) * (1. - t);
    };

getKc_im_Kb_t_1mt()

double Bsgamma::getKc_im_Kb_t_1mt ( double  t )

inline

The function \(Re(k_b(t))Im(k_c(t)t(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))Im(k_c(t)t(1-t)\)

Definition at line 660 of file bsgamma.h.

    {
        return kappa(Mc,t).imag() * kappa(Mb_kin,t).real() * t * (1. - t);
    };

getKc_im_Kb_t_1mt2()

double Bsgamma::getKc_im_Kb_t_1mt2 ( double  t )

inline

The function \(Re(k_b(t))Im(k_c(t)t(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))Im(k_c(t)t(1-t)^2\)

Definition at line 682 of file bsgamma.h.

    {
        return kappa(Mc,t).imag() * kappa(Mb_kin,t).real() * t * (1. - t) * (1. - t);
    };

getKc_im_t()

double Bsgamma::getKc_im_t ( double  t )

inline

The function \(Im(k_c(t))t\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Im(k_c(t))t\)

Definition at line 363 of file bsgamma.h.

    {
        return kappa(Mc,t).imag() * t ;
    };

getKc_im_t_1mt()

double Bsgamma::getKc_im_t_1mt ( double  t )

inline

The function \(Im(k_c(t))t(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Im(k_c(t))t(1-t)\)

Definition at line 385 of file bsgamma.h.

    {
        return kappa(Mc,t).imag() * t * (1. - t);
    };

getKc_im_t_1mt2()

double Bsgamma::getKc_im_t_1mt2 ( double  t )

inline

The function \(Im(k_c(t))t(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Im(k_c(t))t(1-t)^2\)

Definition at line 407 of file bsgamma.h.

    {
        return kappa(Mc,t).imag() * t * (1. - t) * (1. - t);
    };

getKc_re_1mt()

double Bsgamma::getKc_re_1mt ( double  t )

inline

The function \(Re(k_c(t))(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_c(t))(1-t)\)

Definition at line 418 of file bsgamma.h.

    {
        return kappa(Mc,t).real() * (1. - t);
    };

getKc_re_1mt2()

double Bsgamma::getKc_re_1mt2 ( double  t )

inline

The function \(Re(k_c(t))(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_c(t))(1-t)^2\)

Definition at line 440 of file bsgamma.h.

    {
        return kappa(Mc,t).real() * (1. - t) * (1. - t);
    };

getKc_re_Kb_1mt()

double Bsgamma::getKc_re_Kb_1mt ( double  t )

inline

The function \(Re(k_b(t))Re(k_c(t))(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))Re(k_c(t))(1-t)\)

Definition at line 605 of file bsgamma.h.

    {
        return kappa(Mc,t).real() * kappa(Mb_kin,t).real() * (1. - t);
    };

getKc_re_Kb_1mt2()

double Bsgamma::getKc_re_Kb_1mt2 ( double  t )

inline

The function \(Re(k_b(t))Re(k_c(t))(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))Re(k_c(t))(1-t)^2\)

Definition at line 627 of file bsgamma.h.

    {
        return kappa(Mc,t).real() * kappa(Mb_kin,t).real() * (1. - t) * (1. - t);
    };

getKc_re_Kb_t_1mt()

double Bsgamma::getKc_re_Kb_t_1mt ( double  t )

inline

The function \(Re(k_b(t))Re(k_c(t)t(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))Re(k_c(t)t(1-t)\)

Definition at line 649 of file bsgamma.h.

    {
        return kappa(Mc,t).real() * kappa(Mb_kin,t).real() * t * (1. - t);
    };

getKc_re_Kb_t_1mt2()

double Bsgamma::getKc_re_Kb_t_1mt2 ( double  t )

inline

The function \(Re(k_b(t))Re(k_c(t)t(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_b(t))Re(k_c(t)t(1-t)^2\)

Definition at line 671 of file bsgamma.h.

    {
        return kappa(Mc,t).real() * kappa(Mb_kin,t).real() * t * (1. - t) * (1. - t);
    };

getKc_re_t()

double Bsgamma::getKc_re_t ( double  t )

inline

The function \(Re(k_c(t))t\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_c(t))t\)

Definition at line 352 of file bsgamma.h.

    {
        return kappa(Mc,t).real() * t ;
    };

getKc_re_t_1mt()

double Bsgamma::getKc_re_t_1mt ( double  t )

inline

The function \(Re(k_c(t))t(1-t)\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_c(t))t(1-t)\)

Definition at line 374 of file bsgamma.h.

    {
        return kappa(Mc,t).real() * t * (1. - t);
    };

getKc_re_t_1mt2()

double Bsgamma::getKc_re_t_1mt2 ( double  t )

inline

The function \(Re(k_c(t))t(1-t)^2\).

Parameters

[in]

t

dummy variable to be integrated out

Returns

\(Re(k_c(t))t(1-t)^2\)

Definition at line 396 of file bsgamma.h.

    {
        return kappa(Mc,t).real() * t * (1. - t) * (1. - t);
    };

h27_2()

double Bsgamma::h27_2	(	double	z,
		double	E0
	)

The \( h_{27}^{(2)}(z,\delta) \) function from arXiv:1009.5685 and arXiv:1503.01791.

Parameters

[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)
[in]	E0	energy cutoff

Returns

\( h_{27}^{(2)}(z,\delta) \)

Definition at line 1661 of file bsgamma.cpp.

{
    double d = delta(E0);
    double d2 = d*d;
    
    if (E0 == 0.){
        return ( 41./27. - 2./9. * M_PI*M_PI
            - 2.24 * sqrt(z) - 7.04 * z + 23.72 * pow(z,3./2.)
            + ( -9.86 * z + 31.28 * z * z ) * log(z));
    } else return - 0.1755402735503456 - 1.4553730660088837 * d 
            + 1.1192806367180177 * d2 
            + ( 0.7259818237183779 - 7.230418135384073 * d 
            + 5.977206932166958 * d2 ) * sqrt(z) 
            + ( 13.786205094458156 + 113.71026116073105 * d 
            - 100.3588074342665 * d2 ) * z 
            + ( -145.05588751363894 - 307.05884309429547 * d 
            + 388.54181686721904 * d2 ) * pow(z,3./2.) 
            + ( 475.2039505292043 + 312.9832308573048 * d 
            - 775.8088176670707 * d2 ) * z * z
            + ( -509.7299390734172 - 126.08888075477071 * d 
            + 646.2084041395774 * d2 ) * pow(z,5./2.);
}

Int_b1()

double Bsgamma::Int_b1

(

double

E0

)

Integral of the functions getKb_re_1mt() and getKb_re_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))(1-t)^2\)

Definition at line 358 of file bsgamma.cpp.

{
    if (Intb1Cached == 0) {
        double t1 = (1. - delta(E0));
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_re_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_re_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt2 = avaINT;
 
        CacheIntb1 = delta(E0)*mt + mt2;
        Intb1Cached = 1;
    }
 
    return CacheIntb1;
}

Int_b2()

double Bsgamma::Int_b2

(

double

E0

)

Integral of the functions getKb_re_t_1mt() and getKb_re_t_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))t(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))t(1-t)^2\)

Definition at line 381 of file bsgamma.cpp.

{
    if (Intb2Cached == 0) {
        double t1 = (1. - delta(E0));
    
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_re_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_re_t_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt2 = avaINT;
 
        CacheIntb2 = delta(E0)*mt + mt2;
        Intb2Cached = 1;
    }
 
    return CacheIntb2;
}

Int_b3()

double Bsgamma::Int_b3

(

double

E0

)

Integral of the functions getKb_re_t() and getKb_re_t_1mt().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))t + \int_{1-\delta(E_0)}^1 Re(k_b(t))t(1-t)\)

Definition at line 405 of file bsgamma.cpp.

{
    if (Intb3Cached == 0) {
        double t1 = (1. - delta(E0));
    
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_re_t);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double t = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_re_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt = avaINT;
 
        CacheIntb3 = delta(E0)*t + mt;
        Intb3Cached = 1;
    }
 
    return CacheIntb3;
}

Int_b4()

double Bsgamma::Int_b4

(

double

E0

)

Integral of the functions getKb_re_t2_1mt() and getKb_re_t2_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))t^2(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))t^2(1-t)^2\)

Definition at line 429 of file bsgamma.cpp.

{
    if (Intb4Cached == 0) {
        double t1 = (1. - delta(E0));
    
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_re_t2_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_re_t2_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt2 = avaINT;
 
        CacheIntb4 = delta(E0)*mt + mt2;
        Intb4Cached = 1;
    }
 
    return CacheIntb4;
}

Int_bb1()

double Bsgamma::Int_bb1

(

double

E0

)

Integral of the functions getKb_abs2_1mt() and getKb_abs2_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} |(k_b(t)|^2(1-t) + \int_{1-\delta(E_0)}^1 |(k_b(t)|^2(1-t)^2\)

Definition at line 453 of file bsgamma.cpp.

{
    if (Intbb1Cached == 0) {
        double t1 = (1. - delta(E0));
    
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_abs2_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_abs2_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt2 = avaINT;
 
        CacheIntbb1 = delta(E0)*mt + mt2;
        Intbb1Cached = 1;
    }
 
    return CacheIntbb1;
}

Int_bb2()

double Bsgamma::Int_bb2

(

double

E0

)

Integral of the functions getKb_abs2_t_1mt() and getKb_abs2_t_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} |(k_b(t)|^2t(1-t) + \int_{1-\delta(E_0)}^1 |(k_b(t)|^2t(1-t)^2\)

Definition at line 477 of file bsgamma.cpp.

{
    if (Intbb2Cached == 0) {
        double t1 = (1. - delta(E0));
    
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_abs2_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_abs2_t_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt2 = avaINT;
 
        CacheIntbb2 = delta(E0)*mt + mt2;
        Intbb2Cached = 1;
    }
 
    return CacheIntbb2;
}

Int_bb4()

double Bsgamma::Int_bb4

(

double

E0

)

Integral of the functions getKb_abs2_t2_1mt() and getKb_abs2_t2_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} |(k_b(t)|^2t^2(1-t) + \int_{1-\delta(E_0)}^1 |(k_b(t)|^2t^2(1-t)^2\)

Definition at line 501 of file bsgamma.cpp.

{
    if (Intbb4Cached == 0) {
        double t1 = (1. - delta(E0));
    
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_abs2_t2_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKb_abs2_t2_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt2 = avaINT;
 
        CacheIntbb4 = delta(E0)*mt + mt2;
        Intbb4Cached = 1;
    }
 
    return CacheIntbb4;
}

Int_bc1()

gslpp::complex Bsgamma::Int_bc1

(

double

E0

)

Integral of the functions getKc_re_Kb_1mt(), getKc_im_Kb_1mt() and getKc_re_Kb_1mt2(), getKc_im_Kb_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))k_c(t)(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))k_c(t)(1-t)^2\)

Definition at line 525 of file bsgamma.cpp.

{
    if (Intbc1Cached == 0) {
        double t1 = (1. - delta(E0));
    
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_Kb_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_Kb_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        mt += gslpp::complex::i() * avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_Kb_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex mt2 = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_Kb_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        mt2 += gslpp::complex::i() * avaINT;
 
        CacheIntbc1 = delta(E0)*mt + mt2;
        Intbc1Cached = 1;
    }
 
    return CacheIntbc1;
}

Int_bc2()

gslpp::complex Bsgamma::Int_bc2

(

double

E0

)

Integral of the functions getKc_re_Kb_t_1mt(), getKc_im_Kb_t_1mt() and getKc_re_Kb_t_1mt2(), getKc_im_Kb_t_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))k_c(t)t(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))k_c(t)t(1-t)^2\)

Definition at line 561 of file bsgamma.cpp.

{
    if (Intbc2Cached == 0) {
        double t1 = (1. - delta(E0));
    
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_Kb_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_Kb_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        mt += gslpp::complex::i() * avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_Kb_t_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex mt2 = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_Kb_t_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        mt2 += gslpp::complex::i() * avaINT;
 
        CacheIntbc2 = delta(E0)*mt + mt2;
        Intbc2Cached = 1;
    }
 
    return CacheIntbc2;
}

Int_c1()

gslpp::complex Bsgamma::Int_c1

(

double

E0

)

Integral of the functions getKc_re_1mt(), getKc_im_1mt() and getKc_re_1mt2(), getKc_im_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} k_c(t)(1-t) + \int_{1-\delta(E_0)}^1 k_c(t)(1-t)^2\)

Definition at line 597 of file bsgamma.cpp.

{
    if (Intc1Cached == 0) {
        double t1 = (1. - delta(E0));
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        mt += gslpp::complex::i() * avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex mt2 = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        mt2 += gslpp::complex::i() * avaINT;
 
        CacheIntc1 = delta(E0)*mt + mt2;
        Intc1Cached = 1;
    }
 
    return CacheIntc1;
}

Int_c2()

gslpp::complex Bsgamma::Int_c2

(

double

E0

)

Integral of the functions getKc_re_t_1mt(), getKc_im_t_1mt() and getKc_re_t_1mt2(), getKc_im_t_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} k_c(t)t(1-t) + \int_{1-\delta(E_0)}^1 k_c(t)t(1-t)^2\)

Definition at line 633 of file bsgamma.cpp.

{
    if (Intc2Cached == 0) {
        double t1 = (1. - delta(E0));
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        mt += gslpp::complex::i() * avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_t_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex mt2 = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_t_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        mt2 += gslpp::complex::i() * avaINT;        
 
        CacheIntc2 = delta(E0)*mt + mt2;
        Intc2Cached = 1;
    }
 
    return CacheIntc2;
}

Int_c3()

gslpp::complex Bsgamma::Int_c3

(

double

E0

)

Integral of the functions getKc_re_t(), getKc_im_t() and getKc_re_t_1mt(), getKc_im_t_1mt().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} k_c(t)t + \int_{1-\delta(E_0)}^1 k_c(t)t(1-t)\)

Definition at line 669 of file bsgamma.cpp.

{
    if (Intc3Cached == 0) {
        double t1 = (1. - delta(E0));
    
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_t);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex t = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_t);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        t += gslpp::complex::i() * avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_re_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        gslpp::complex mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_im_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        mt += gslpp::complex::i() * avaINT;        
 
        CacheIntc3 = delta(E0)*t + mt;
        Intc3Cached = 1;
    }
 
    return CacheIntc3;
}

Int_cc()

double Bsgamma::Int_cc

(

double

E0

)

Integral of the functions getKc_abs2_t() and getKc_abs2_t_1mt().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} |k_c(t)|^2t + 2\int_{1-\delta(E_0)}^1 |k_c(t)|^2t(1-t)\)

Definition at line 705 of file bsgamma.cpp.

{
    if (IntccCached == 0) {
        double t1 = (1. - delta(E0));
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_abs2_t);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_abs2_t_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt2 = avaINT;
        
        CacheIntcc = delta(E0)*mt + 2. * mt2;
        IntccCached = 1;
    }
    
    return CacheIntcc;
}

Int_cc1()

double Bsgamma::Int_cc1

(

double

E0

)

Integral of the functions getKc_abs2_1mt() and getKc_abs2_1mt^().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} |k_c(t)|^2(1-t) + \int_{1-\delta(E_0)}^1 |k_c(t)|^2(1-t)^2\)

Definition at line 729 of file bsgamma.cpp.

{
    if (Intcc1Cached == 0) {
        double t1 = (1. - delta(E0));
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_abs2_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt = avaINT;
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_abs2_1mt2);
        ig.SetFunction(wf);
        avaINT = ig.Integral(t1, 1.);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
        double mt2 = avaINT;
 
        CacheIntcc1 = delta(E0)*mt + mt2;
        Intcc1Cached = 1;
    }
 
    return CacheIntcc1;
}

Int_cc1_part1()

double Bsgamma::Int_cc1_part1

(

double

E0

)

Integral of the functions getKc_abs2_1mt().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} |k_c(t)|^2(1-t)\)

Definition at line 753 of file bsgamma.cpp.

