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EWSMTwoLoopEW Class Reference
<br>

A class for \(O(\alpha^2)\) two-loop corrections to the EW precision observables. More...

#include <EWSMTwoLoopEW.h>

Detailed Description

A class for \(O(\alpha^2)\) two-loop corrections to the EW precision observables.

Author
HEPfit Collaboration
Copyright
GNU General Public License

This class handles two-loop EW contributions of \(O(\alpha^2)\) to the following quantities, which are relevant to the EW precision observables:

  • \(\Delta\alpha_{\mathrm{lept}}(M_Z^2)\)   (with DeltaAlpha_l()),
  • \(\Delta\alpha_{\mathrm{top}}(M_Z^2)\)   (with DeltaAlpha_t()),
  • \(\Delta\rho\)       (with DeltaRho()),
  • \(\Delta r_{\mathrm{rem}}\)   (with DeltaR_rem()),
  • \(\delta\rho_{\mathrm{rem}}^{f}\)   (with deltaRho_rem_l() and deltaRho_rem_q()),
  • \(\delta\kappa_{\mathrm{rem}}^{f}\)   (with deltaKappa_rem_l() and deltaKappa_rem_q()),

and the \(O(\alpha^2)\) corrections to \(\Delta\rho\) and to \(Zb\bar{b}\):

  • \(\rho^{(2)}\)       (with rho_2()),
  • \(\tau^{(2)}\)       (with tau_2()).

See also the description of EWSM class for their definitions. The \(O(\alpha^2)\) two-loop EW contributions to the vacuum polarization amplitudes of the gauge bosons were calculated in [Barbieri:1992nz], [Barbieri:1992dq], [Fleischer:1993ub], [Fleischer:1994cb], [Degrassi:1996mg], [Degrassi:1996ps] and [Degrassi:1999jd] with large- \(m_t\) expansion. In the current class, the \(O(\alpha^2(m_t^4/m_Z^4 + m_t^2/M_Z^2))\) corrections to \(\Delta\rho\), \(\Delta r_{\mathrm{rem}}\), \(\delta\rho_{\mathrm{rem}}^{f}\) and \(\delta\kappa_{\mathrm{rem}}^{f}\) and the \(O(\alpha^2 m_t^4/M_Z^4)\) corrections to \(Zb\bar{b}\), denoted by \(\rho^{(2)}\) and \(\tau^{(2)}\), are computed with the auxiliary functions defined as private members. In [Degrassi:1996mg], the former corrections were calculated in the MSbar scheme in order to undertake resummations correctly. In subsequent papers [Degrassi:1996ps] and [Degrassi:1999jd], the resultant two-loop contributions were rewritten in terms of parameters in the on-shell scheme by taking into account additional contributions, which correspond to the member functions with the word "Add".

Definition at line 57 of file EWSMTwoLoopEW.h.

Public Member Functions

double DeltaAlpha_l (const double s) const
 Leptonic contribution of \(O(\alpha^2)\) to the electromagnetic coupling \(\alpha\), denoted as \(\Delta\alpha_{\mathrm{lept}}^{\alpha^2}(s)\). More...
 
double DeltaAlpha_t (const double s) const
 Top-quark contribution of \(O(\alpha^2)\) to the electromagnetic coupling \(\alpha\), denoted as \(\Delta\alpha_{\mathrm{top}}^{\alpha^2}(s)\). More...
 
gslpp::complex deltaKappa_rem_f (const Particle f, const double Mw_i) const
 Remainder contribution of \(O(\alpha^2)\) to the effective couplings \(\kappa_Z^f\), denoted as \(\delta\kappa_{\mathrm{rem}}^{f,\, \alpha^2}\). More...
 
double DeltaR_rem (const double Mw_i) const
 Remainder contribution of \(O(\alpha^2)\) to \(\Delta r\), denoted as \(\Delta r_{\mathrm{rem}}^{\alpha^2}\). More...
 
double DeltaRho (const double Mw_i) const
 Leading two-loop contribution of \(O(\alpha^2)\) to \(\Delta\rho\), denoted as \(\Delta\rho^{\alpha^2}\). More...
 
gslpp::complex deltaRho_rem_f (const Particle f, const double Mw_i) const
 Remainder contribution of \(O(\alpha^2)\) to the effective couplings \(\rho_Z^f\), denoted as \(\delta\rho_{\mathrm{rem}}^{f,\, \alpha^2}\). More...
 
 EWSMTwoLoopEW (const EWSMcache &cache_i)
 Constructor. More...
 
double rho_2 () const
 The function \(\rho^{(2)}\). More...
 
double tau_2 () const
 The function \(\tau^{(2)}\). More...
 