{
    if (Intcc1p1Cached == 0) {
        double t1 = (1. - delta(E0));
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::getKc_abs2_1mt);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0., t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
 
        CacheIntcc1p1 = delta(E0)*avaINT;
        Intcc1p1Cached = 1;
    }
    
    return CacheIntcc1p1;
}

Int_Phi77_2rem()

double Bsgamma::Int_Phi77_2rem

(

double

E0

)

The integral of omega77()

Parameters

[in]

E0

energy cutoff

Returns

\( \int_0^{1-\delta(E_0)} omega_{77} \)

Definition at line 1874 of file bsgamma.cpp.

{
    if (IntPhi772rCached == 0) {
        double t1 = (1. - delta(E0));
 
        wf=ROOT::Math::Functor1D(&(*this),&Bsgamma::omega77);
        ig.SetFunction(wf);
        avaINT = ig.Integral(0.,t1);
        if (ig.Status() != 0) return std::numeric_limits<double>::quiet_NaN();
 
        CacheIntPhi772r = avaINT;
        IntPhi772rCached = 1;
    }
    
    return CacheIntPhi772r;
}

K77_2_z1()

double Bsgamma::K77_2_z1	(	double	E0,
		double	mu
	)

The \( K_{77}^{(2),z=1} \) function computed in the limit \( m_b = m_c \).

Parameters

[in]	E0	energy cutoff
[in]	mu	b quark scale

Returns

\( K_{77}^{(2),z=1} \)

Definition at line 1903 of file bsgamma.cpp.

{
    double K77_1 = Kij_1(7,7,E0,mu).real();
    double Pi2 = M_PI*M_PI;
    double xm = 8./9. * M_PI * alsUps;
    double Lb = 2.*log(mu_b/Mb_kin);
    
    return ( K77_1 - 4. * Phi77_1(E0) ) * K77_1 - 1178948./729. + 18593./729. * Pi2 
            - 628./405. * Pi2*Pi2 + 428./27. * Pi2 * log(2.) + 61294./81. * gsl_sf_zeta(3.) 
            - 880./9. * Lb * Lb + ( 440./27. * Pi2 - 14698./27. ) * Lb 
            + 64./3. * xm + 4. * (Phi77_2beta0(E0,mu) + Phi77_2rem(E0));
}

kappa()

gslpp::complex Bsgamma::kappa	(	double	Mq,
		double	t
	)

The function \( k \) as defined in [Pott:1995if] .

Parameters

[in]	Mq	quark mass
[in]	t	dummy variable to be integrated out

Returns

\( k \)

Definition at line 352 of file bsgamma.cpp.

{
    double s = t * Mb_kin*Mb_kin/Mq/Mq;
    return 1./2. + Gamma_t(s)/s;
}

Kij_1()

gslpp::complex Bsgamma::Kij_1	(	int	i,
		int	j,
		double	E0,
		double	mu
	)

The \( K_{ij}^{(1)} \) function from [Misiak:2006ab] .

Parameters

[in]	i	first index
[in]	j	second index
[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( K_{ij}^{(1)} \)

Definition at line 1169 of file bsgamma.cpp.

{
    if (i > 8 || j>8 || i<1 || j<1) throw std::runtime_error("Bsgamma::Kij_1(): indices (i,j) must be included in (1,..,8)");
    
    double gamma_i7[8] = {-208./243., 416./81., -176./81., -152./243., -6272./81., 4624./243., 32./3., -32./9.};
    gslpp::complex K_ij[8][8] = {{0.}};
    double Lb = log(mu/Mb_kin);
    
    K_ij[0][0] = 4.*Phi11_1(E0);
    K_ij[0][1] = 2.*Phi12_1(E0);
    K_ij[0][2] = 2.*Phi13_1(E0);
    K_ij[0][3] = 2.*Phi14_1(E0);
    K_ij[0][4] = 2.*Phi15_1(E0);
    K_ij[0][5] = 2.*Phi16_1(E0);
    K_ij[0][6] = r1(1,zeta()) - gamma_i7[0]*Lb + 2.*Phi17_1(E0, zeta());
    K_ij[0][7] = 2.*Phi18_1(E0, zeta());
    
    K_ij[1][1] = 4.*Phi22_1(E0);
    K_ij[1][2] = 2.*Phi23_1(E0);
    K_ij[1][3] = 2.*Phi24_1(E0);
    K_ij[1][4] = 2.*Phi25_1(E0);
    K_ij[1][5] = 2.*Phi26_1(E0);
    K_ij[1][6] = r1(2,zeta()) - gamma_i7[1]*Lb + 2.*Phi27_1(E0, zeta());
    K_ij[1][7] = 2.*Phi28_1(E0, zeta());
    
    K_ij[2][2] = 4.*Phi33_1(E0);
    K_ij[2][3] = 2.*Phi34_1(E0);
    K_ij[2][4] = 2.*Phi35_1(E0);
    K_ij[2][5] = 2.*Phi36_1(E0);
    K_ij[2][6] = r1(3,zeta()) - gamma_i7[2]*Lb + 2.*Phi37_1(E0);
    K_ij[2][7] = 2.*Phi38_1(E0);
    
    K_ij[3][3] = 4.*Phi44_1(E0);
    K_ij[3][4] = 2.*Phi45_1(E0);
    K_ij[3][5] = 2.*Phi46_1(E0);
    K_ij[3][6] = r1(4,zeta()) - gamma_i7[3]*Lb + 2.*Phi47_1(E0);
    K_ij[3][7] = 2.*Phi48_1(E0);
    
    K_ij[4][4] = 4.*Phi55_1(E0);
    K_ij[4][5] = 2.*Phi56_1(E0);
    K_ij[4][6] = r1(5,zeta()) - gamma_i7[4]*Lb + 2.*Phi57_1(E0);
    K_ij[4][7] = 2.*Phi58_1(E0);
    
    K_ij[5][5] = 4.*Phi66_1(E0);
    K_ij[5][6] = r1(6,zeta()) - gamma_i7[5]*Lb + 2.*Phi67_1(E0);
    K_ij[5][7] = 2.*Phi68_1(E0);
    
    K_ij[6][6] = -182./9. + 8./9.*M_PI*M_PI - gamma_i7[6]*2.*Lb + 4.*Phi77_1(E0);
    K_ij[6][7] =  r1(8,zeta()) - gamma_i7[7]*Lb + 2.*Phi78_1(E0);
    
    K_ij[7][7] = 4.*Phi88_1(E0);
    
    if (j >= i ) return K_ij[i-1][j-1];
    else return K_ij[j-1][i-1].conjugate();
}

Kij_2()

double Bsgamma::Kij_2	(	int	i,
		int	j,
		double	E0,
		double	mu_b,
		double	mu_c
	)

The \( K_{ij}^{(2)} \) function from arXiv:1503.01791.

Parameters

[in]	i	first index
[in]	j	second index
[in]	E0	energy cutoff
[in]	mu_b	b quark scale
[in]	mu_c	c quark scale

Returns

\( K_{ij}^{(2)} \)

Definition at line 1916 of file bsgamma.cpp.

{
    if (i<1 || i > 2)
        if (i < 7)
            throw std::runtime_error("Bsgamma::Kij_2(): index i must be included in (1,2,7,8)");
    if (j<1 || j > 2)
        if (j < 7)
            throw std::runtime_error("Bsgamma::Kij_2(): index j must be included in (1,2,7,8)");
    
    int temp;
    
    if (i > j) {temp=i; i=j; j=temp;}
    
    double K_ij[8][8] = {{0.}};
    double z = zeta();
    double d = delta(E0);
    double r = sqrt(z);
    double Lb = 2.*log(mu_b/Mb_kin);
    double Lb2 = Lb*Lb;
    double Lc = 2.*log(mu_c/Mc);
    double Lcb = log(Mc/Mb_kin);
    double xm = 8./9. * M_PI * alsUps;
    
    double A1 = 22.604961348474838;
    double A2 = 75.60281607240395;
    
    K_ij[1][1] = (r1(2,zeta()).real() - 208./81.*Lb) * (r1(2,zeta()).real() - 208./81.*Lb)
            + r1(2,zeta()).imag() * r1(2,zeta()).imag()
            + 4.*Phi22_2beta0(E0,mu_b) * SM.Beta0(3)/SM.Beta0(5) + 16./3. * Phi22_1(E0) * (Lcb - Lb)
            + xm * (delddel_Phi22_1(E0) - 2. * zdz_Phi22_1(E0));
    K_ij[1][6] = A2 + F_2(z) - 27./2. * f_q(z,E0) + f_b(z) + f_c(z)
            + 4./3. * Phi27_1(E0,z).real() * log(z) + (8. * Lc - 2. * xm) * zdz_f_NLO(z,E0)
            + xm * mddel_f_NLO(z,E0) + 416./81. * xm
            + (10./3. * Kij_1(2,7,E0,mu_b).real() - 2./3. * Kij_1(4,7,E0,mu_b).real()
            - 208./81. * Kij_1(7,7,E0,mu_b).real() - 35./27. * Kij_1(7,8,E0,mu_b).real()
            - 254./81.) * Lb - 5948./729. * Lb2;
    K_ij[1][7] = (r1(2,zeta()).real() - 208./81.*Lb) * (r1(8,zeta()).real() + 16./9.*Lb)
            + r1(2,zeta()).imag() * r1(8,zeta()).imag()
            + 2.*Phi28_2beta0(E0,mu_b) * SM.Beta0(3)/SM.Beta0(5) + 8./3. * Phi28_1(E0,z).real() * (Lcb - Lb)
            + xm * (delddel_Phi28_1(z,E0) - 2. * zdz_Phi28_1(z,E0));
    
    K_ij[0][0] = 1./36. * K_ij[1][1];
    K_ij[0][1] = -1./6. * K_ij[1][1];
    K_ij[0][6] = - 1./6. * K_ij[1][6] + A1 + F_1(z)
            + (- 3./2. * Kij_1(2,7,E0,mu_b).real() - 3./4. * Kij_1(7,8,E0,mu_b).real()
            + 94./81.) * Lb - 34./27. * Lb2;
    K_ij[0][7] = -1./6. * K_ij[1][7];
    
    K_ij[6][6] = K77_2_z1(E0,mu_b) + ( 1972./81. - 16./27. * M_PI*M_PI + 8./3. * Phi77_1(E0)) * log(zeta())
            + 2./3. * (f(r) - f(1.)) - 128./3. * (Delta(r) - Delta(1.)) 
            - 16. * (f_u(r) - f_u(1.));
    K_ij[6][7] = 2./3. * Y2(E0,mu_b) + (16./9.*M_PI*M_PI - 164./9. - 32./6. * Lb) * Y1(E0,mu_b) 
            - 32./81. * alsUps * M_PI * (3. + 7.*d - 3.*d*d + d*d*d - 4.*d*log(d) );
    
    K_ij[7][7] = (r1(8,zeta()).real() + 16./9.*Lb) * (r1(8,zeta()).real() + 16./9.*Lb)
            + r1(8,zeta()).imag() * r1(8,zeta()).imag()
            + 4.*Phi88_2beta0(E0,mu_b) * SM.Beta0(3)/SM.Beta0(5) + 16./3. * Phi88_1(E0) * (Lcb - Lb)
            + xm * (delddel_Phi88_1(E0));
    
    return K_ij[i-1][j-1];
}

mddel_f_NLO()

double Bsgamma::mddel_f_NLO	(	double	z,
		double	E0
	)

The \( (1. - \delta)\frac{d}{d\delta}f_{\rm NLO}(z,\delta) \) function from arXiv:1503.01791.

Parameters

[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)
[in]	E0	energy cutoff

Returns

\( (1. - \delta)\frac{d}{d\delta}f_{\rm NLO}(z,\delta) \)

Definition at line 1630 of file bsgamma.cpp.

{
    double d = delta(E0);
    double d2 = d*d;
    double sqrt1d = sqrt(1. - d);
    double sqrt1d4z = sqrt(1. - d - 4. * z);
    double sqrtz = sqrt(z);
    double LogSqrt = log((sqrt1d + sqrt1d4z)/(2. * sqrtz));
    double SumSqrt = sqrt1d + sqrt1d4z;
    double ProdSqrt = sqrt1d * sqrt1d4z;
    
    return 2. * (1. - d) * ( -2./27. * d * (-3. + 2. * d) 
            - 2./27. * (3. - 3. * d + d2) 
            + 1./9. * (2. - d) * (-7. + 2. * M_PI * M_PI) * z 
            - 1./9. * d * (-7. + 2. * M_PI * M_PI) * z 
            + 4. * d * (-1./(2. * sqrt1d) - 1./(2. * sqrt1d4z))
            * ProdSqrt * z  / (3. * SumSqrt) 
            + 4./9. * (3. - 2. * M_PI * M_PI) * z * z 
            + 4./3. * ProdSqrt * z * LogSqrt 
            - 16. * d * (-1./(2. * sqrt1d) - 1./(2. * sqrt1d4z)) 
            * (2. - d - 4. * z) * z * LogSqrt / (9. * SumSqrt) 
            + 2. * d * z * (-2. + 2. * d + 4. * z) * LogSqrt / (3. * ProdSqrt) 
            + 16. * (-1./(2. * sqrt1d) - 1./(2. * sqrt1d4z)) * z
            * (1 - 4. * z + 6. * z * z) * LogSqrt / (9. * SumSqrt) 
            + 8./9. * d * z * LogSqrt * LogSqrt 
            - 8./9. * (2. - d - 4. * z) * z * LogSqrt * LogSqrt 
            + 4./3. * (1. - 2. * z) * z 
            * ( (1./(2. * sqrt1d) + 1./(2. * sqrt1d4z)) * ProdSqrt/SumSqrt 
            - (-2. + 2. * d + 4. * z) * LogSqrt/(2. * ProdSqrt)));
}

N()

double Bsgamma::N	(	double	E0,
		double	mu
	)

The non perturbative part of the \(BR\) as defined in [Benzke:2010js] , \(N\).

Parameters

[in]	E0	energy cutoff
[in]	mu	b quark scale

Returns

\(N\)

Definition at line 2397 of file bsgamma.cpp.

{
    return N_27() + N_77(E0,mu) + BLNPcorr * P0(E0);
}

N_27()

double Bsgamma::N_27

(

)

The non perturbative part of the \(BR\) due to \(Q_2-Q_7\) interference as defined in [Gambino:2001ew] , \(N_{27}\).

Returns

\(N_{27}\)

Definition at line 2342 of file bsgamma.cpp.

{
    double mcnorm = 1.131; // value fixed according to arXiv:1003.5012, in order to employ the remaining corrections given in that work
    double lambda2 = mu_G2/3.;
    
    return -1./18. * (C7_0 * ( 2.*C2_0 - C1_0/3. )).real() * lambda2/mcnorm/mcnorm;
}

N_77()

double Bsgamma::N_77	(	double	E0,
		double	mu
	)

The non perturbative part of the \(BR\) due to \(Q_7-Q_7\) interference as defined in arXiv:0911.2175, \(N_{77}\).

Parameters

[in]	E0	energy cutoff
[in]	mu	b quark scale

Returns

\(N_{77}\)

Definition at line 2350 of file bsgamma.cpp.

{
    double z = 1. - delta(E0);
    double z2 = z*z;
    double z3 = z2*z;
    double z4 = z3*z;
    double umz2 = (1.-z)*(1.-z);
    double Lz = log(1. - z);
    double Lz2 = Lz*Lz;
    double Lb = 2. * log(mu/Mb_kin);
    
    double corrLambda2_rad;
    double corrLambda2_sem;
    double corrLambda2_mix;
    double corrLambda2;
    double corrLambda3;
    
    double alsb = SM.Alstilde5(Mb_kin);
    double Lambda_pert = 64./9. * alsb * mu_kin * 
                (1. + 4. * alsb * (9./2. * (log(Mb_kin/2./mu_kin) + 8./3.)
                - 3. * (M_PI*M_PI/6. - 13./12.)) );
    double mu_pi2_pert = 3./4. * mu_kin * Lambda_pert - 48. * alsb*alsb * mu_kin*mu_kin;
    double rho_D3_pert = 1./2. * mu_kin*mu_kin * Lambda_pert - 128./3. * alsb*alsb * mu_kin*mu_kin*mu_kin;
    
    double lambda1 = -mu_pi2 + mu_pi2_pert;
    double lambda2 = mu_G2/3.;
    double rho1 = rho_D3 - rho_D3_pert;
    
    double f1EGN = 16./9. * ( 4. - M_PI*M_PI) - 8./3. * Lz2 - 
             ( 4. * z * ( 30. - 63. * z + 31. * z2 + 5. * z3))/(9. * umz2) -
             ( 4. * (30. - 72. * z + 51. * z2 - 2. * z3 - 3. * z4))/(9. * umz2) * Lz;
    double f2EGN = -2./9. * ( 87. + 32. * M_PI*M_PI) - 32./3. * Lz2 + 
             2. * ( 162. - 244. * z + 113. * z2 - 7. * z3)/(3. * (1. - z)) * Lz +
             2. * z * ( 54 - 49. * z + 15. * z2)/(1. - z);
    
    corrLambda2_rad = lambda1 * ( f1EGN/8.  - 4./3. * (Lb + 1.) ) 
            + lambda2 * (f2EGN/8.  + 12. * (Lb + 1.) );
    corrLambda2_sem = -3. * 4.98 * lambda2 + (25. - 4. * M_PI*M_PI)/12.*lambda1;
    corrLambda2_mix = 1./8. * (9. * lambda2 - lambda1) * Kij_1(7,7,E0,mu).real();
    
    corrLambda2 = corrLambda2_rad - corrLambda2_sem + corrLambda2_mix;
    
    corrLambda3 = (-88./6. + 16.*log(2.))* rho1 /Mb_kin/Mb_kin/Mb_kin;
    
    return (C7_0.abs2() + C7p_0.abs2()) * (4. * Alstilde / Mb_kin / Mb_kin * corrLambda2 + corrLambda3);
}

omega()

double Bsgamma::omega

(

double

E0

)

The cutoff energy function \( \omega \) as defined in [Kaminski:2012eb] .

Parameters

[in]

E0

cutoff energy

Returns

\( \omega(E0) \)

Definition at line 117 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 3./2. * d2 - 2. * d3 + d4;
}

omega77()

double Bsgamma::omega77

(

double

z

)

The \( \omega_{77} \) function, linear combination of the functions \( F^{(2,a)} \), \( F^{(2,na)} \) and \( F^{(2,nf)} \) from hep-ph/0505097.

Parameters

[in]

z

integration variable

Returns

\( \omega_{77} \)

Definition at line 1829 of file bsgamma.cpp.

{
    double z2 = z*z;
    double z3 = z2*z;
    double z4 = z3*z;
    double z5 = z4*z;
    double z6 = z5*z;
    double z7 = z6*z;
    double z8 = z7*z;
    double omz = 1. - z;
    double omz2 = omz * omz;
    double omz3 = omz2 * omz;
    double Lz = log(z);
    double Lomz = log (1. - z);
    double Lomz2 = Lomz*Lomz;
    double Lomz3 = Lomz2*Lomz;
    double Ltmz = log (2. - z);
    double Ltmz2 = Ltmz*Ltmz;
    double Li2omz = gsl_sf_dilog(1. - z);
    double Li2zmo = gsl_sf_dilog(z - 1.);
    Polylogarithms Poly;
    double Pi2 = M_PI*M_PI;
    
    return 4./9. * (z3 - 4. * z2 + 4. * z + 1.)/omz * ( 2. * Poly.Li3( 1./(2.-z) ) 
            - Poly.Li3( z/(2.-z) ) + Poly.Li3( z/(z-2.) ) 
            + Ltmz * ( Lomz2 - 1./3. * Ltmz2 + 1./6. * Pi2 ) ) 
            + 4./9. * (z3 + 36. * z - 43.)/omz * Poly.Li3(z) 
            + 8./9. * (z3 - 2. * z2 + 19. * z - 22.)/omz * Poly.Li3(1.-z) 
            - 16./9. * omz2 * Poly.Li3(z-1.) 
            - 4./9. * (z3 + 35. * z - 44.)/omz * Li2omz * Lomz 
            - 4./9. * (z3 - 2. * z2 + 2. * z - 3.)/omz * Li2zmo * Lomz 
            - 4./27. * (23. * z6 - 106. * z5 + 145. * z4 + 3. * z3 
            - 180. * z2 + 147. * z - 36.)/(z * omz3) * (Li2omz + Lomz * Lz) 
            + 2./27. * (z8 - 6. * z7 + 9. * z6 + 27. * z5 - 140. * z4 + 219. * z3 
            - 124. * z2 + 28. * z - 6.)/(z * omz3) * (Li2zmo + Lomz * Ltmz) 
            - 8./9. * (z2 + 8. * z - 11.)/omz * Lomz2 * Lz 
            - 2./9. * (z4 - 3. * z3 - 5. * z2 + 15. * z + 8.)/(z * omz) * Lomz3 
            - (z6 - 4. * z5 - 46. * z4 + 101. * z3 - 461. * z2 + 1057. * z - 72.)/(27. * z * omz) * Lomz2 
            + 2./27. * (z3 - 2. * z2 + 4. * z - 5.)/omz * Pi2 * Lomz 
            + (2. * z5 - 29. * z4 - 113. * z3 + 153. * z2 - 827. * z - 162.)/(27. * z * omz) * Lomz 
            - (3. * z3 - 8. * z2 + 144. * z - 157.)/(9. * omz) * gsl_sf_zeta(3.) 
            + (z6 - 4. * z5 + 48. * z4 - 106. * z3 - 58. * z2 + 158. * z - 75.)/(81. * z * omz) * Pi2 
            + (2. * z4 - 92. * z3 + 88. * z2 - 713. * z - 18.)/(27. * omz);
}

P()

double Bsgamma::P	(	double	E0,
		double	mu_b,
		double	mu_c,
		orders	order
	)

The perturbative part of the \(BR\) as defined in [Misiak:2006ab] , \(P\).

Parameters

[in]	E0	energy cutoff
[in]	mu_b	b quark scale
[in]	mu_c	c quark scale
[in]	order	perturbation theory order

Returns

\(P\)

Definition at line 2310 of file bsgamma.cpp.

{
 
    switch(order) {
        case NNLO:
            /*std::cout << "p0 w/ tree, VubLO: " << P0(E0) << std::endl;
            std::cout << "p11: " << P11() << std::endl;
            std::cout << "p21: " << P21(E0,mu_b) << std::endl;
            std::cout << "p12: " << P12() << std::endl;
            std::cout << "p22: " << P22(E0,mu_b,mu_c) << std::endl;
            std::cout << "p32: " << P32(E0,mu_b) << std::endl;
            std::cout << "Vub_NLO: " << Vub_NLO(E0) << std::endl;
            std::cout << "Vub_NNLO: " << Vub_NNLO(E0) << std::endl;
            std::cout << "EW_NLO: " << EW_NLO(mu_b) << std::endl;*/
            return P0(E0) 
                    + Alstilde * (P11() + P21(E0,mu_b)) + Vub_NLO(E0) + AleatMztilde * EW_NLO(mu_b)
                    + Alstilde * Alstilde * (P12() + P22(E0,mu_b,mu_c) + P32(E0,mu_b)) + Vub_NNLO(E0);
            break;
        case NLO:
            return P0(E0) 
                    + Alstilde * (P11() + P21(E0,mu_b)) + Vub_NLO(E0) + AleatMztilde * EW_NLO(mu_b);
            break;
        case LO:
            return P0(E0);
            break;
        default:
            std::stringstream out;
            out << order;
            throw std::runtime_error("Bsgamma::P(): order " + out.str() + " not implemented");
    }
}

P0()

double Bsgamma::P0

(

double

E0

)

The perturbative part \( P^{(0)} \) of the BR as defined in [Misiak:2006ab] .

Parameters

[in]

E0

energy cutoff

Returns

\( P^{(0)} \)

Definition at line 2046 of file bsgamma.cpp.

{
    return C7_0.abs2() + C7p_0.abs2() + P0_4body(E0,Mb_kin*Mb_kin/Ms/Ms);
}

P0_4body()

double Bsgamma::P0_4body	(	double	E0,
		double	t
	)

The 4-body LO contribution as defined in [Kaminski:2012eb] .

Parameters

[in]	E0	cutoff energy
[in]	t	squared ratio between b quark and s quark masses

Returns

\( P_{tree}^{(0)} \)

Definition at line 171 of file bsgamma.cpp.

{
    gslpp::complex la_u =-CKMu;
    
    double A1sq =C1_0.abs2()*CKMusq;
    double A2sq =C2_0.abs2()*CKMusq;
    
    double C13re = (C1_0.real()*C3_0.real() + C1_0.imag()*C3_0.imag());
    double C14re = (C1_0.real()*C4_0.real() + C1_0.imag()*C4_0.imag());
    double C15re = (C1_0.real()*C5_0.real() + C1_0.imag()*C5_0.imag());
    double C16re = (C1_0.real()*C6_0.real() + C1_0.imag()*C6_0.imag());
    
    double C13im = (C1_0.real()*C3_0.imag() + C1_0.imag()*C3_0.real());
    double C14im = (C1_0.real()*C4_0.imag() + C1_0.imag()*C4_0.real());
    double C15im = (C1_0.real()*C5_0.imag() + C1_0.imag()*C5_0.real());
    double C16im = (C1_0.real()*C6_0.imag() + C1_0.imag()*C6_0.real());
    
    double C23re = (C2_0.real()*C3_0.real() + C2_0.imag()*C3_0.imag());
    double C24re = (C2_0.real()*C4_0.real() + C2_0.imag()*C4_0.imag());
    double C25re = (C2_0.real()*C5_0.real() + C2_0.imag()*C5_0.imag());
    double C26re = (C2_0.real()*C6_0.real() + C2_0.imag()*C6_0.imag());
    
    double C23im = (C2_0.real()*C3_0.imag() + C2_0.imag()*C3_0.real());
    double C24im = (C2_0.real()*C4_0.imag() + C2_0.imag()*C4_0.real());
    double C25im = (C2_0.real()*C5_0.imag() + C2_0.imag()*C5_0.real());
    double C26im = (C2_0.real()*C6_0.imag() + C2_0.imag()*C6_0.real());
    
    double C13 = (C13re*la_u.real() - C13im*la_u.imag());
    double C14 = (C14re*la_u.real() - C14im*la_u.imag());
    double C15 = (C15re*la_u.real() - C15im*la_u.imag());
    double C16 = (C16re*la_u.real() - C16im*la_u.imag());
    double C23 = (C23re*la_u.real() - C23im*la_u.imag());
    double C24 = (C24re*la_u.real() - C24im*la_u.imag());
    double C25 = (C25re*la_u.real() - C25im*la_u.imag());
    double C26 = (C26re*la_u.real() - C26im*la_u.imag());
    double C33 = C3_0.abs2();
    double C34 = (C3_0.real()*C4_0.real() + C3_0.imag()*C4_0.imag());
    double C35 = (C3_0.real()*C5_0.real() + C3_0.imag()*C5_0.imag());
    double C36 = (C3_0.real()*C6_0.real() + C3_0.imag()*C6_0.imag());
    double C44 = C4_0.abs2();
    double C45 = (C4_0.real()*C5_0.real() + C4_0.imag()*C5_0.imag());
    double C46 = (C4_0.real()*C6_0.real() + C4_0.imag()*C6_0.imag());
    double C55 = C5_0.abs2();
    double C56 = (C5_0.real()*C6_0.real() + C5_0.imag()*C6_0.imag());
    double C66 = C6_0.abs2();
    
    return (C33 + 20. * C35 + 2./9. * C44 + 40./9. * C46 + 136. * C55 + 272./9. * C66) * T1(E0,t) +
            
            (2./9. * A1sq + A2sq 
            + 8./9. * C13 - 4./27. * C14 + 128./9. * C15 - 64./27. * C16
            + 2./3. * C23 + 8./9. * C24 + 32./3. * C25 + 128./9. * C26) * T2(E0,t) +
            
            (C33 + 8./3. * C34 + 32. * C35 + 128./3. * C36 - 2./9. * C44 + 128./3. * C45 
            - 64./9. * C46 + 256. * C55 + 2048./3 * C56 - 512./9. * C66) * T3(E0,t);
}

P11()

double Bsgamma::P11

(

)

The perturbative part \( P_1^{(1)} \) of the BR as defined in [Misiak:2006ab] .

Returns

\( P_1^{(1)} \)

Definition at line 2051 of file bsgamma.cpp.

{
    return 2.*( C7_0.real()*C7_1.real() + C7_0.imag()*C7_1.imag()
            + C7p_0.real()*C7p_1.real() + C7p_0.imag()*C7p_1.imag() ); /*CHECK SIGN*/
}

P12()

double Bsgamma::P12

(

)

The perturbative part \( P_1^{(2)} \) of the BR as defined in [Misiak:2006ab] .

Returns

\( P_1^{(2)} \)

Definition at line 2109 of file bsgamma.cpp.

{
    
   return C7_1.abs2() + C7p_1.abs2() + 2.*(C7_0*C7_2).real(); /*CHECK SIGN*/
}

P21()

double Bsgamma::P21	(	double	E0,
		double	mu
	)

The perturbative part \( P_2^{(1)} \) of the BR as defined in [Misiak:2006ab] .

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( P_2^{(1)} \)

Definition at line 2057 of file bsgamma.cpp.

{
    int i,j;
    gslpp::complex C0[8]={C1_0,C2_0,C3_0,C4_0,C5_0,C6_0,C7_0,C8_0};
    gslpp::complex C0p[8]={C7p_0}; /*IMPLEMENT OTHER WC*/
    double p21=0.;
    
    for(i=0;i<8;i++)
    {
        for(j=0;j<8;j++)
        {
            p21 += ( C0[i].real()*C0[j].real() + C0[i].imag()*C0[j].imag() ) * Kij_1(i+1,j+1,E0,mu).real();
        }
    }
    
    for(i=6;i<7;i++) /*CHECK ALGORITHM*/
    {
        for(j=6;j<7;j++)
        {
            p21 += (C0p[i].real()*C0p[j].real() + C0p[i].imag()*C0p[j].imag()) * Kij_1(i+1,j+1,E0,mu).real();
        }
    }
    
    return p21;
}

P21_CPodd()

double Bsgamma::P21_CPodd	(	double	E0,
		double	mu
	)

The CP odd part of the perturbative part \( P_2^{(1)} \) of the BR as defined in [Misiak:2006ab] .

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( P_2^{(1)} \)

Definition at line 2083 of file bsgamma.cpp.

{
    int i,j;
    gslpp::complex C0[8]={C1_0,C2_0,C3_0,C4_0,C5_0,C6_0,C7_0,C8_0};
    gslpp::complex C0p[8]={C7p_0}; /*IMPLEMENT OTHER WC*/
    double p21=0.;
    
    for(i=0;i<8;i++)
    {
        for(j=0;j<8;j++)
        {
            p21 += - ( C0[i].real()*C0[j].imag() - C0[i].imag()*C0[j].real() ) * Kij_1(i+1,j+1,E0,mu).imag();
        }
    }
    
    for(i=6;i<7;i++) /*CHECK ALGORITHM*/
    {
        for(j=6;j<7;j++)
        {
            p21 += - ( C0p[i].real()*C0p[j].imag() - C0p[i].imag()*C0p[j].real() ) * Kij_1(i+1,j+1,E0,mu).imag();
        }
    }
    
    return p21;
}

P22()

double Bsgamma::P22	(	double	E0,
		double	mu_b,
		double	mu_c
	)

The perturbative part \( P_2^{(2)} \) of the BR as defined in [Misiak:2006ab] .

Parameters

[in]	E0	energy cutoff
[in]	mu_b	b quark scale
[in]	mu_c	c quark scale

Returns

\( P_2^{(2)} \)

Definition at line 2115 of file bsgamma.cpp.

{
    
    int i,j, temp_i,temp_j;
    gslpp::complex C0[4]={C1_0,C2_0,C7_0,C8_0};
    double p22=0.;
    
    for(i=0;i<4;i++)
    {
        for(j=0;j<4;j++)
        {
            if (i > 1) {
                temp_i=i+4;
            } else temp_i=i;
            if (j > 1) {
                temp_j=j+4;
            } else temp_j=j;
            p22 += (C0[i]*C0[j]).real() * Kij_2(temp_i+1,temp_j+1,E0,mu_b,mu_c);
        }
    }
    
    return p22;
}

P32()

double Bsgamma::P32	(	double	E0,
		double	mu
	)

The perturbative part \( P_3^{(2)} \) of the BR as defined in [Misiak:2006ab] .

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( P_3^{(2)} \)

Definition at line 2139 of file bsgamma.cpp.