Private Member Functions

double deltaEoverE2 () const
 The auxiliary function \((\delta e/e)^{(2)}\). More...
 
double DeltaEta2 (const double Mw_i) const
 The auxiliary function \(\Delta\hat{\eta}^{(2)}\). More...
 
gslpp::complex DeltaEta2Add_f (const Particle f, const double Mw_i) const
 The auxiliary function \(\Delta\bar{\eta}_{\rm add}^{(2)}\) for \(Z\to f\bar{f}\). More...
 
gslpp::complex DeltaEta2Add_tmp (const double I3f, const double Qf, const double Mw_i) const
 The auxiliary function \(\Delta\bar{\eta}_{\rm add}^{(2)}\). More...
 
gslpp::complex DeltaEtaf1 (const double I3f, const double Qf, const double Mw_i) const
 The auxiliary function \(\Delta\bar{\eta}^{(1)}_f\). More...
 
double DeltaKappa2 (const double Mw_i) const
 The auxiliary function \(\Delta\hat{\kappa}^{(2)}\). More...
 
gslpp::complex DeltaKappa2Add_f (const Particle f, const double Mw_i) const
 The auxiliary function \(\Delta\bar{\kappa}_{\rm add}^{(2)}\) for \(Z\to f\bar{f}\). More...
 
gslpp::complex DeltaKappa2Add_tmp (const double I3f, const double Qf, const double Mw_i) const
 The auxiliary function \(\Delta\bar{\kappa}_{\rm add}^{(2)}\). More...
 
double DeltaRho2 (const double Mw_i) const
 The auxiliary function \(\Delta\hat{\rho}^{(2)}\). More...
 
double DeltaRho2Add (const double Mw_i) const
 The auxiliary function \(\Delta\bar{\rho}_{\mathrm{add}}^{(2)}\). More...
 
double DeltaRw2 (const double Mw_i) const
 The auxiliary function \(\Delta \hat{r}_W^{(2)}\). More...
 
double f0 (const double a) const
 The auxiliary function \(f(a,0)\). More...
 
double f1 (const double a) const
 The auxiliary function \(f(a,1)\). More...
 
double f2Add (const double Mw_i) const
 The auxiliary function \(\bar{f}_{\rm add}^{(2)}\). More...
 
gslpp::complex FV (const double x) const
 The auxiliary function \(f(x)\). More...
 
double g (const double a) const
 The auxiliary function \(g(a)\). More...
 
gslpp::complex GV (const double x) const
 The auxiliary function \(g(x)\). More...
 
double Lambda (const double x) const
 The auxiliary function \(\Lambda(x)\). More...
 
double phi (const double x) const
 The auxiliary function \(\phi(x)\). More...
 
gslpp::complex Vadd (const double I3f, const double Qf, const double Mw_i) const
 The auxiliary function \(V_{\rm add}\). More...
 
gslpp::complex Vfi (const double I3f, const double Qf, const double q2, const double Mw_i) const
 The auxiliary function \({\cal V}_{fi}(q^2)\). More...
 

Private Attributes

const EWSMcache & cache
 A reference to an object of type EWSMcache. More...
 
const EWSMOneLoopEW myOneLoopEW
 An object of type EWSMOneLoopEW. More...
 

Constructor & Destructor Documentation

◆ EWSMTwoLoopEW()

EWSMTwoLoopEW::EWSMTwoLoopEW ( const EWSMcache &  cache_i)

Constructor.

Parameters
[in]cache_ia reference to an object of type EWSMcache

Definition at line 15 of file EWSMTwoLoopEW.cpp.

16: cache(cache_i), myOneLoopEW(cache_i)
17{
18}
EWSMTwoLoopEW::myOneLoopEW
const EWSMOneLoopEW myOneLoopEW
An object of type EWSMOneLoopEW.
Definition: EWSMTwoLoopEW.h:208
EWSMTwoLoopEW::cache
const EWSMcache & cache
A reference to an object of type EWSMcache.
Definition: EWSMTwoLoopEW.h:207

Member Function Documentation

◆ DeltaAlpha_l()

double EWSMTwoLoopEW::DeltaAlpha_l ( const double  s) const

Leptonic contribution of \(O(\alpha^2)\) to the electromagnetic coupling \(\alpha\), denoted as \(\Delta\alpha_{\mathrm{lept}}^{\alpha^2}(s)\).

The expressions used here can be found in [Steinhauser:1998rq].

Parameters
[in]sinvariant mass squared
Returns
\(\Delta\alpha_{\mathrm{lept}}^{\alpha^2}(s)\)
Attention
This function is valid in the limit of \(s\gg m_l^2\).

Definition at line 23 of file EWSMTwoLoopEW.cpp.