{
    
    int i,j;
    gslpp::complex C0[8]={C1_0,C2_0,C3_0,C4_0,C5_0,C6_0,C7_0,C8_0};
    gslpp::complex C1[8]={C1_1,C2_1,C3_1,C4_1,C5_1,C6_1,C7_1,C8_1};
    double p32=0.;
    
    for(i=0;i<8;i++)
    {
        for(j=0;j<8;j++)
        {
            p32 += 2.*(C0[i]*C1[j]).real() * Kij_1(i+1,j+1,E0,mu).real();
        }
    }
 
    return p32;
}

Phi11_1()

double Bsgamma::Phi11_1

(

double

E0

)

The \( \Phi_{11}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{11}^{(1)} \)

Definition at line 844 of file bsgamma.cpp.

{
    return Phi22_1(E0)/36.;
}

Phi12_1()

double Bsgamma::Phi12_1

(

double

E0

)

The \( \Phi_{12}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{12}^{(1)} \)

Definition at line 849 of file bsgamma.cpp.

{
    return -Phi22_1(E0)/3.;
}

Phi13_1()

gslpp::complex Bsgamma::Phi13_1

(

double

E0

)

The \( \Phi_{13}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{13}^{(1)} \)

Definition at line 854 of file bsgamma.cpp.

{
    return -Phi23_1(E0)/6.;
}

Phi14_1()

gslpp::complex Bsgamma::Phi14_1

(

double

E0

)

The \( \Phi_{14}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{14}^{(1)} \)

Definition at line 859 of file bsgamma.cpp.

{
    return -Phi24_1(E0)/6.;
}

Phi15_1()

gslpp::complex Bsgamma::Phi15_1

(

double

E0

)

The \( \Phi_{15}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{15}^{(1)} \)

Definition at line 864 of file bsgamma.cpp.

{
    return -Phi25_1(E0)/6.;
}

Phi16_1()

gslpp::complex Bsgamma::Phi16_1

(

double

E0

)

The \( \Phi_{16}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{16}^{(1)} \)

Definition at line 869 of file bsgamma.cpp.

{
    return -Phi26_1(E0)/6.;
}

Phi17_1()

gslpp::complex Bsgamma::Phi17_1	(	double	E0,
		double	z
	)

The \( \Phi_{17}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]	E0	energy cutoff
[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( \Phi_{17}^{(1)} \)

Definition at line 874 of file bsgamma.cpp.

{
    return -Phi27_1(E0,z)/6.;
}

Phi18_1()

gslpp::complex Bsgamma::Phi18_1	(	double	E0,
		double	z
	)

The \( \Phi_{18}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]	E0	energy cutoff
[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( \Phi_{18}^{(1)} \)

Definition at line 879 of file bsgamma.cpp.

{
    return Phi27_1(E0,z)/18.;
}

Phi22_1()

double Bsgamma::Phi22_1

(

double

E0

)

The \( \Phi_{22}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{22}^{(1)} \)

Definition at line 884 of file bsgamma.cpp.

{
    return 16./27. * Int_cc1(E0);
}

Phi22_2beta0()

double Bsgamma::Phi22_2beta0	(	double	E0,
		double	mu
	)

The \( \Phi_{22}^{(2)\beta_0} \) function from arXiv:1009.5685.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( \Phi_{22}^{(2)\beta_0} \)

Definition at line 1257 of file bsgamma.cpp.

{
    double Lb = 2*log(mu/Mb_kin);
    double d = delta(E0);
    double d2 = d*d;
    double mcmb = Mc/Mb_kin;
    double mcmb2 = mcmb*mcmb;
    double mcmb3 = mcmb2*mcmb;
    
    return SM.Beta0(5) * (Phi22_1(E0)*Lb
            + 0.013698269459646965 + 0.3356948452887703 * d 
            - 0.086677232161681  * d2 
            + ( 0.3575455009710223 + 1.8248223618702617 * d 
            - 0.374324331239819 * d2 ) * mcmb 
            + (-2.3059130759599302 - 5.799640881350228 * d 
            - 6.226247001127346 * d2 ) * mcmb2 
            + ( 3.4485885608332834 - 0.5479757965141787 * d 
            + 17.272487170738795 * d2 ) * mcmb3);
}

Phi23_1()

gslpp::complex Bsgamma::Phi23_1

(

double

E0

)

The \( \Phi_{23}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{23}^{(1)} \)

Definition at line 897 of file bsgamma.cpp.

{
    return -8./27. * (Int_c1(E0) + Int_c2(E0) + 2.*Int_bc1(E0) - 2.*Int_bc2(E0))
            - Phi23_1_4body(E0);
}

Phi23_1_4body()

double Bsgamma::Phi23_1_4body

(

double

E0

)

The \( \Phi_{23}^{(1),{\rm 4-body}} \) function obtained from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{23}^{(1),{\rm 4-body}} \)

Definition at line 889 of file bsgamma.cpp.

{
    if (FOUR_BODY)
        return 0.0039849625073434735;
    else
        return 0.;
}

Phi24_1()

gslpp::complex Bsgamma::Phi24_1

(

double

E0

)

The \( \Phi_{24}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{24}^{(1)} \)

Definition at line 911 of file bsgamma.cpp.

{
    return -1./6. * (Phi23_1(E0) + Phi23_1_4body(E0))
            - Phi24_1_4body(E0);
}

Phi24_1_4body()

double Bsgamma::Phi24_1_4body

(

double

E0

)

The \( \Phi_{24}^{(1),{\rm 4-body}} \) function obtained from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{24}^{(1),{\rm 4-body}} \)

Definition at line 903 of file bsgamma.cpp.

{
    if (FOUR_BODY)
        return 0.012330977673588935;
    else
        return 0.;
}

Phi25_1()

gslpp::complex Bsgamma::Phi25_1

(

double

E0

)

The \( \Phi_{25}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{25}^{(1)} \)

Definition at line 925 of file bsgamma.cpp.

{
    return -32./27. * (4.*Int_c1(E0) + Int_c2(E0) + 8.*Int_bc1(E0) - 2.*Int_bc2(E0))
            - Phi25_1_4body(E0);
}

Phi25_1_4body()

double Bsgamma::Phi25_1_4body

(

double

E0

)

The \( \Phi_{25}^{(1),{\rm 4-body}} \) function obtained from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{25}^{(1),{\rm 4-body}} \)

Definition at line 917 of file bsgamma.cpp.

{
    if (FOUR_BODY)
        return 0.06375940011749558;
    else
        return 0.;
}

Phi26_1()

gslpp::complex Bsgamma::Phi26_1

(

double

E0

)

The \( \Phi_{26}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{26}^{(1)} \)

Definition at line 939 of file bsgamma.cpp.

{
    return 16./81. * (4.*Int_c1(E0) + Int_c2(E0) - 10.*Int_bc1(E0) - 2.*Int_bc2(E0) + 36.*Int_cc1(E0))
            - Phi26_1_4body(E0);
}

Phi26_1_4body()

double Bsgamma::Phi26_1_4body

(

double

E0

)

The \( \Phi_{26}^{(1),{\rm 4-body}} \) function obtained from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{26}^{(1),{\rm 4-body}} \)

Definition at line 931 of file bsgamma.cpp.

{
    if (FOUR_BODY)
        return 0.11932481422855279;
    else
        return 0.;
}

Phi27_1()

gslpp::complex Bsgamma::Phi27_1	(	double	E0,
		double	z
	)

The \( \Re \Phi_{27}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]	E0	energy cutoff
[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( \Re \Phi_{27}^{(1)} \)

Definition at line 945 of file bsgamma.cpp.

{
    double d = delta(E0);
    double d2 = d*d;
    double z2 = z*z;
    double Pi2 = M_PI*M_PI;
    double st0 = sqrt(1. - 4.*z);
    double std = sqrt( (1. - d - 4.*z) * (1. - d) );
    double L0 = log( ( 1. + st0 ) / ( 2.*sqrt(z) ) );
    double Ld = log( ( sqrt(1. - d) + sqrt(1. - d - 4.*z) ) / ( 2.*sqrt(z) ) );
    
    gslpp::complex res;
    
    if (d == 1) {
        res = -2./27. + (2.*Pi2 - 7.)/9. * z + 4.*(3. - 2.*Pi2)/9. * z * z
                + 4./3. * z * (1. - 2.*z) * st0 * L0
                - 8./9. * z * (6.*z*z - 4.*z + 1.) * L0*L0 + 4./3. * Pi2 * z * z *z;
    } else res = -2./27. * d * (3. - 3.*d + d2) + (2.*Pi2 - 7.)/9. * z * d * (2. - d)
            + 4.*(3. - 2.*Pi2)/9. * z * z * d 
            + 4./3. * z * (1. - 2.*z) * ( st0 * L0 - std * Ld ) 
            + 4./3. * z * d * std * Ld 
            - 8./9. * z * (6.*z*z - 4.*z + 1.) * ( L0*L0 - Ld*Ld ) 
            - 8./9. * z * d * (2. - d - 4.*z) * Ld * Ld;
    
    if (z < (1. - d)/4.)
        res += gslpp::complex::i() * 8./9. * M_PI * z * ( (1. - 4. * z + 6. * z2)* (L0-Ld) - 3./4. * (1. - 2. * z) * (st0-std) 
                + d * (2. - d - 4. * z) * Ld - 3./4. * d * std );
    else
        res += gslpp::complex::i() * 8./9. * M_PI * z * ( (1. - 4. * z + 6. * z2) * L0 - 3./4. * (1. - 2. * z) * st0 );
    
    return res;
}

Phi28_1()

gslpp::complex Bsgamma::Phi28_1	(	double	E0,
		double	z
	)

The \( \Phi_{28}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]	E0	energy cutoff
[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( \Phi_{28}^{(1)} \)

Definition at line 978 of file bsgamma.cpp.

{
    return -Phi27_1(E0, z)/3.;
}

Phi28_2beta0()

double Bsgamma::Phi28_2beta0	(	double	E0,
		double	mu
	)

The \( \Phi_{28}^{(2)\beta_0} \) function from arXiv:1009.5685.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( \Phi_{28}^{(2)\beta_0} \)

Definition at line 1277 of file bsgamma.cpp.

{
    double Lb = 2*log(mu/Mb_kin);
    double d = delta(E0);
    double d2 = d*d;
    double mcmb = Mc/Mb_kin;
    double mcmb2 = mcmb*mcmb;
    double mcmb3 = mcmb2*mcmb;
    double mcmb4 = mcmb3*mcmb;
    double mcmb5 = mcmb4*mcmb;
    
    return SM.Beta0(5) * (Phi28_1(E0, zeta()).real()*Lb
            + 0.026054745293391798 + 0.1678721564514209 * d 
            - 0.19700988587274693 * d2 
            + ( -0.03801105485376407 + 0.601712887338462 * d 
            - 0.7557529126506585 * d2 ) * mcmb 
            + ( 2.7551159092192132 - 10.034450524236696 * d 
            + 11.271837772655209 * d2 ) * mcmb2 
            + ( -27.045289848315868 + 68.46851531490181 * d 
            - 72.50921751760909 * d2 ) * mcmb3 
            + ( 85.86574743951778 - 289.3441408351491 * d 
            + 297.6777008484198 * d2 ) * mcmb4 
            + ( -91.5260435658921 + 399.81982774456964 * d 
            - 399.85440571662446 * d2 ) * mcmb5);
}

Phi33_1()

double Bsgamma::Phi33_1

(

double

E0

)

The \( \Phi_{33}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{33}^{(1)} \)

Definition at line 983 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 2./27. * (Int_b1(E0) + 8.*Int_b2(E0) - 4.*Int_b4(E0)
            + 33.*Int_bb1(E0) - 20.*Int_bb2(E0) + 4.*Int_bb4(E0))
            + 1./18. * d * ( 1./2. - 1./2.*d2 + 1./3.*d3 - 1./15.*d4 );
}

Phi34_1()

double Bsgamma::Phi34_1

(

double

E0

)

The \( \Phi_{34}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{34}^{(1)} \)

Definition at line 995 of file bsgamma.cpp.

{
    return -1./3.*Phi33_1(E0);
}

Phi35_1()

double Bsgamma::Phi35_1

(

double

E0

)

The \( \Phi_{35}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{35}^{(1)} \)

Definition at line 1000 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 32./27. * (2.*Int_b1(E0) + 4.*Int_b2(E0) - 2.*Int_b4(E0)
            + 18.*Int_bb1(E0) - 13.*Int_bb2(E0) + 2.*Int_bb4(E0))
            + 4./9. * d * ( 4./3. - d2 + 1./2.*d3 - 1./15.*d4 );
}

Phi36_1()

gslpp::complex Bsgamma::Phi36_1

(

double

E0

)

The \( \Phi_{36}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{36}^{(1)} \)

Definition at line 1012 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 8./81. * (5.*Int_b1(E0) + Int_b2(E0) + 4.*Int_b4(E0)
            - 18.*Int_bb1(E0) + 8.*Int_bb2(E0) - 4.*Int_bb4(E0))
            + 6. * (Phi23_1(E0) + Phi23_1_4body(E0))
            - 2./27. * d * ( 4./3. - d2 + 1./2.*d3 - 1./15.*d4 );
}

Phi37_1()

double Bsgamma::Phi37_1

(

double

E0

)

The \( \Phi_{37}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{37}^{(1)} \)

Definition at line 1025 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    
    return -4./3. * Int_b3(E0) + 1./9. * d * (1. - d + 1./3.*d2) + 1./4.*ff7_sMP(E0);
}

Phi38_1()

double Bsgamma::Phi38_1

(

double

E0

)

The \( \Phi_{38}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{38}^{(1)} \)

Definition at line 1033 of file bsgamma.cpp.

{
    return -1./3. * ( Phi37_1(E0) - 1./4.*ff7_sMP(E0) ) + 1./4.*ff8_sMP(E0);
}

Phi44_1()

double Bsgamma::Phi44_1

(

double

E0

)

The \( \Phi_{44}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{44}^{(1)} \)

Definition at line 1038 of file bsgamma.cpp.

{
    return 1./36. * Phi33_1(E0);
}

Phi45_1()

double Bsgamma::Phi45_1

(

double

E0

)

The \( \Phi_{45}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{45}^{(1)} \)

Definition at line 1043 of file bsgamma.cpp.

{
    return -1./6. * Phi35_1(E0);
}

Phi46_1()

gslpp::complex Bsgamma::Phi46_1

(

double

E0

)

The \( \Phi_{46}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{46}^{(1)} \)

Definition at line 1048 of file bsgamma.cpp.

{
    return -1./6. * Phi36_1(E0);
}

Phi47_1()

double Bsgamma::Phi47_1

(

double

E0

)

The \( \Phi_{47}^{(1)} \) function from [Gambino:2001ew] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{47}^{(1)} \)

Definition at line 1053 of file bsgamma.cpp.

{
    return -1./6. * ( Phi37_1(E0) - 1./4.*ff7_sMP(E0) ) 
            + 1./4. * (-1./6. * ff7_sMP(E0) + ff7_dMP(E0));
}

Phi48_1()

double Bsgamma::Phi48_1

(

double

E0

)

The \( \Phi_{48}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{48}^{(1)} \)

Definition at line 1059 of file bsgamma.cpp.

{
    return -1./3. * (Phi47_1(E0) - 1./4. * (-1./6. * ff7_sMP(E0) + ff7_dMP(E0)) ) 
            + 1./4. * (-1./6. * ff8_sMP(E0) + ff8_dMP(E0));
}

Phi55_1()

double Bsgamma::Phi55_1

(

double

E0

)

The \( \Phi_{55}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{55}^{(1)} \)

Definition at line 1065 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 128./27. * (4.*Int_b1(E0) + 2.*Int_b2(E0) - Int_b4(E0)
            + 12.*Int_bb1(E0) - 8.*Int_bb2(E0) + Int_bb4(E0))
            + 8./9. * d * ( 11./3. - 2.*d2 + 2./3.*d3 - 1./15.*d4 );
}

Phi56_1()

gslpp::complex Bsgamma::Phi56_1

(

double

E0

)

The \( \Phi_{56}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{56}^{(1)} \)

Definition at line 1077 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 32./81. * (20.*Int_b1(E0) + Int_b2(E0) + 4.*Int_b4(E0)
            + 24.*Int_bb1(E0) + 14.*Int_bb2(E0) - 4.*Int_bb4(E0))
            + 6. * (Phi25_1(E0) + Phi25_1_4body(E0))
            - 8./27. * d * ( 11./3. - 2.*d2 + 2./3.*d3 - 1./15.*d4 );
}

Phi57_1()

double Bsgamma::Phi57_1

(

double

E0

)

The \( \Phi_{57}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{57}^{(1)} \)

Definition at line 1090 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    
    return 16./9. * d * ( 1. - d + 1./3.*d2) + 4. * ff7_sMP(E0);
}

Phi58_1()

double Bsgamma::Phi58_1

(

double

E0

)

The \( \Phi_{58}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{58}^{(1)} \)

Definition at line 1098 of file bsgamma.cpp.

{
    return -1./3. * (Phi57_1(E0) - 4. *  ff7_sMP(E0)) 
            + 4. * ff8_sMP(E0);
}

Phi66_1()

gslpp::complex Bsgamma::Phi66_1

(

double

E0

)

The \( \Phi_{66}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{66}^{(1)} \)

Definition at line 1104 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return -8./243. * (56.*Int_b1(E0) + 10.*Int_b2(E0) + 4.*Int_b4(E0)
            + 15.*Int_bb1(E0) - 4.*Int_bb2(E0) - 4.*Int_bb4(E0))
            + 32./27. * (4.*Int_c1(E0) + Int_c2(E0) - Int_bc1(E0) 
            - 2.*Int_bc2(E0) + 9.*Int_cc1(E0))
            + 2./81. * d * ( 11./3. - 2.*d2 + 2./3.*d3 - 1./15.*d4 );
}

Phi67_1()

gslpp::complex Bsgamma::Phi67_1

(

double

E0

)

The \( \Phi_{67}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{67}^{(1)} \)

Definition at line 1118 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    
    return 8./3. * (Int_b3(E0) - 2.*Int_c3(E0)) - 8./27. * d * ( 1. - d + 1./3.*d2) 
            + 1./4. * (-8./3. * ff7_sMP(E0) + 10. * ff7_dMP(E0));
}

Phi68_1()

gslpp::complex Bsgamma::Phi68_1

(

double

E0

)

The \( \Phi_{68}^{(1)} \) function obtained using the prescription of [Chetyrkin:1996vx] and adding the 4-body contribution from [Huber:2014nna] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{68}^{(1)} \)

Definition at line 1127 of file bsgamma.cpp.

{
    return -1./3. * (Phi67_1(E0) - 1./4. * (-8./3. * ff7_sMP(E0) + 10. * ff7_dMP(E0)) ) 
            + 1./4. * (-8./3. * ff8_sMP(E0) + 10. * ff8_dMP(E0));
}

Phi77_1()

double Bsgamma::Phi77_1

(

double

E0

)

The \( \Phi_{77}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{77}^{(1)} \)

Definition at line 1133 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    
    return -2./3.*pow(log(d),2.) - 7./3.*log(d) - 31./9. + 10./3.*d + d2/3. - 2./9.*d3 + d*(d - 4.)*log(d)/3.;
}

Phi77_2beta0()

double Bsgamma::Phi77_2beta0	(	double	E0,
		double	mu
	)

The \( \Phi_{77}^{(2)\beta_0} \) function from [Misiak:2006ab] ..

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( \Phi_{77}^{(2)\beta_0} \)

Definition at line 1303 of file bsgamma.cpp.

{
    double Lb = 2*log(mu/Mb_kin);
    double d = delta(E0);
    double d2 = d*d;
    double d3 = d2*d;
    double Ld = log(d);
    double zeta3 = gsl_sf_zeta_int(3);
    double Li2 = gsl_sf_dilog(1. - d);
    Polylogarithms Poly;
    double Li3 = Poly.Li3(d);
    
    return SM.Beta0(5) * (Phi77_1(E0)*Lb
            + ( -3. + 4./3. * d - 1./3. * d2 - 4./3. * Ld ) * Li2 
            + ( 13./18. + 2. * d - 1./2. * d2 - 4./3. * log(1. - d) 
            + 2./3. * Ld ) * Ld*Ld 
            - 8./3. * (Li3 - zeta3) 
            + ( 4./9. * M_PI*M_PI - 85./18. - 47./9. * d 
            + 19./18. * d2 + 2./9. * d3 ) * Ld 
            - 49./6. + 80./9. * d + 1./18. * d2 - 7./9. * d3);
}

Phi77_2rem()

double Bsgamma::Phi77_2rem

(

double

E0

)

The part of the \( K_{77}^{(2)} \) function with no \( \beta_0 \) dependance, as defined in [Misiak:2006ab] .

Parameters

[in]

E0

energy cutoff

Returns

\( K_{77}^{(2), {\rm rem}} \)

Definition at line 1891 of file bsgamma.cpp.

{
    double xm = 8./9. * M_PI * alsUps;
    double d = delta(E0);
    double d2 = d*d;
    double d3 = d2*d;
    double d4 = d3*d;
    
    return Int_Phi77_2rem(E0) - xm/3./ d * 
            ((4. - 6. * d2 + 2. * d3) * log(d) + 7. - 13. * d + 3. * d2 + 5. * d3 - 2. * d4);
}

Phi78_1()

double Bsgamma::Phi78_1

(

double

E0

)

The \( \Phi_{78}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{78}^{(1)} \)

Definition at line 1142 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    
    double Li2 = gsl_sf_dilog(1. - d);
    
    double pi2=M_PI*M_PI;
    
    return 8./9.*( Li2 -  pi2/6. - d*log(d) + 9./4.*d - d2/4. + d3/12.);
}

Phi88_1()

double Bsgamma::Phi88_1

(

double

E0

)

The \( \Phi_{88}^{(1)} \) function from [Gambino:2001ew] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{88}^{(1)} \)

Definition at line 1155 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    
    double Li2 = gsl_sf_dilog(1. - d);
    
    double pi2=M_PI*M_PI;
    
    return 1./27.*( -2.*log(Mb_kin/Ms)*( d2 + 2.*d + 4.*log(1. - d) ) + 4.*Li2 - 2./3.*pi2 - d*(2. + d)*log(d) 
            + 8.*log(1. - d) -  2./3.*d3 + 3.*d2 +7*d);
}

Phi88_2beta0()

double Bsgamma::Phi88_2beta0	(	double	E0,
		double	mu
	)

The \( \Phi_{88}^{(2)\beta_0} \) function from arXiv:1009.5685.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( \Phi_{88}^{(2)\beta_0} \)

Definition at line 1325 of file bsgamma.cpp.

{
    double Lb = 2*log(mu/Mb_kin);
    double d = delta(E0);
    double d2 = d*d;
    double d3 = d2*d;
    double Ld = log(d);
    double L1d = log(1. - d);
    double Li2 = gsl_sf_dilog(1. - d);
    Polylogarithms Poly;
    double Li3 = Poly.Li3(d);
    
    return SM.Beta0(5) * (Phi88_1(E0)*Lb
            + 4./27. * ( - 2. * ( Li2 - 1./6. * M_PI*M_PI + 3. * L1d 
            - 1./4. * d * (2. + d) * Ld + 8./3. * d + 5./6. * d2 
            - 1./18. * d3 ) * log(Mb_kin/Ms) - 2. * Li3 
            + ( 5. - 2. * Ld ) * ( Li2 - 1./6. * M_PI*M_PI ) 
            + ( 1./2. * d + 1./4. * d2 - L1d ) * Ld * Ld
            - 1./12. * M_PI*M_PI * d * (2. + d) 
            + ( 151./18. - 1./3. * M_PI*M_PI ) * L1d 
            + ( - 53./12. * d - 19./12. * d2 + 2./9. * d3 ) * Ld 
            + 787./72. * d + 227./72. * d2 - 41./72. * d3 ));
}

r1()

gslpp::complex Bsgamma::r1	(	int	i,
		double	z
	)

The funcion \( r_i^{(1)}(z) \) as defined in [Buras:2002tp] .

Parameters

[in]	i	function index
[in]	z	squared ratio between m_c and m_b^{\rm kin}

Returns

\( r_i(z)^{(1)} \)

Definition at line 285 of file bsgamma.cpp.

{
    double Xb = -0.16844083981858157;
    
    switch(i){
        case 1:
            return 833./729. - (a(z) + b(z))/3. + 40./243.*gslpp::complex::i()*M_PI;
        case 2:
            return - 1666./243. + 2.*(a(z) + b(z)) - 80./81.*gslpp::complex::i()*M_PI;
        case 3:
            return 2392./243. + 8.*M_PI/3./sqrt(3.) + 32./9.*Xb - a(1.) + 2.*b(1.) + 56./81.*gslpp::complex::i()*M_PI;
        case 4:
            return -761./729. - 4.*M_PI/9./sqrt(3.) - 16./27.*Xb + a(1.)/6. + 5.*b(1.)/3. + 2.*b(z) - 148./243.*gslpp::complex::i()*M_PI;
        case 5:
            return 56680./243. + 32.*M_PI/3./sqrt(3.) + 128./9.*Xb - 16.*a(1.) + 32.*b(1.) + 896./81.*gslpp::complex::i()*M_PI;
        case 6:
            return 5710./729. - 16.*M_PI/9./sqrt(3.) - 64./27.*Xb - 10./3.*a(1.) + 44./3.*b(1.) + 12.*a(z) + 20.*b(z) 
                    - 2296./243.*gslpp::complex::i()*M_PI;
        case 8:
            return 44./9. - 8./27.*M_PI*M_PI + 8./9.*gslpp::complex::i()*M_PI;
        default:
            std::stringstream out;
            out << i;
            throw std::runtime_error("Bsgamma::r1(): index " + out.str() + " not implemented");
    }
}

r1_ew()

gslpp::complex Bsgamma::r1_ew	(	int	i,
		double	z
	)

The funcion \( r_{i,ew}^{(1)}(z) \) as defined in [Gambino:2001au] .

Parameters

[in]	i	function index
[in]	z	squared ratio between m_c and m_b^{\rm kin}

Returns

\( r_i(z)^{(1)} \)

Definition at line 312 of file bsgamma.cpp.

{
    double Xb = -0.16844083981858157;
    double PI2 = M_PI*M_PI;
    gslpp::complex iPI = gslpp::complex::i()*M_PI;
    
    switch(i){
        case 1:
            return 3332./2187. - 4.*(a(z) + b(z))/9. + 160./729.*iPI;
        case 2:
            return 833./729. - (a(z) + b(z))/3. + 40./243.*iPI;
        case 3:
            return 748./729. + 2.*M_PI/9./sqrt(3.) - 2./81.*PI2 + 8./27.*Xb 
                    - a(1.)/12. + 7.*b(1.)/6. - 2.*b(z) + 26./243.*iPI;
        case 4:
            return 2680./2187. + 8.*M_PI/27./sqrt(3.) - 8./243.*PI2 + 32./81.*Xb 
                    - a(1.)/9. + 2.*b(1.)/9. + 56./729.*iPI;
        case 5:
            return 78301./729. + 8.*M_PI/9./sqrt(3.) - 40./81.*PI2 + 32./27.*Xb 
                    - 13.*a(1.)/3. + 38.*b(1.)/3. - 12.*a(z) - 20.*b(z) + 3908./243.*iPI;
        case 6:
            return 62440./2187. + 32.*M_PI/27./sqrt(3.) - 160./243.*PI2 + 128./81.*Xb 
                    - 16.*a(1.)/9. + 32.*b(1.)/9. + 896./729.*iPI;
        case 7:
            return -25./27. - 2./9.*iPI;
        default:
            std::stringstream out;
            out << i;
            throw std::runtime_error("Bsgamma::r1_ew(): index " + out.str() + " not implemented");
    }
}

Rer22()

double Bsgamma::Rer22

(

double

z

)

The \( Re r_2^{(2)} \) function from [Misiak:2006ab] .

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( Re r_2^{(2)} \)

Definition at line 1225 of file bsgamma.cpp.

{
    double L = log(z);
    double L2 = L*L;
    double L3 = L2*L;
    double L4 = L3*L;
    double z32 = sqrt(z)*z;
    double z2 = z*z;
    double z52 = z32*z;
    double z3 = z2*z;
    double z72 = z52*z;
    double z4 = z3*z;
    double Pi2 = M_PI*M_PI;
    double zeta3 = gsl_sf_zeta_int(3);
    
    return 67454./6561. - 124./729. * Pi2 
            - 4./1215. * (11280. - 1520. * Pi2 - 171. * Pi2*Pi2 - 5760. * zeta3 
            + 6840. * L - 1440. * Pi2*L - 2520. * zeta3*L 
            + 120. * L2 + 100. * L3 - 30. * L4) * z 
            - 64./243. * Pi2*( 43. - 12. * log(2.) - 3. * L) * z32 
            - 2./1215. * (11475. - 380. * Pi2 + 96. * Pi2*Pi2 
            + 7200. * zeta3 - 1110. * L - 1560. * Pi2*L + 1440. * zeta3*L 
            + 990. * L2 + 260. * L3 - 60. * L4) * z2 
            + 2240./243. * Pi2 * z52
            - 2./2187. * (62471. - 2424. * Pi2 - 33264. * zeta3 - 19494. * L 
            - 504. * Pi2*L - 5184. * L2 + 2160. * L3) * z3 
            - 2464./6075. * Pi2 * z72
            + ( - 15103841./546750. + 7912./3645. * Pi2 + 2368./81. * zeta3 
            + 147038./6075. * L + 352./243. * Pi2*L + 88./243. * L2 
            - 512./243. * L3 ) * z4; 
}

rho()

double Bsgamma::rho

(

double

E0

)

The cutoff energy function \( \rho \) as defined in [Kaminski:2012eb] .

Parameters

[in]

E0

cutoff energy

Returns

\( \rho(E0) \)

Definition at line 109 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d4=d*d*d*d;
    
    return d + d4/6. + log(1. - d);
}

T1()

double Bsgamma::T1	(	double	E0,
		double	t
	)

The cutoff energy function \( T_1 \) as defined in [Kaminski:2012eb] .

Parameters

[in]	E0	cutoff energy
[in]	t	squared ratio between b quark and s quark masses

Returns

\( T_1(E0) \)

Definition at line 127 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    double Li2 = gsl_sf_dilog(d);
    
    return 109./18. * d + 17./18. * d2 - 191./108. * d3 + 23./16. * d4 
            + 79./18. * log(1. - d) - 5./3. * Li2 
            - (5./3. * rho(E0) + 2./9. * omega(E0)) * log(t*d) 
            /* + rho(E0)/9.*log(ms^5/(mu^4*md)) */;
}

T2()

double Bsgamma::T2	(	double	E0,
		double	t
	)

The cutoff energy function \( T_2 \) as defined in [Kaminski:2012eb] .

Parameters

[in]	E0	cutoff energy
[in]	t	squared ratio between b quark and s quark masses

Returns

\( T_2(E0) \)

Definition at line 142 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    double Li2 = gsl_sf_dilog(d);
    
    return 187./108. * d + 7./18. * d2 - 395./648. * d3 + 1181./2592. * d4 
            + 133./108. * log(1. - d) - Li2/2. 
            - (rho(E0)/2. + 2./27. * omega(E0)) * log(t*d) 
            /* + rho(E0)/9.*log(ms/mu) */;
}

T3()

double Bsgamma::T3	(	double	E0,
		double	t
	)

The cutoff energy function \( T_3 \) as defined in [Kaminski:2012eb] .

Parameters

[in]	E0	cutoff energy
[in]	t	squared ratio between b quark and s quark masses

Returns

\( T_3(E0) \)

Definition at line 157 of file bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    double Li2 = gsl_sf_dilog(d);
    
    return 35./162. * d + 1./72. * d2 - 89./1944. * d3 + 341./7776. * d4 
            + 13./81. * log(1. - d) - Li2/18. 
            - (rho(E0)/18. + omega(E0)/162.) * log(t*d);
}

updateParameters()

void Bsgamma::updateParameters

(

)

The update parameter method for bsgamma.

Definition at line 2410 of file bsgamma.cpp.