24{
25 double xl[3] = {s / cache.mf(cache.getSM().getLeptons(StandardModel::ELECTRON)) / cache.mf(cache.getSM().getLeptons(StandardModel::ELECTRON)),
26 s / cache.mf(cache.getSM().getLeptons(StandardModel::MU)) / cache.mf(cache.getSM().getLeptons(StandardModel::MU)),
27 s / cache.mf(cache.getSM().getLeptons(StandardModel::TAU)) / cache.mf(cache.getSM().getLeptons(StandardModel::TAU))};
28 double log_l[3];
29 if (s == cache.getSM().getMz() * cache.getSM().getMz()) {
30 log_l[0] = 2.0 * cache.logMZtoME();
31 log_l[1] = 2.0 * cache.logMZtoMMU();
32 log_l[2] = 2.0 * cache.logMZtoMTAU();
33 } else {
34 log_l[0] = log(xl[0]);
35 log_l[1] = log(xl[1]);
36 log_l[2] = log(xl[2]);
37 }
38
39 double twoLoop[3];
40 for (int i = 0; i < 3; i++) {
41 twoLoop[i] = -5.0 / 24.0 + cache.getZeta3() + log_l[i] / 4.0
42 + 3.0 / xl[i] * log_l[i];
43 }
44
45 return ( pow(cache.getSM().getAle() / M_PI, 2.0)
46 *(twoLoop[0] + twoLoop[1] + twoLoop[2]));
47}
EWSMcache::logMZtoMTAU
double logMZtoMTAU() const
A cache method.
Definition: EWSMcache.cpp:106
EWSMcache::logMZtoME
double logMZtoME() const
A cache method.
Definition: EWSMcache.cpp:78
EWSMcache::logMZtoMMU
double logMZtoMMU() const
A cache method.
Definition: EWSMcache.cpp:92
EWSMcache::getZeta3
double getZeta3() const
A get method to access the value of the zeta function .
Definition: EWSMcache.h:146
EWSMcache::mf
double mf(const Particle f, const double mu=0.0, const orders order=FULLNNLO) const
The mass of an SM fermion.
Definition: EWSMcache.cpp:49
EWSMcache::getSM
const StandardModel & getSM() const
Definition: EWSMcache.h:56
QCD::MU
@ MU
Definition: QCD.h:314
QCD::ELECTRON
@ ELECTRON
Definition: QCD.h:312
QCD::TAU
@ TAU
Definition: QCD.h:316
StandardModel::getLeptons
const Particle & getLeptons(const QCD::lepton p) const
A get method to retrieve the member object of a lepton.
Definition: StandardModel.h:744
StandardModel::getMz
const double getMz() const
A get method to access the mass of the boson .
Definition: StandardModel.h:753
StandardModel::getAle
const double getAle() const
A get method to retrieve the fine-structure constant .
Definition: StandardModel.h:789
s
Test Observable.

◆ DeltaAlpha_t()

double EWSMTwoLoopEW::DeltaAlpha_t ( const double  s) const

Top-quark contribution of \(O(\alpha^2)\) to the electromagnetic coupling \(\alpha\), denoted as \(\Delta\alpha_{\mathrm{top}}^{\alpha^2}(s)\).

This contribution is not implemented, since it is tiny and negligible.

Parameters
[in]sinvariant mass squared
Returns
\(\Delta\alpha_{\mathrm{top}}^{\alpha^2}(s)=0\)

Definition at line 49 of file EWSMTwoLoopEW.cpp.

50{
51 return (0.0);
52}

◆ deltaEoverE2()

double EWSMTwoLoopEW::deltaEoverE2 ( ) const
private

The auxiliary function \((\delta e/e)^{(2)}\).

See [Degrassi:1999jd].

Returns
\(\displaystyle\bigg(\frac{\delta e}{e}\bigg)^{(2)}\)

Definition at line 345 of file EWSMTwoLoopEW.cpp.

346{
347 double Mt = cache.getSM().getMtpole(), Mt2 = Mt*Mt;
348 double mh = cache.getSM().getMHl(), mh2 = mh*mh;
349 double ht = mh2 / Mt2;
350 double ht2 = ht*ht, ht3 = ht2*ht;
351 double mu = Mt; // renormalization scale
352
353 double dEoE2;
354 if (mh < 0.3 * Mt) {
355 dEoE2 = 61.0 / 72.0 - 16.0 * sqrt(ht) * M_PI / 27.0 - 13.0 / 18.0 * log(Mt2 / mu / mu);
356 } else {
357 dEoE2 = (231.0 - 32.0 * ht) / 216.0 - 2.0 / 27.0 * (4.0 - ht) * sqrt(ht) * g(ht)
358 + 2.0 * (6.0 + 27.0 * ht - 10.0 * ht2 + ht3) / 27.0 / (ht - 4.0) * log(ht)
359 - 13.0 / 18.0 * log(Mt2 / mu / mu)
360 - 4.0 * (ht - 1.0) / 9.0 / (ht - 4.0) / ht * phi(ht / 4.0);
361 }
362 return dEoE2;
363}
EWSMTwoLoopEW::g
double g(const double a) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:167
EWSMTwoLoopEW::phi
double phi(const double x) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:594
QCD::getMtpole
const double getMtpole() const
A get method to access the pole mass of the top quark.
Definition: QCD.h:600
StandardModel::getMHl
virtual const double getMHl() const
A get method to retrieve the Higgs mass .
Definition: StandardModel.h:809

◆ DeltaEta2()

double EWSMTwoLoopEW::DeltaEta2 ( const double  Mw_i) const
private

The auxiliary function \(\Delta\hat{\eta}^{(2)}\).