{
    mu_kin=SM.getOptionalParameter("mukin");
    BRsl=SM.getOptionalParameter("BRsem")/100.;
    Mb_kin=SM.getOptionalParameter("Mbkin");
    Mc=SM.getOptionalParameter("Mcatmuc");
    mu_pi2=SM.getOptionalParameter("mupi2");
    rho_D3=SM.getOptionalParameter("rhoD3");
    mu_G2=SM.getOptionalParameter("muG2");
    rho_LS3=SM.getOptionalParameter("rhoLS3");
    mu_b=SM.getOptionalParameter("mu_b_bsgamma");
    mu_c=SM.getOptionalParameter("mu_c_bsgamma");
    C=C_sem();
    
    ale=SM.getAle();
    alsUps=8./M_PI * mu_kin/Mb_kin * ( 1. + 3./8. * mu_kin/Mb_kin );
    Alstilde = SM.Alstilde5(mu_b);
    AleatMztilde=SM.ale_OS(SM.getMz())/4./M_PI;
    Ms=SM.getQuarks(QCD::STRANGE).getMass();
    Mb=SM.getQuarks(QCD::BOTTOM).getMass();
    Mz=SM.getMz();
    V_ub=SM.getCKM().getV_ub();
    V_cb=SM.getCKM().getV_cb();
    V_tb=SM.getCKM().getV_tb();
    
    if(WET_NP_btos){
        C_7_NP = SM.getOptionalParameter("C7_NP");
        C_7p_NP = SM.getOptionalParameter("C7p_NP");
    }
    else if(SMEFT_NP_btos){
            gslpp::complex SMEFT_factor = (M_PI/SM.getAle())*(SM.v()*1.e-3)*(SM.v()*1.e-3)/SM.getCKM().computelamt_s();
            C_7_NP = SM.getOptionalParameter("CdB")-SM.getOptionalParameter("CdW");
            C_7_NP *= SMEFT_factor*SM.getAle()*8.*M_PI*SM.v()/Mb;
            C_7p_NP = SM.getOptionalParameter("CpdB")-SM.getOptionalParameter("CpdW");
            C_7p_NP *= SMEFT_factor*SM.getAle()*8.*M_PI*SM.v()/Mb;
    }
    else{
        C_7_NP = 0.;
        C_7p_NP = 0.;        
    }
    
    if (SUM) {
        CKMratio=(V_tb/V_cb).abs2()*(1. - V_tb.abs2());
        CKMu=-V_ub.abs2()/(1. - V_tb.abs2());
        CKMusq = (V_ub/V_tb).abs2() * (1. - V_ub.abs2())/(1. - V_tb.abs2());
        }
    else
        switch (quark) {
            case StandardModel::STRANGE:
                CKMratio=(SM.getCKM().computelamt_s()/V_cb).abs2();
                CKMu=SM.getCKM().computelamu_s().conjugate() / SM.getCKM().computelamt_s().conjugate(); // -0.00802793 + 0.0180942*gslpp::complex::i(); //
                CKMusq = CKMu.abs2();
                break;
            case StandardModel::DOWN:
                CKMratio=(SM.getCKM().computelamt_d()/V_cb).abs2();
                CKMu=SM.getCKM().computelamu_d().conjugate() / SM.getCKM().computelamt_d().conjugate(); //  0.00745398 - 0.40416*gslpp::complex::i(); //
                CKMusq = CKMu.abs2();
                break;
            default:
                std::stringstream out;
                out << quark;
                throw std::runtime_error("bqgamma: quark " + out.str() + " not implemented");
        }
    
    BLNPcorr=SM.getOptionalParameter("BLNPcorr");
    
    checkCache();
    
    if (Intb_updated == 0) {
        Intb1Cached = 0;
        Intb2Cached = 0;
        Intb3Cached = 0;
        Intb4Cached = 0;
        Intbb1Cached = 0;
        Intbb2Cached = 0;
        Intbb4Cached = 0;
        IntPhi772rCached = 0;
    }
    if (Intbc_updated == 0) {
        Intbc1Cached = 0;
        Intbc2Cached = 0;
        Intc1Cached = 0;
        Intc1imCached = 0;
        Intc2Cached = 0;
        Intc3Cached = 0;
        IntccCached = 0;
        Intcc1Cached = 0;
        Intcc1p1Cached = 0;
    }
    
    computeCoeff(mu_b);
    
    overall = BRsl * CKMratio * 6. * ale / (M_PI * C);
    
}

Vub_NLO()

double Bsgamma::Vub_NLO

(

double

E0

)

The total NLO Vub part of the \(BR\), \(Vub^{NLO}\).

Parameters

[in]

E0

energy cutoff

Returns

\(Vub^{NLO}\)

Definition at line 2290 of file bsgamma.cpp.

{
    return Vub_NLO_2body() + Vub_NLO_3body_A(E0) + Vub_NLO_3body_B(E0) + Vub_NLO_4body(E0);
}

Vub_NLO_2body()

double Bsgamma::Vub_NLO_2body

(

)

The 2 body NLO Vub part of the \(BR\) as defined in [Gambino:2001ew] , \(Vub^{NLO}_{2b}\).

Returns

\(Vub^{NLO}_{2b}\)

Definition at line 2191 of file bsgamma.cpp.

{
    double z = zeta();
    
    return 4. * Alstilde * 
            ((C7_0.real()*( C2_0-C1_0/6. ).real() + C7_0.imag()*( C2_0-C1_0/6. ).imag()) * CKMu.real() +
            (C7_0.real()*( C2_0-C1_0/6. ).imag() - C7_0.imag()*( C2_0-C1_0/6. ).real()) * CKMu.imag())
            * ( a(z)+b(z) ).real();
}

Vub_NLO_2body_CPodd()

double Bsgamma::Vub_NLO_2body_CPodd

(

)

The CP odd part of the 2 body NLO Vub part of the \(BR\) as defined in [Gambino:2001ew] , \(Vub^{NLO}_{2b,CPodd}\).

Returns

\(Vub^{NLO}_{2b}\)

Definition at line 2201 of file bsgamma.cpp.

{
    double z = zeta();
    
    return - 4. * Alstilde * 
            ((C7_0.real()*( C2_0-C1_0/6. ).real() + C7_0.imag()*( C2_0-C1_0/6. ).imag()) * CKMu.imag() +
            (C7_0.real()*( C2_0-C1_0/6. ).imag() - C7_0.imag()*( C2_0-C1_0/6. ).real()) * CKMu.real() ) 
            * ( a(z)+b(z) ).imag();
}

Vub_NLO_3body_A()

double Bsgamma::Vub_NLO_3body_A

(

double

E0

)

The first piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,A,CPodd}\).

Parameters

[in]

E0

energy cutoff

Returns

\(Vub^{NLO}_{3b}\)

Definition at line 2211 of file bsgamma.cpp.

{
    double d = delta(E0);
    
    return 64./27. * Alstilde * ( C2_0 - C1_0/6. ).abs2() *
            ( CKMu.real() * ( 2. * Int_cc1(E0) - Int_c1(E0).real() )
            + CKMusq *  ( Int_cc1(E0) - Int_c1(E0).real() + 1./8. * d * ( 1. - 1./3. * d*d ) ));
}

Vub_NLO_3body_A_CPodd()

double Bsgamma::Vub_NLO_3body_A_CPodd

(

double

E0

)

The CP odd part of the first piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,A}\).

Parameters

[in]

E0

energy cutoff

Returns

\(Vub^{NLO}_{3b}\)

Definition at line 2220 of file bsgamma.cpp.

{
    return - 64./27. * Alstilde * ( C2_0 - C1_0/6. ).abs2() * CKMu.imag() * Int_c1(E0).imag();
}

Vub_NLO_3body_B()

double Bsgamma::Vub_NLO_3body_B

(

double

E0

)

The second piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,B,CPodd}\).

Parameters

[in]

E0

energy cutoff

Returns

\(Vub^{NLO}_{3b}\)

Definition at line 2225 of file bsgamma.cpp.

{
    double d = delta(E0);
    gslpp::complex wc1 = C7_0 - C8_0/3.;
    gslpp::complex wc2 = C2_0 - C1_0/6.;
    gslpp::complex me = Phi27_1(E0,zeta()) + 2./9. * d * ( 1. - d + 1./3. * d*d );
    
    return 4. * Alstilde * 
            (( wc1.real() * wc2.real() + wc1.imag() * wc2.imag()) * CKMu.real() +
            ( wc1.real() * wc2.imag() - wc1.imag() * wc2.real()) * CKMu.imag() )
            * me.real();
}

Vub_NLO_3body_B_CPodd()

double Bsgamma::Vub_NLO_3body_B_CPodd

(

double

E0

)

The CP odd part of the second piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,B}\).

Parameters

[in]

E0

energy cutoff

Returns

\(Vub^{NLO}_{3b}\)

Definition at line 2238 of file bsgamma.cpp.

{
    double d = delta(E0);
    gslpp::complex wc1 = C7_0 - C8_0/3.;
    gslpp::complex wc2 = C2_0 - C1_0/6.;
    gslpp::complex me = Phi27_1(E0,zeta()) + 2./9. * d * ( 1. - d + 1./3. * d*d );
    
    return - 4. * Alstilde * 
            (( wc1.real() * wc2.real() + wc1.imag() * wc2.imag()) * CKMu.imag() +
            ( wc1.real() * wc2.imag() - wc1.imag() * wc2.real()) * CKMu.real() )
            * me.imag();
}

Vub_NLO_4body()

double Bsgamma::Vub_NLO_4body

(

double

E0

)

The 4 body NLO Vub part of the \(BR\) obtained from [Huber:2014nna] , \(Vub^{NLO}_{4b,CPodd}\).

Parameters

[in]

E0

energy cutoff

Returns

\(Vub^{NLO}_{4b}\)

Definition at line 2251 of file bsgamma.cpp.

{
    if (FOUR_BODY) {
        double d = delta(E0);
        double d2 = d*d;
        double d3 = d2*d;
        double Ld = log(d);
        double Lumd = log(1. - d);
        double Lq = log(Ms/Mb_kin);
 
        double uphib427 = ( 2. * d * (-63. + 30. * d + 35. * d2 - 2. * d3 
                    + 3. * d * (-18. - 7. * d + d2) * Ld) ) / ( 243. * (d - 1.) );
        double uphib428 = ( 108. * (d - 1.) * (d - 1.) * Lumd*Lumd 
                    - 12. * Lumd * (- 25. - 18. * Lq - 18. * d * (5. + 4. * Lq) 
                    + 9. * d2 * (5. + 4. * Lq) + (9. + 36. * d - 18. * d2) * Ld) 
                    + d * (24. * (17. + 9. * Lq) + 27. * d * (43. + 26. * Lq) 
                    - d2 * (127. + 72. * Lq) + 9. * (-12. - 39. * d + 4. * d2) * Ld) 
                    + 108. * (-1. - 4. * d + 2. * d2) * gsl_sf_dilog(d) ) / 729.;
 
        return 4. * Alstilde * ( 
                ( C2_0 - C1_0/6. ).abs2() * CKMu.real() * 0.005025213076791178
                + (( C2_0 - C1_0/6. ).real() * (C7_0.real() * uphib427 + C8_0.real() * uphib428)
                + ( C2_0 - C1_0/6. ).imag() * (C7_0.imag() * uphib427 + C8_0.imag() * uphib428) ) * CKMu.real() 
                + (( C2_0 - C1_0/6. ).real() * (C7_0.imag() * uphib427 + C8_0.imag() * uphib428)
                - ( C2_0 - C1_0/6. ).imag() * (C7_0.real() * uphib427 + C8_0.real() * uphib428) ) * CKMu.imag() );
    }
    
    else return 0.;
}

Vub_NLO_4body_CPodd()

double Bsgamma::Vub_NLO_4body_CPodd

(

double

E0

)

The CP odd part of the 4 body NLO Vub part of the \(BR\) obtained from [Huber:2014nna] , \(Vub^{NLO}_{4b}\).

Parameters

[in]

E0

energy cutoff

Returns

\(Vub^{NLO}_{4b}\)

Definition at line 2281 of file bsgamma.cpp.

{
    if (FOUR_BODY) {
        return 4. * Alstilde * ( C2_0 - C1_0/6. ).abs2() * CKMu.imag() * 0.013978889449487913;
    }
    
    else return 0.;
}

Vub_NLO_CPodd()

double Bsgamma::Vub_NLO_CPodd

(

double

E0

)

The CP odd part of the total NLO Vub part of the \(BR\), \(Vub^{NLO}_{CPodd}\).

Parameters

[in]

E0

energy cutoff

Returns

\(Vub^{NLO}\)

Definition at line 2295 of file bsgamma.cpp.

{
    return Vub_NLO_2body_CPodd() + Vub_NLO_3body_A_CPodd(E0) + Vub_NLO_3body_B_CPodd(E0) + Vub_NLO_4body_CPodd(E0);
}

Vub_NNLO()

double Bsgamma::Vub_NNLO

(

double

E0

)

The NNLO Vub part of the \(BR\) as defined in xxxxxxxxx, \(Vub^{NLO}\).

Parameters

[in]

E0

energy cutoff

Returns

\(Vub^{NLO}\)

Definition at line 2300 of file bsgamma.cpp.

{
    double r12 = (( C2_1 - C1_1/6. )/( C2_0 - C1_0/6. )).real();
    double r78 = (( C7_1 - C8_1/3. )/( C7_0 - C8_0/3. )).real();
    double r7 = (C7_1/C7_0).real();
    
    return Alstilde * ( (r12 + r7) * Vub_NLO_2body() 
            + 2. * r12 * Vub_NLO_3body_A(E0) + (r12 + r78) * Vub_NLO_3body_B(E0));
}

Y1()

double Bsgamma::Y1	(	double	E0,
		double	mu
	)

The \( Y^{(1)}(z_0,\mu) \) function from arXiv:0805.3911v2.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( Y^{(1)}(z_0,\mu) \)

Definition at line 1357 of file bsgamma.cpp.

{
    double Lb = log(mu/Mb_kin);
    
    return 4./9.*(29. - 2.*M_PI*M_PI) + 16./3.*Lb - dY1(E0);
}

Y2()

double Bsgamma::Y2	(	double	E0,
		double	mu
	)

The \( Y^{(2)}(z_0,\mu) \) function from arXiv:0805.3911v2 and arXiv:1005.5587v1.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( Y^{(2)}(z_0,\mu) \)

Definition at line 1516 of file bsgamma.cpp.

{
    double CF = 4./3.;
    double CA = 3.;
    double TR = 1./2.;
    double NL = 3.;
    double NV = 1.;
    double NH = 1.;
    
    return CF*Y2CF(E0,mu) + CA*Y2CA(E0,mu) 
            + TR * ( NL*Y2NL(E0,mu) + NV*Y2NV(E0,mu) + NH*Y2NH(E0,mu) );
}

Y2CA()

double Bsgamma::Y2CA	(	double	E0,
		double	mu
	)

The \( Y^{(2,CA)}(z_0,\mu) \) function from arXiv:1005.5587v1.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( Y^{(2,CA)}(z_0,\mu) \)

Definition at line 1391 of file bsgamma.cpp.

{
    double Lb = log(mu/Mb_kin);
    double z0 = 1. - delta(E0);
    double z02 = z0*z0;
    double z03 = z02*z0;
    double z04 = z03*z0;
    double z05 = z04*z0;
    double z06 = z05*z0;
    double z07 = z06*z0;
    double z08 = z07*z0;
    double z09 = z08*z0;
    double z010 = z09*z0;
    double z011 = z010*z0;
    double Lz = log(1. - z0);
    double Li2 = gsl_sf_dilog(z0);
    
    return 22.8959 + 76.5729 * Lb + 30.2222 * Lb*Lb + 2.94616 * z0 - 60.4444 * Lb*z0 
            - 13.2522 * z02 - 6.96907 * z03 - 2.51852 * Lb*z03 + 0.117907 * z04 
            - 2.02988 * z05 + 2.90402 * z06 - 3.53904 * z07 + 2.55728 * z08 
            - 0.941549 * z09 + 0.0173599 * z010 + 0.0598012 * z011 
            + (2.94616 - 30.2222 * Lb- 12.3947 * z0 + 30.2222 * Lb*z0 + 9.44855 * z02) * Lz 
            - 6.61587 * (1. - z0) * (1. - z0) * Lz*Lz + 30.2222 * Lb*Li2
            + (0.69995 - 1.3999 * z0 + 0.69995 * z02) * Lz*Lz*Lz;
}

Y2CF()

double Bsgamma::Y2CF	(	double	E0,
		double	mu
	)

The \( Y^{(2,CF)}(z_0,\mu) \) function from arXiv:1005.5587v1.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( Y^{(2,CF)}(z_0,\mu) \)

Definition at line 1364 of file bsgamma.cpp.