See [Degrassi:1999jd].

Parameters
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\hat{\eta}^{(2)}\)

Definition at line 383 of file EWSMTwoLoopEW.cpp.

384{
385 double Mz = cache.getSM().getMz(), Mz2 = Mz*Mz;
386 double Mw = Mw_i, Mw2 = Mw*Mw;
387 double cW2 = cache.getSM().cW2(Mw);
388 double cW4 = cW2*cW2, cW6 = cW4*cW2;
389 double Mt = cache.getSM().getMtpole(), Mt2 = Mt*Mt;
390 double mh = cache.getSM().getMHl(), mh2 = mh*mh;
391 double zt = Mz2 / Mt2;
392 double zt2 = zt*zt, zt3 = zt2*zt;
393 double ht = mh2 / Mt2;
394 double ht2 = ht*ht, ht3 = ht2*ht, ht4 = ht3*ht, ht5 = ht4*ht;
395 double mu = Mt; // renormalization scale
396
397 double dEta2;
398 if (mh < 0.57 * Mt) {
399 double B0_Mt2_Mz2_Mw2_Mw2 = cache.getPV().B0(Mt2, Mz2, Mw2, Mw2).real();
400 double B0_Mt2_Mz2_mh2_Mz2 = cache.getPV().B0(Mt2, Mz2, mh2, Mz2).real();
401 dEta2 = (ht3 - 6.0 * ht2 * zt + 11.0 * ht * zt2) / 9.0 / cW2 / (ht - 4.0 * zt) / zt2
402 + (49.0 - 289.0 * cW2 - 349.0 * cW4 + 292.0 * cW6) / 216.0 / cW2 / (1.0 - 4.0 * cW2)
403 + (1.0 + 18.0 * cW2 - 16.0 * cW4) / 12.0 / (1.0 - 4.0 * cW2) * log(cW2)
404 - (17.0 - 40.0 * cW2 + 32.0 * cW4) / 54.0 / cW2 * (sqrt(ht) * M_PI - 2.0)
405 + (11.0 * ht2 * zt - 2.0 * ht3 - 24.0 * ht * zt2 + 24.0 * zt3)
406 / 18.0 / cW2 / (ht - 4.0 * zt) / zt2 * log(ht)
407 + (1.0 - 4.0 * cW2 + 44.0 * cW4 - 32.0 * cW6) / 24.0 / cW2 / (1.0 - 4.0 * cW2)
408 * B0_Mt2_Mz2_Mw2_Mw2
409 + (13.0 * ht2 * zt - 2.0 * ht3 - 32.0 * ht * zt2 + 36.0 * zt3)
410 / 18.0 / cW2 / (ht - 4.0 * zt) / zt2 * B0_Mt2_Mz2_mh2_Mz2
411 - (17.0 - 34.0 * cW2 + 26.0 * cW4) / 36.0 / cW2 * log(Mt2 / mu / mu)
412 + (ht * (2.0 * ht - 5.0 * zt) / 18.0 / cW2 / zt / (ht - 4.0 * zt)
413 + (10.0 - 39.0 * cW2 - 70.0 * cW4 + 48.0 * cW6) / 36.0 / cW2 / (4.0 * cW2 - 1.0))
414 * log(zt);
415 } else {
416 double B0_Mt2_Mz2_Mw2_Mw2 = cache.getPV().B0(Mt2, Mz2, Mw2, Mw2).real();
417 dEta2 = (-17.0 + 40.0 * cW2 - 32.0 * cW4) * ht / 216.0 / cW2
418 + 5.0 / 144.0 / cW2 / (ht - 4.0)
419 + (707.0 - 4720.0 * cW2 + 5900.0 * cW4 - 3696.0 * cW6) / 864.0 / cW2 / (1.0 - 4.0 * cW2)
420 + (10.0 / 27.0 - 17.0 / 108.0 / cW2 - 8.0 * cW2 / 27.0)*(1.0 - ht / 4.0) * sqrt(ht) * g(ht)
421 + (1.0 + 18.0 * cW2 - 16.0 * cW4) / 12.0 / (1.0 - 4.0 * cW2) * log(cW2)
422 + (4.0 - ht) / 12.0 / cW2 / ht * Lambda(ht)
423 + (2.0 - 7.0 * cW2 - 70.0 * cW4 + 48.0 * cW6) / 36.0 / cW2 / (4.0 * cW2 - 1.0) * log(zt)
424 + (1.0 - 4.0 * cW2 + 44.0 * cW4 - 32.0 * cW6) / 24.0 / cW2 / (1.0 - 4.0 * cW2) * B0_Mt2_Mz2_Mw2_Mw2
425 - (17.0 - 34.0 * cW2 + 26.0 * cW4) / 36.0 / cW2 * log(Mt2 / mu / mu)
426 + ((4.0 * cW2 - 5.0)*(6.0 + 27.0 * ht - 10.0 * ht2 + ht3) / 54.0 / (ht - 4.0)
427 - (1152.0 + 606.0 * ht + 1467.0 * ht2 - 1097.0 * ht3 + 238.0 * ht4 - 17.0 * ht5)
428 / 432.0 / cW2 / (ht - 4.0) / (ht - 4.0) / ht) * log(ht)
429 + ((5.0 - 4.0 * cW2)*(ht - 1.0) / 9.0 / (ht - 4.0) / ht
430 - (384.0 + 10.0 * ht - 238.0 * ht2 + 63.0 * ht3 - 3.0 * ht4)
431 / 144.0 / cW2 / (ht - 4.0) / (ht - 4.0) / ht2) * phi(ht / 4.0);
432 }
433 return dEta2;
434}
EWSMTwoLoopEW::Lambda
double Lambda(const double x) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:584
EWSMcache::getPV
const PVfunctions getPV() const
A get method to access the member reference to the object of type StandardModel passed to the constru...
Definition: EWSMcache.h:106
Mw
An observable class for the -boson mass.
Definition: Mw.h:22
PVfunctions::B0
gslpp::complex B0(const double mu2, const double p2, const double m02, const double m12) const
.
Definition: PVfunctions.cpp:41
StandardModel::cW2
virtual const double cW2(const double Mw_i) const
The square of the cosine of the weak mixing angle in the on-shell scheme, denoted as .
Definition: StandardModel/src/StandardModel.cpp:1076

◆ DeltaEta2Add_f()

gslpp::complex EWSMTwoLoopEW::DeltaEta2Add_f ( const Particle  f,
const double  Mw_i 
) const
private

The auxiliary function \(\Delta\bar{\eta}_{\rm add}^{(2)}\) for \(Z\to f\bar{f}\).

See [Degrassi:1999jd].

Parameters
[in]fa lepton or quark
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\bar{\eta}_{\rm add}^{(2)}\)

Definition at line 461 of file EWSMTwoLoopEW.cpp.

462{
463 double I3f = cache.I3_f(f);
464 double Qf = cache.Q_f(f);
465 return DeltaEta2Add_tmp(I3f, Qf, Mw_i);
466}
EWSMTwoLoopEW::DeltaEta2Add_tmp
gslpp::complex DeltaEta2Add_tmp(const double I3f, const double Qf, const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:436
EWSMcache::Q_f
double Q_f(const Particle f) const
The charge of an SM fermion .
Definition: EWSMcache.h:268
EWSMcache::I3_f
double I3_f(const Particle f) const
The isospin of an SM fermion .
Definition: EWSMcache.h:278

◆ DeltaEta2Add_tmp()

gslpp::complex EWSMTwoLoopEW::DeltaEta2Add_tmp ( const double  I3f,
const double  Qf,
const double  Mw_i 
) const
private

The auxiliary function \(\Delta\bar{\eta}_{\rm add}^{(2)}\).

This functions is used in DeltaEta2Add_l() and DeltaEta2Add_q(). See [Degrassi:1999jd].

Parameters
[in]I3fthe isospin of a final-state fermion
[in]Qfthe electric charge of a final-state fermion
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\bar{\eta}_{\rm add}^{(2)}\)

Definition at line 436 of file EWSMTwoLoopEW.cpp.

438{
439 double Mz = cache.getSM().getMz(), Mz2 = Mz*Mz;
440 double Mw = Mw_i, Mw2 = Mw*Mw;
441 double cW2 = cache.getSM().cW2(Mw);
442 double cW4 = cW2*cW2, cW6 = cW4*cW2;
443 double Mt = cache.getSM().getMtpole(), Mt2 = Mt*Mt;
444 double zt = Mz2 / Mt2;
445 double mu = Mt; // renormalization scale
446
447 double B0_Mt2_Mz2_Mw2_Mw2 = cache.getPV().B0(Mt2, Mz2, Mw2, Mw2).real();
448
449 gslpp::complex dEta2add = 16.0 * M_PI * M_PI * DeltaEtaf1(I3f, Qf, Mw_i) + Vadd(I3f, Qf, Mw_i)
450 - (197.0 - 1378.0 * cW2 + 1064.0 * cW4) / 27.0 / (1.0 - 4.0 * cW2)
451 - (1.0 + 16.0 * cW2 - 20.0 * cW4 + 48.0 * cW6) / 3.0 / (1.0 - 4.0 * cW2)
452 * B0_Mt2_Mz2_Mw2_Mw2
453 - 2.0 * cW2 * (1.0 + 26.0 * cW2 + 24.0 * cW4) / 3.0 / (1.0 - 4.0 * cW2)
454 * log(cW2)
455 + (41.0 / 3.0 - 46.0 * cW2 / 3.0) * log(Mt2 / mu / mu)
456 + 2.0 * (50.0 - 283.0 * cW2 + 242.0 * cW4 - 72.0 * cW6)
457 / 9.0 / (1.0 - 4.0 * cW2) * log(zt);
458 return dEta2add;
459}
EWSMTwoLoopEW::DeltaEtaf1
gslpp::complex DeltaEtaf1(const double I3f, const double Qf, const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:551
EWSMTwoLoopEW::Vadd
gslpp::complex Vadd(const double I3f, const double Qf, const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:536