{
    double Lb = log(mu/Mb_kin);
    double z0 = 1. - delta(E0);
    double z02 = z0*z0;
    double z03 = z02*z0;
    double z04 = z03*z0;
    double z05 = z04*z0;
    double z06 = z05*z0;
    double z07 = z06*z0;
    double z08 = z07*z0;
    double z09 = z08*z0;
    double z010 = z09*z0;
    double z011 = z010*z0;
    double Lz = log(1. - z0);
    double Li2 = gsl_sf_dilog(z0);
    
    return -21.9087 - 112.464 * Lb - 42.6667 * Lb*Lb - 77.7675 * z0 + 10.6667 * Lb*z0 
            + 68.5848 * z02 - 5.33333 * Lb * z02 - 4.42133 * z03 + 6.22222 * Lb * z03 
            - 4.0317 * z04 + 6.64376 * z05 - 11.647 * z06 + 15.8697 * z07 
            - 14.8006 * z08 + 8.85514 * z09 - 2.9929 * z010 + 0.433254 * z011 
            + (-77.7675 + 85.8251 * z0 - 28.6855 * z02 
            + Lb * (-21.3333 - 21.3333 * z0 + 5.33333 * z02)) * Lz 
            + (-12.2881 - 10.6667 * Lb + 6.12213 * z0 + 0.27227 * z02) * Lz*Lz 
            + (-2.88573 + 5.77146 * z0 - 2.88573 * z02) * Lz*Lz*Lz - 32. * Lb*Li2;
}

Y2NH()

double Bsgamma::Y2NH	(	double	E0,
		double	mu
	)

The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( Y^{(2,NL)}(z_0,\mu) \)

Definition at line 1505 of file bsgamma.cpp.

{
    double Lb = log(mu/Mb_kin);
    double zeta3 = gsl_sf_zeta_int(3);
    double Cl2 = gsl_sf_clausen(M_PI/3.);
    
    return 8./81. * (244. - 27.*sqrt(3.)*M_PI - 61.*M_PI*M_PI) 
            - 64./27.*(18. - M_PI*M_PI)*Lb - 64./9.*Lb*Lb - 64./27.*zeta3
            + 32.*sqrt(3.)*Cl2 + 8./3.*Lb*dY1(E0);
}

Y2NL()

double Bsgamma::Y2NL	(	double	E0,
		double	mu
	)

The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( Y^{(2,NL)}(z_0,\mu) \)

Definition at line 1417 of file bsgamma.cpp.

{
    double z0 = 1. - delta(E0);
    double Lz = log(1. - z0);
    double Lb = log(mu/Mb_kin);
    double zeta3 = gsl_sf_zeta_int(3);
    double Li2 = gsl_sf_dilog(z0);
    Polylogarithms Poly;
    double Li3 = Poly.Li3(z0);
    double Li3min = Poly.Li3(1. - z0);
    
    return -16./81. * (328. - 13.*M_PI*M_PI) - 64./27. * (18. - M_PI*M_PI)*Lb
            -64./9. * Lb*Lb + 64./3. * zeta3
            +4./27. * z0*(7.*z0*z0 - 17.*z0 + 238.) + 8./3. * Lb*dY1(E0)
            -8./27. * (z0*z0*z0 - 6.*z0*z0 + 80.*z0 - 75. + 6.*M_PI*M_PI)*Lz
            +16./3. * (z0 - 1.)*Lz*Lz + 16./3. * log(z0)*Lz*Lz
            +32./27. * (3.*z0 - 8.)*Li2 + 32./3. * Lz*Li2
            -32./9. * Li3 + 32./3. * Li3min - 32./3. * zeta3;
}

Y2NV()

double Bsgamma::Y2NV	(	double	E0,
		double	mu
	)

The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2.

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( Y^{(2,NL)}(z_0,\mu) \)

Definition at line 1482 of file bsgamma.cpp.

{
    double Lb = log(mu/Mb_kin);
    double rho = zeta();
    double rho2 = rho*rho;
    double rho32 = rho*sqrt(rho);
    double Lr = log(rho);
    double Li2 = gsl_sf_dilog(1. - rho);
    double Li2sqrt = gsl_sf_dilog(1. - sqrt(rho));
    Polylogarithms Poly;
    double Li3 = Poly.Li3(1. - rho);
    double Li3ov = Poly.Li3(1. - 1./rho);
    
    return -16./81. * (157. - 279.*rho - M_PI*M_PI*(5. + 9.*rho2 - 42.*rho32))
            -64./27. * (18. - M_PI*M_PI)*Lb - 64./9. * Lb*Lb
            +16./27. * (22. - M_PI*M_PI + 10.*rho)*Lr + 16./27. * (8. + 9.*rho2)*Lr*Lr
            -16./27. * Lr*Lr*Lr - 8./9. * (1. - 6.*rho2)*Y2NV_PHI1(rho)
            -8./27. * (19. - 46.*rho)*Y2NV_PHI2(rho) - 32./27. * (13. + 14.*rho)*Y2NV_PHI3(rho)
            -64./9. * Y2NV_PHI4(rho) - 32./9. * Lr*Li2 
            +32./27. * (5. + 9.*rho2 + 14.*rho32)*Li2 - 1792./27. * rho32*Li2sqrt
            +64./9. * Li3 + 64./9. * Li3ov + 4./3.*(2.*Lb - Lr)*dY1(E0);
}

Y2NV_PHI1()

double Bsgamma::Y2NV_PHI1

(

double

rho

)

The \( \Phi_1(\rho) \) function from arXiv:0805.3911v2.

Parameters

[in]

rho

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\(\Phi_1(\rho) \)

Definition at line 1437 of file bsgamma.cpp.

{
    double y = (1. - sqrt(1. - 4.*rho)) / (1. + sqrt(1. - 4.*rho));
    
    if (rho < 1./4.) 
        return log(y)*log(y) - M_PI*M_PI;
    else 
        return - acos( 1. - 1./(2. * rho) ) * acos( 1. - 1./(2. * rho) );
}

Y2NV_PHI2()

double Bsgamma::Y2NV_PHI2

(

double

rho

)

The \( \Phi_2(\rho) \) function from arXiv:0805.3911v2.

Parameters

[in]

rho

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\(\Phi_2(\rho) \)

Definition at line 1448 of file bsgamma.cpp.

{
    double y = (1. - sqrt(1. - 4.*rho)) / (1. + sqrt(1. - 4.*rho));
    
    if (rho < 1./4.) 
        return log(y) * sqrt(1. - 4.*rho);
    else 
        return - acos( 1. - 1./(2. * rho) ) * sqrt(4.*rho - 1.);
}

Y2NV_PHI3()

double Bsgamma::Y2NV_PHI3

(

double

rho

)

The \( \Phi_3(\rho) \) function from arXiv:0805.3911v2.

Parameters

[in]

rho

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\(\Phi_3(\rho) \)

Definition at line 1459 of file bsgamma.cpp.

{
    double y = (1. - sqrt(1. - 4.*rho)) / (1. + sqrt(1. - 4.*rho));
    
    if (rho < 1./4.) 
        return ( gsl_sf_dilog(-y) + log(y)*log(y)/4. + M_PI*M_PI/12. ) * sqrt(1. - 4.*rho);
    else 
        return - gsl_sf_clausen(2. * asin( 1./(2. * sqrt(rho)) )) * sqrt(4.*rho - 1.);
}

Y2NV_PHI4()

double Bsgamma::Y2NV_PHI4

(

double

rho

)

The \( \Phi_4(\rho) \) function from arXiv:0805.3911v2.

Parameters

[in]

rho

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\(\Phi_4(\rho) \)

Definition at line 1470 of file bsgamma.cpp.

{
    double y = (1. - sqrt(1. - 4.*rho)) / (1. + sqrt(1. - 4.*rho));
    Polylogarithms Poly;
    ClausenFunctions Clausen;
    
    if (rho < 1./4.) 
        return Poly.Li3(- y) + log(y)*log(y)*log(y)/12. + log(y)*M_PI*M_PI/12.;
    else 
        return Clausen.Cl3(2. * asin( 1./(2. * sqrt(rho)) ));
}

zdz_f_NLO()

double Bsgamma::zdz_f_NLO	(	double	z,
		double	E0
	)

The \( z \frac{d}{dz}f_{\rm NLO}(z,\delta) \) function from arXiv:1503.01791.

Parameters

[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)
[in]	E0	energy cutoff

Returns

\( z \frac{d}{dz}f_{\rm NLO}(z,\delta)) \)

Definition at line 1534 of file bsgamma.cpp.

{
    double d = delta(E0);
    double sqrt1d = sqrt(1. - d);
    double sqrt4z = sqrt(1. - 4. * z);
    double sqrt1d4z = sqrt(1. - d - 4. * z);
    double sqrtz = sqrt(z);
    double sqrt1ovz = sqrt(1./z);
    double sqrt4m1ovz = sqrt(-4. + 1./z);
    double SumSqrt = sqrt1d + sqrt1d4z;
    double ProdSqrt = sqrt1d * sqrt1d4z;
    double ProdSqrtz = sqrtz * sqrt1d4z;
    double LogSumSqrt = log(SumSqrt/(2. * sqrtz));
    double LogSqrt4z = log((1. + sqrt4z)/(2. * sqrtz));
    double LogSqrtov = log((sqrt4m1ovz + sqrt1ovz)/2.);
    
    double z2=z*z;
    double z3=z2*z;
    double z4=z3*z;
    double z5=z4*z;
    double Lz = log(z);
    
    double Pi2 = M_PI*M_PI;
    double zeta3 = gsl_sf_zeta_int(3);
    
    double zdz_f_NLO_E0;
    
    if (E0 == 0. ){
        zdz_f_NLO_E0 = 2./27. * (3. * (-7. + 2. * M_PI*M_PI) 
                + 2. * (36. - 24. * M_PI*M_PI) * z 
                + 108. * M_PI*M_PI * z2 
                - ( 36. * (-pow(1./z,3./2.)/2. - 1./(2. * sqrt4m1ovz * z2)) 
                * sqrt4m1ovz * (-1. + 2. * z))/((sqrt4m1ovz + sqrt1ovz) * pow(1./z,3./2.)) 
                - (72. * sqrt4m1ovz * LogSqrtov)/pow(1./z,3./2.) 
                - (54. * sqrt4m1ovz * (-1. + 2. * z) * LogSqrtov)/sqrt1ovz 
                + (18. * sqrt1ovz * (-1. + 2. * z) * LogSqrtov)/sqrt4m1ovz 
                - (48. * (-pow(1./z,3./2.)/2. - 1./(2. * sqrt4m1ovz * z2))
                * z * (1. - 4. * z + 6. * z2) * LogSqrtov)/(sqrt4m1ovz + sqrt1ovz) 
                - 24. * z * (-4. + 12. * z) * LogSqrtov * LogSqrtov 
                - 24. * (1. - 4. * z + 6. * z2) * LogSqrtov * LogSqrtov);
    } else zdz_f_NLO_E0 = 2. * ((2. - d) * d * (-7. + 2. * Pi2) / 9. 
            + 8./9. * d * (3. - 2. * Pi2) * z 
            + (8. * d * (-SumSqrt/( 4. * pow(z,3./2.) ) - 1./ProdSqrtz) 
            * ProdSqrt * pow(z,3./2.))/(3. * SumSqrt) 
            + 4./3. * d * ProdSqrt * LogSumSqrt 
            - (8. * (1. - d) * d * z * LogSumSqrt)/(3. * ProdSqrt) 
            - (32. * d * (-SumSqrt/( 4. * pow(z,3./2.) ) - 1./ProdSqrtz)
            * (2. - d - 4. * z) * pow(z,3./2.) * LogSumSqrt)/(9. * SumSqrt) 
            - 8./9. * d * (2. - d - 4. * z) * LogSumSqrt * LogSumSqrt 
            + 32./9. * d * z * LogSumSqrt * LogSumSqrt 
            + 4./3. * (1. - 2. * z) * z * 
            ((2. * (-( (1. + sqrt4z)/(4. * pow(z,3./2.)) ) 
            - 1./(sqrt4z * sqrtz)) * sqrt4z * sqrtz)/(1. + sqrt4z) 
            - (2. * ( -(SumSqrt/(4. * pow(z,3./2.)) ) - 1./ProdSqrtz)
            * ProdSqrt * sqrtz)/(SumSqrt) - 2. * LogSqrt4z/sqrt4z 
            + 2. * (1. - d) * LogSumSqrt/ProdSqrt) 
            + 4./3. * (1. - 2. * z) * (sqrt4z * LogSqrt4z - ProdSqrt * LogSumSqrt) 
            - 8./3. * z * (sqrt4z * LogSqrt4z - ProdSqrt * LogSumSqrt) 
            - 8./9. * z * (1 - 4. * z + 6. * z2) * 
            (( 4. * (-( (1. + sqrt4z)/(4. * pow(z,3./2.)) ) 
            - 1./(sqrt4z * sqrtz)) * sqrtz * LogSqrt4z)/(1. + sqrt4z) 
            - (4. * (-SumSqrt/(4. * pow(z,3./2.)) - 1./ProdSqrtz) * sqrtz * LogSumSqrt)/SumSqrt) 
            - 8./9. * (LogSqrt4z*LogSqrt4z - LogSumSqrt*LogSumSqrt) 
            * ( z * (-4. + 12. * z)  + (1. - 4. * z + 6. * z2) )) ;
    
    return z * (zdz_f_NLO_E0
            
            - 16./9. * (-4. + Pi2/6. - Pi2 * sqrtz 
            - Lz - z2 * (19./18. - 4. * Lz) + z * (-2. - Lz) 
            + z3 * (137./30. + 4. * Lz) 
            + z4 * (887./84. + 10. * Lz) 
            + z5 * (16597./540. + 28. * Lz) 
            - 3. * z2 * (25./12. + Pi2/9. + 19. * Lz/18. - 2. * Lz * Lz) 
            + 2. * z * (1./2. + Pi2 - 2. * Lz - Lz * Lz/2) 
            + 4. * z3 * (-1376./225. + 2. * Pi2/3 + 137. * Lz/30. + 2. * Lz * Lz) 
            + 5. * z4 * (-131317./11760. + 5. * Pi2/3. + 887. * Lz/84. + 5. * Lz * Lz) 
            + 6. * z5 * (-2807617./97200. + 14. * Pi2/3. + 16597. * Lz/540. + 14. * Lz * Lz)) 
   
            + 32./9. * (5./2. - Pi2/3. + (5./2. - 3. * Pi2/4.) * Lz 
            + Lz * Lz/4 + Lz * Lz * Lz/12. 
            + z5 * (-3303./800. - 63. * Lz/10.) 
            + z4 * (-185./144. - 35. * Lz/12.) 
            + z3 * (-1./72. - 5. * Lz/3.) 
            + z2 * (2. - 3. * Lz/2.) 
            + 6. * z5 * (67801./8000. - 21. * Pi2/20. 
            - 3303. * Lz/800. - 63. * Lz * Lz/20.) 
            + 5. * z4 * (35101./8640. - 35. * Pi2/72. 
            - 185. * Lz/144. - 35. * Lz * Lz/24.) 
            + 4. * z3 * (457./216. - 5. * Pi2/18. - Lz/72. - 5. * Lz * Lz/6.) 
            + 3. * z2 * (-7./6. - Pi2/4. + 2. * Lz - 3. * Lz * Lz/4.) 
            + z * (-Pi2/2. - Lz/2. + Lz * Lz/4.) 
            + 5./2. - 3. * Pi2/4. + Lz/2. + Lz * Lz/4. 
            + 2. * z * (7./4. + 2. * Pi2/3. - Pi2 * Lz/2. - Lz * Lz/4. 
            + Lz * Lz * Lz/12.) - 3. * zeta3));
}

zdz_Phi22_1()

double Bsgamma::zdz_Phi22_1

(

double

E0

)

Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines.