◆ DeltaEtaf1()

gslpp::complex EWSMTwoLoopEW::DeltaEtaf1 ( const double  I3f,
const double  Qf,
const double  Mw_i 
) const
private

The auxiliary function \(\Delta\bar{\eta}^{(1)}_f\).

This functions is used in DeltaEta2Add_tmp(). See [Degrassi:1990ec] and [Degrassi:1999jd].

Parameters
[in]I3fthe isospin of a final-state fermion
[in]Qfthe electric charge of a final-state fermion
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\bar{\eta}^{(1)}_f\)

Definition at line 551 of file EWSMTwoLoopEW.cpp.

553{
554 double Mz = cache.getSM().getMz(), Mz2 = Mz*Mz;
555 double Mw = Mw_i;
556 double cW2 = cache.getSM().cW2(Mw);
557
558 gslpp::complex SigmaPrime_ZZ = myOneLoopEW.SigmabarPrime_ZZ_bos_Mz2(Mz, Mw)
559 + myOneLoopEW.SigmabarPrime_ZZ_fer_Mz2(Mz, Mw);
560
561 gslpp::complex dEtaf1 = 1.0 / 16.0 / M_PI / M_PI
562 * (-SigmaPrime_ZZ / cW2 - 4.0 * cW2 * log(cW2) + Vfi(I3f, Qf, Mz2, Mw));
563 return dEtaf1;
564}
EWSMOneLoopEW::SigmabarPrime_ZZ_bos_Mz2
gslpp::complex SigmabarPrime_ZZ_bos_Mz2(const double mu, const double Mw_i) const
The derivative of the bosonic contribution to the self-energy of the boson for in the Unitary gauge...
Definition: EWSMOneLoopEW.cpp:698
EWSMOneLoopEW::SigmabarPrime_ZZ_fer_Mz2
gslpp::complex SigmabarPrime_ZZ_fer_Mz2(const double mu, const double Mw_i) const
The derivative of the fermionic contribution to the self-energy of the boson for in the Unitary gau...
Definition: EWSMOneLoopEW.cpp:746
EWSMTwoLoopEW::Vfi
gslpp::complex Vfi(const double I3f, const double Qf, const double q2, const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:566

◆ DeltaKappa2()

double EWSMTwoLoopEW::DeltaKappa2 ( const double  Mw_i) const
private

The auxiliary function \(\Delta\hat{\kappa}^{(2)}\).

See [Degrassi:1999jd].

Parameters
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\hat{\kappa}^{(2)}\)

Definition at line 468 of file EWSMTwoLoopEW.cpp.

469{
470 double Mz = cache.getSM().getMz(), Mz2 = Mz*Mz;
471 double Mw = Mw_i, Mw2 = Mw*Mw;
472 double cW2 = cache.getSM().cW2(Mw), sW2 = cache.getSM().sW2(Mw);
473 double Mt = cache.getSM().getMtpole(), Mt2 = Mt*Mt;
474 double mh = cache.getSM().getMHl(), mh2 = mh*mh;
475 double zt = Mz2 / Mt2;
476 double ht = mh2 / Mt2;
477 double ht2 = ht*ht, ht3 = ht2*ht;
478 double mu = Mt; // renormalization scale
479
480 double B0_Mt2_Mz2_Mw2_Mw2 = cache.getPV().B0(Mt2, Mz2, Mw2, Mw2).real();
481
482 double dKappa2;
483 if (mh < 0.57 * Mt) {
484 dKappa2 = (-175.0 + 366.0 * sW2) / 432.0
485 + (3.0 / 8.0 - sW2 / 3.0) * B0_Mt2_Mz2_Mw2_Mw2 - cW2 / 6.0 * log(cW2)
486 - 2.0 * M_PI / 27.0 * sqrt(ht)*(8.0 * sW2 - 3.0)
487 - (1.0 / 4.0 + 2.0 / 9.0 * sW2) * log(Mt2 / mu / mu)
488 + (3.0 * sW2 - 2.0) / 18.0 * log(zt);
489 } else {
490 dKappa2 = (-211.0 + 24.0 * ht + 462.0 * sW2 - 64.0 * ht * sW2) / 432.0
491 + (3.0 / 8.0 - sW2 / 3.0) * B0_Mt2_Mz2_Mw2_Mw2
492 - cW2 / 6.0 * log(cW2)
493 + (ht - 4.0) * sqrt(ht)*(8.0 * sW2 - 3.0) * g(ht) / 108.0
494 - (6.0 + 27.0 * ht - 10.0 * ht2 + ht3)*(3.0 - 8.0 * sW2)
495 / 108.0 / (ht - 4.0) * log(ht)
496 - (1.0 / 4.0 + 2.0 / 9.0 * sW2) * log(Mt2 / mu / mu)
497 + (3.0 * sW2 - 2.0) / 18.0 * log(zt)
498 + (ht - 1.0)*(8.0 * sW2 - 3.0) / 18.0 / (4.0 - ht) / ht * phi(ht / 4.0);
499 }
500 return dKappa2;
501}
StandardModel::sW2
virtual const double sW2(const double Mw_i) const
The square of the sine of the weak mixing angle in the on-shell scheme, denoted as .
Definition: StandardModel/src/StandardModel.cpp:1087