Parameters

[in]

E0

energy cutoff

Returns

\( 4z \frac{d\Phi_{22}^{(1)}}{d\,z} \)

Definition at line 1720 of file bsgamma.cpp.

{
    return 64./27. * ( Int_cc1(E0) - Int_cc(E0));
}

zdz_Phi28_1()

double Bsgamma::zdz_Phi28_1	(	double	z,
		double	E0
	)

Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines.

Parameters

[in]

E0

energy cutoff

Returns

\( 2z \frac{d\Phi_{28}^{(1)}}{d\,z} \)

Definition at line 1739 of file bsgamma.cpp.

{
    double d = delta(E0);
    double Sq = sqrt( (1. - d) * (1. - d - 4.*z) );
    double Log1 = log( ( sqrt(1. - d) + sqrt(1. - d - 4.*z) ) / 2. / sqrt(z) );
    double Log2 = log( ( 1. + sqrt(1. - 4.*z) ) / 2. / sqrt(z) );
    
    return 2./27. * z * (d*d * (-7. - 8. * (-1. + Log1) * Log1 + 2. * M_PI*M_PI) 
            - 20. * Log2 * sqrt(1. - 4. * z) + 72. * Log2 * sqrt(1. - 4. * z) * z 
            + (48. * Log1 * Sq * z * z) / (-1. + d + 4. * z) 
            + (8. * z * ( -(3. + 4. * Log1) * Sq*Sq + 2. * (3. + 8. * Log1) * Sq * z 
            - 24. * Log1 * z * z )) / (-1. + d - Sq + 4. * z) 
            - 2. * d * (-7. - 3. * Sq + Log1 * (8. + 6. * Sq) + M_PI*M_PI * (2. - 8. * z) 
            + 12. * z + 8. * Log1*Log1 * (-1. + 4. * z)) 
            + 2. * (-3. * (-1. + Sq + 2. * (1. + Sq) * z) 
            + Log1 * (4. + Sq * (6. - 52. * z) + 24. * z * z) 
            + 4. * ( Log2 * Log2 - Log1 * Log1) * (1. + 2. * z * (-4. + 9. * z))));
}

zeta()

double Bsgamma::zeta

(

)

The squared ratio between \(m_c\) and \(m_b^{\rm kin}\), \( z \).

Returns

\( z \)

Definition at line 227 of file bsgamma.cpp.

{
    return Mc*Mc/Mb_kin/Mb_kin;
}

Member Data Documentation

ale

double Bsgamma::ale

private

alpha electromagnetic

Definition at line 1746 of file bsgamma.h.

AleatMztilde

double Bsgamma::AleatMztilde

private

alpha electromagnetic at Mz divided by 4 pi

Definition at line 1747 of file bsgamma.h.

allcoeff

gslpp::vector<gslpp::complex>** Bsgamma::allcoeff

private

vector that contains the Wilson coeffients

Definition at line 1778 of file bsgamma.h.

allcoeffprime

gslpp::vector<gslpp::complex>** Bsgamma::allcoeffprime

private

vector that contains the primed Wilson coeffients

Definition at line 1779 of file bsgamma.h.

Alstilde

double Bsgamma::Alstilde

private

alpha strong divided by 4 pi

Definition at line 1749 of file bsgamma.h.

alsUps

double Bsgamma::alsUps

private

alpha strong Upsilon

Definition at line 1748 of file bsgamma.h.

avaINT

double Bsgamma::avaINT

private

integral variable

Definition at line 1809 of file bsgamma.h.

BLNPcorr

double Bsgamma::BLNPcorr

private

non perturbative correction from [Benzke:2010js]

Definition at line 1771 of file bsgamma.h.

BRsl

double Bsgamma::BRsl

private

BR of the semileptonic decay \(B \to X_c e \nu\)

Definition at line 1758 of file bsgamma.h.

C

double Bsgamma::C

private

The semileptonic phase space ratio

Definition at line 1759 of file bsgamma.h.

C1_0

gslpp::complex Bsgamma::C1_0

private

LO term of the Wilson coeffients \(C_1\)

Definition at line 1781 of file bsgamma.h.

C1_1

gslpp::complex Bsgamma::C1_1

private

NLO term of the Wilson coeffients \(C_1\)

Definition at line 1790 of file bsgamma.h.

C2_0

gslpp::complex Bsgamma::C2_0

private

LO term of the Wilson coeffients \(C_2\)

Definition at line 1782 of file bsgamma.h.

C2_1

gslpp::complex Bsgamma::C2_1

private

NLO term of the Wilson coeffients \(C_2\)

Definition at line 1791 of file bsgamma.h.

C3_0

gslpp::complex Bsgamma::C3_0

private

LO term of the Wilson coeffients \(C_3\)

Definition at line 1783 of file bsgamma.h.

C3_1

gslpp::complex Bsgamma::C3_1

private

NLO term of the Wilson coeffients \(C_3\)

Definition at line 1792 of file bsgamma.h.

C4_0

gslpp::complex Bsgamma::C4_0

private

LO term of the Wilson coeffients \(C_4\)

Definition at line 1784 of file bsgamma.h.

C4_1

gslpp::complex Bsgamma::C4_1

private

NLO term of the Wilson coeffients \(C_4\)

Definition at line 1793 of file bsgamma.h.

C5_0

gslpp::complex Bsgamma::C5_0

private

LO term of the Wilson coeffients \(C_5\)

Definition at line 1785 of file bsgamma.h.

C5_1

gslpp::complex Bsgamma::C5_1

private

NLO term of the Wilson coeffients \(C_5\)

Definition at line 1794 of file bsgamma.h.

C6_0

gslpp::complex Bsgamma::C6_0

private

LO term of the Wilson coeffients \(C_6\)

Definition at line 1786 of file bsgamma.h.

C6_1

gslpp::complex Bsgamma::C6_1

private

NLO term of the Wilson coeffients \(C_6\)

Definition at line 1795 of file bsgamma.h.

C7_0

gslpp::complex Bsgamma::C7_0

private

LO term of the Wilson coeffients \(C_7\)

Definition at line 1787 of file bsgamma.h.

C7_1

gslpp::complex Bsgamma::C7_1

private

NLO term of the Wilson coeffients \(C_7\)

Definition at line 1796 of file bsgamma.h.

C7_1ew

gslpp::complex Bsgamma::C7_1ew

private

ew-NLO term of the Wilson coeffients \(C_7\)

Definition at line 1799 of file bsgamma.h.

C7_2

gslpp::complex Bsgamma::C7_2

private

NNLO term of the Wilson coeffients \(C_7\)

Definition at line 1801 of file bsgamma.h.

C7p_0

gslpp::complex Bsgamma::C7p_0

private

LO term of the Wilson coeffients \(C'_7\)

Definition at line 1803 of file bsgamma.h.

C7p_1

gslpp::complex Bsgamma::C7p_1

private

NLO term of the Wilson coeffients \(C_7\)

Definition at line 1804 of file bsgamma.h.

C8_0

gslpp::complex Bsgamma::C8_0

private

LO term of the Wilson coeffients \(C_8\)

Definition at line 1788 of file bsgamma.h.

C8_1

gslpp::complex Bsgamma::C8_1

private

NLO term of the Wilson coeffients \(C_8\)

Definition at line 1797 of file bsgamma.h.

C_7_NP

gslpp::complex Bsgamma::C_7_NP

private

Definition at line 1806 of file bsgamma.h.

C_7p_NP

gslpp::complex Bsgamma::C_7p_NP

private

Definition at line 1807 of file bsgamma.h.

CacheIntb1

double Bsgamma::CacheIntb1

private

Cache variable

Definition at line 1831 of file bsgamma.h.

CacheIntb2

double Bsgamma::CacheIntb2

private

Cache variable

Definition at line 1832 of file bsgamma.h.

CacheIntb3

double Bsgamma::CacheIntb3

private

Cache variable

Definition at line 1833 of file bsgamma.h.

CacheIntb4

double Bsgamma::CacheIntb4

private

Cache variable

Definition at line 1834 of file bsgamma.h.

CacheIntbb1

double Bsgamma::CacheIntbb1

private

Cache variable

Definition at line 1835 of file bsgamma.h.

CacheIntbb2

double Bsgamma::CacheIntbb2

private

Cache variable

Definition at line 1836 of file bsgamma.h.

CacheIntbb4

double Bsgamma::CacheIntbb4

private

Cache variable

Definition at line 1837 of file bsgamma.h.

CacheIntbc1

gslpp::complex Bsgamma::CacheIntbc1

private

Cache variable

Definition at line 1838 of file bsgamma.h.

CacheIntbc2

gslpp::complex Bsgamma::CacheIntbc2

private

Cache variable

Definition at line 1839 of file bsgamma.h.

CacheIntc1

gslpp::complex Bsgamma::CacheIntc1

private

Cache variable

Definition at line 1840 of file bsgamma.h.

CacheIntc2

gslpp::complex Bsgamma::CacheIntc2

private

Cache variable

Definition at line 1841 of file bsgamma.h.

CacheIntc3

gslpp::complex Bsgamma::CacheIntc3

private

Cache variable

Definition at line 1842 of file bsgamma.h.

CacheIntcc

double Bsgamma::CacheIntcc

private

Cache variable

Definition at line 1843 of file bsgamma.h.

CacheIntcc1

double Bsgamma::CacheIntcc1

private

Cache variable

Definition at line 1844 of file bsgamma.h.

CacheIntcc1p1

double Bsgamma::CacheIntcc1p1

private

Cache variable

Definition at line 1845 of file bsgamma.h.

CacheIntPhi772r

double Bsgamma::CacheIntPhi772r

private

Cache variable

Definition at line 1846 of file bsgamma.h.

CKMratio

double Bsgamma::CKMratio

private

Vckm factor

Definition at line 1760 of file bsgamma.h.

CKMu

gslpp::complex Bsgamma::CKMu

private

Vckm factor

Definition at line 1764 of file bsgamma.h.

CKMusq

double Bsgamma::CKMusq

private

Vckm factor

Definition at line 1765 of file bsgamma.h.

EWflag

bool Bsgamma::EWflag

private

Flag to include EW NLO corrections (currently partialy hard-coded)

Definition at line 1742 of file bsgamma.h.

FOUR_BODY

bool Bsgamma::FOUR_BODY

private

Flag to include NLO 4_body corrections (currently partialy hard-coded)

Definition at line 1743 of file bsgamma.h.

ig

ROOT::Math::GSLIntegrator Bsgamma::ig

private

GSL integrator

Definition at line 1810 of file bsgamma.h.

Intb1Cached

unsigned int Bsgamma::Intb1Cached

private

Cache variable

Definition at line 1813 of file bsgamma.h.

Intb2Cached

unsigned int Bsgamma::Intb2Cached

private

Cache variable

Definition at line 1814 of file bsgamma.h.

Intb3Cached

unsigned int Bsgamma::Intb3Cached

private

Cache variable

Definition at line 1815 of file bsgamma.h.

Intb4Cached

unsigned int Bsgamma::Intb4Cached

private

Cache variable

Definition at line 1816 of file bsgamma.h.

Intb_cache

double Bsgamma::Intb_cache

private

Cache variable

Definition at line 1851 of file bsgamma.h.

Intb_updated

unsigned int Bsgamma::Intb_updated

private

Cache variable

Definition at line 1848 of file bsgamma.h.

Intbb1Cached

unsigned int Bsgamma::Intbb1Cached

private

Cache variable

Definition at line 1817 of file bsgamma.h.

Intbb2Cached

unsigned int Bsgamma::Intbb2Cached

private

Cache variable

Definition at line 1818 of file bsgamma.h.

Intbb4Cached

unsigned int Bsgamma::Intbb4Cached

private

Cache variable

Definition at line 1819 of file bsgamma.h.

Intbc1Cached

unsigned int Bsgamma::Intbc1Cached

private

Cache variable

Definition at line 1820 of file bsgamma.h.

Intbc2Cached

unsigned int Bsgamma::Intbc2Cached

private

Cache variable

Definition at line 1821 of file bsgamma.h.

Intbc_cache

gslpp::vector<double> Bsgamma::Intbc_cache

private

Cache variable

Definition at line 1852 of file bsgamma.h.

Intbc_updated

unsigned int Bsgamma::Intbc_updated

private

Cache variable

Definition at line 1849 of file bsgamma.h.

Intc1Cached

unsigned int Bsgamma::Intc1Cached

private

Cache variable

Definition at line 1822 of file bsgamma.h.

Intc1imCached

unsigned int Bsgamma::Intc1imCached

private

Cache variable

Definition at line 1823 of file bsgamma.h.

Intc2Cached

unsigned int Bsgamma::Intc2Cached

private

Cache variable

Definition at line 1824 of file bsgamma.h.

Intc3Cached

unsigned int Bsgamma::Intc3Cached

private

Cache variable

Definition at line 1825 of file bsgamma.h.

Intcc1Cached

unsigned int Bsgamma::Intcc1Cached

private

Cache variable

Definition at line 1827 of file bsgamma.h.

Intcc1p1Cached

unsigned int Bsgamma::Intcc1p1Cached

private

Cache variable

Definition at line 1828 of file bsgamma.h.

IntccCached

unsigned int Bsgamma::IntccCached

private

Cache variable

Definition at line 1826 of file bsgamma.h.

IntPhi772rCached

unsigned int Bsgamma::IntPhi772rCached

private

Cache variable

Definition at line 1829 of file bsgamma.h.

Mb

double Bsgamma::Mb

private

b quark mass

Definition at line 1756 of file bsgamma.h.

Mb_kin

double Bsgamma::Mb_kin

private

b quark mass in the kinetic scheme

Definition at line 1753 of file bsgamma.h.

Mc

double Bsgamma::Mc

private

c quark mass

Definition at line 1754 of file bsgamma.h.

Ms

double Bsgamma::Ms

private

s quark mass

Definition at line 1755 of file bsgamma.h.

mu_b

double Bsgamma::mu_b

private

b quark mass scale

Definition at line 1750 of file bsgamma.h.

mu_c

double Bsgamma::mu_c

private

c quark mass scale

Definition at line 1751 of file bsgamma.h.

mu_G2

double Bsgamma::mu_G2

private

B meson expectation value of one of the relevant dim. 5 and 6 local operators

Definition at line 1768 of file bsgamma.h.

mu_kin

double Bsgamma::mu_kin

private

kinetic mass scale

Definition at line 1752 of file bsgamma.h.

mu_pi2

double Bsgamma::mu_pi2

private

B meson expectation value of one of the relevant dim. 5 and 6 local operators

Definition at line 1767 of file bsgamma.h.

Mz

double Bsgamma::Mz

private

Z boson mass

Definition at line 1757 of file bsgamma.h.

obs

int Bsgamma::obs

private

observable type

Definition at line 1773 of file bsgamma.h.

overall

double Bsgamma::overall

private

overall BR factor

Definition at line 1766 of file bsgamma.h.

quark

QCD::quark Bsgamma::quark

private

Final quark type

Definition at line 1739 of file bsgamma.h.

rho_D3

double Bsgamma::rho_D3

private

B meson expectation value of one of the relevant dim. 5 and 6 local operators

Definition at line 1769 of file bsgamma.h.

rho_LS3

double Bsgamma::rho_LS3

private

B meson expectation value of one of the relevant dim. 5 and 6 local operators

Definition at line 1770 of file bsgamma.h.

SMEFT_NP_btos

bool Bsgamma::SMEFT_NP_btos = false

private

Definition at line 1744 of file bsgamma.h.

SUM

bool Bsgamma::SUM

private

Flag to choose whether the BR will be relative to a single quark (s or d) or their sum

Definition at line 1741 of file bsgamma.h.

V_cb

gslpp::complex Bsgamma::V_cb

private

Vckm factor

Definition at line 1762 of file bsgamma.h.

V_tb

gslpp::complex Bsgamma::V_tb

private

Vckm factor

Definition at line 1763 of file bsgamma.h.

V_ub

gslpp::complex Bsgamma::V_ub

private

Vckm factor

Definition at line 1761 of file bsgamma.h.

WET_NP_btos

bool Bsgamma::WET_NP_btos = false

private

Definition at line 1744 of file bsgamma.h.

wf

ROOT::Math::Functor1D Bsgamma::wf

private

GSL integrator function

Definition at line 1811 of file bsgamma.h.

---

The documentation for this class was generated from the following files:

• bsgamma.h
• bsgamma.cpp