◆ DeltaKappa2Add_f()

gslpp::complex EWSMTwoLoopEW::DeltaKappa2Add_f ( const Particle  f,
const double  Mw_i 
) const
private

The auxiliary function \(\Delta\bar{\kappa}_{\rm add}^{(2)}\) for \(Z\to f\bar{f}\).

See [Degrassi:1999jd].

Parameters
[in]fa lepton or quark
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\bar{\kappa}_{\rm add}^{(2)}\)

Definition at line 529 of file EWSMTwoLoopEW.cpp.

530{
531 double I3f = cache.I3_f(f);
532 double Qf = cache.Q_f(f);
533 return DeltaKappa2Add_tmp(I3f, Qf, Mw_i);
534}
EWSMTwoLoopEW::DeltaKappa2Add_tmp
gslpp::complex DeltaKappa2Add_tmp(const double I3f, const double Qf, const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:503

◆ DeltaKappa2Add_tmp()

gslpp::complex EWSMTwoLoopEW::DeltaKappa2Add_tmp ( const double  I3f,
const double  Qf,
const double  Mw_i 
) const
private

The auxiliary function \(\Delta\bar{\kappa}_{\rm add}^{(2)}\).

This functions is used in DeltaKappa2Add_l() and DeltaKappa2Add_q(). See [Degrassi:1999jd].

Parameters
[in]I3fthe isospin of a final-state fermion
[in]Qfthe electric charge of a final-state fermion
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\bar{\kappa}_{\rm add}^{(2)}\)

Definition at line 503 of file EWSMTwoLoopEW.cpp.

505{
506 double Mz = cache.getSM().getMz(), Mz2 = Mz*Mz;
507 double Mw = Mw_i;
508 double cW2 = cache.getSM().cW2(Mw);
509 double cW4 = cW2*cW2;
510 double Mt = cache.getSM().getMtpole(), Mt2 = Mt*Mt;
511 double zt = Mz2 / Mt2;
512 double mu = Mt; // renormalization scale
513
514 gslpp::complex i = gslpp::complex::i();
515
516 gslpp::complex dKappa2add = -238.0 * cW2 / 27.0 + 8.0 * cW4
517 - 2.0 * cW2 * sqrt(4.0 * cW2 - 1.0)*(3.0 + 4.0 * cW2)
518 * atan(1.0 / sqrt(4.0 * cW2 - 1.0))
519 - 16.0 / 9.0 * cW2 * log(zt)
520 + (1.0 - 12.0 * I3f * Qf + 8.0 * Qf * Qf - 8.0 * cW4 * Qf * Qf)
521 / 4.0 / cW2 * FV(1)
522 + 4.0 * cW2 * GV(1.0 / cW2) - 7.0 * cW2 * log(cW2)
523 - 17.0 / 3.0 * cW2 * log(mu * mu / Mz2)
524 + cW2 * (1.0 - 2.0 * Qf * I3f) * FV(1.0 / cW2)
525 - i * 80.0 / 9.0 * M_PI;
526 return dKappa2add;
527}
EWSMTwoLoopEW::FV
gslpp::complex FV(const double x) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:607
EWSMTwoLoopEW::GV
gslpp::complex GV(const double x) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:621

◆ deltaKappa_rem_f()

gslpp::complex EWSMTwoLoopEW::deltaKappa_rem_f ( const Particle  f,
const double  Mw_i 
) const

Remainder contribution of \(O(\alpha^2)\) to the effective couplings \(\kappa_Z^f\), denoted as \(\delta\kappa_{\mathrm{rem}}^{f,\, \alpha^2}\).

This function handles the \(O(\alpha^2)\) remainder contribution to \(\kappa_{Z}^{f}\) in the on-shell scheme, which was calculated in [Degrassi:1999jd] :

\[ \delta\kappa_{\rm rem}^{f,\, \alpha^2} = 3 (X_t^{\alpha})^2 \left[ 16\, {\it zt}\,c_W^2\, \Delta\hat{k}^{(2)} + 4\, {\it zt}\,c_W^2\, \Delta\bar{k}_{\rm add}^{(2)} \right], \]

where the definitions of the symbols can be read from the codes below.

Parameters
[in]fa lepton or quark
[in]Mw_ithe \(W\)-boson mass
Returns
\(\delta\kappa_{\mathrm{rem}}^{f,\, \alpha^2}\)

Definition at line 115 of file EWSMTwoLoopEW.cpp.

116{
117 if (f.is("TOP")) return ( gslpp::complex(0.0, 0.0, false));
118
119 gslpp::complex dKappa = gslpp::complex(0.0, 0.0, false);
120
121#ifdef EW_SUBLEADING_ALPHA2
122 /* O(\alpha^2 Mt^4/Mz^4 + \alpha^2 Mt^2/Mz^2) */
123 double Mz = cache.getSM().getMz();
124 double Mw = Mw_i;
125 double cW2 = cache.getSM().cW2(Mw);
126 double zt = Mz * Mz / cache.getSM().getMtpole() / cache.getSM().getMtpole();
127 dKappa += 3.0 * pow(cache.Xt_alpha(Mw), 2.0)
128 *(16.0 * zt * cW2 * DeltaKappa2(Mw) + 4.0 * zt * cW2 * DeltaKappa2Add_f(f, Mw));
129#endif
130
131 return dKappa;
132}
EWSMTwoLoopEW::DeltaKappa2
double DeltaKappa2(const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:468
EWSMTwoLoopEW::DeltaKappa2Add_f
gslpp::complex DeltaKappa2Add_f(const Particle f, const double Mw_i) const
The auxiliary function for .
Definition: EWSMTwoLoopEW.cpp:529
EWSMcache::Xt_alpha
double Xt_alpha(const double Mw_i) const
The quantity with the coupling .
Definition: EWSMcache.h:355
Particle::is
bool is(std::string name_i) const
Definition: Particle.cpp:23

◆ DeltaR_rem()

double EWSMTwoLoopEW::DeltaR_rem ( const double  Mw_i) const

Remainder contribution of \(O(\alpha^2)\) to \(\Delta r\), denoted as \(\Delta r_{\mathrm{rem}}^{\alpha^2}\).

This function handles the remainder two-loop EW contribution of \(O(\alpha^2(m_t^4/m_Z^4 + m_t^2/M_Z^2))\) to \(\Delta r\) in the on-shell scheme. The expression can be found in [Degrassi:1996mg], [Degrassi:1996ps] and [Degrassi:1999jd] :

\[ \Delta r_{\rm rem}^{\alpha^2} = 3\left(\frac{\alpha}{4\pi s_W^2}\right)^2 \frac{m_t^2}{M_W^2} \left[ \Delta \hat{r}_W^{(2)} + s_W^2 \bigg(\frac{\delta e}{e}\bigg)^{(2)} + \frac{1}{4}\, \bar{f}_{\rm add}^{(2)} \right], \]

where the definitions of the symbols can be read from the codes below.

Parameters
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta r_{\mathrm{rem}}^{\alpha^2}\)

Definition at line 81 of file EWSMTwoLoopEW.cpp.

82{
83 double DeltaRrem = 0.0;
84
85#ifdef EW_SUBLEADING_ALPHA2
86 /* O(\alpha^2 Mt^4/Mz^4 + \alpha^2 Mt^2/Mz^2) */
87 double Mw = Mw_i;
88 double sW2 = cache.getSM().sW2(Mw);
89 DeltaRrem += 3.0 * pow(cache.getSM().getAle() * cache.getSM().getMtpole() / 4.0 / M_PI / sW2 / Mw, 2.0)
90 *(DeltaRw2(Mw) + sW2 * deltaEoverE2() + f2Add(Mw) / 4.0);
91#endif
92
93 return DeltaRrem;
94}
EWSMTwoLoopEW::deltaEoverE2
double deltaEoverE2() const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:345
EWSMTwoLoopEW::f2Add
double f2Add(const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:365
EWSMTwoLoopEW::DeltaRw2
double DeltaRw2(const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:291

◆ DeltaRho()

double EWSMTwoLoopEW::DeltaRho ( const double  Mw_i) const

Leading two-loop contribution of \(O(\alpha^2)\) to \(\Delta\rho\), denoted as \(\Delta\rho^{\alpha^2}\).

This function handles the leading irreducible two-loop EW contribution of \(O(\alpha^2(m_t^4/m_Z^4 + m_t^2/M_Z^2))\) to \(\Delta\rho\) in the on-shell scheme. The expression can be found in [Degrassi:1996mg] and [Degrassi:1996ps] :

\[ \Delta\rho^{\alpha^2} = 3 (X_t^{\alpha})^2 \left( \Delta\hat{\rho}^{(2)} + 4\, {\it zt}\, c_W^2 \Delta\bar{\rho}_{\mathrm{add}}^{(2)} \right) - \left(\frac{\alpha}{4\pi}\right)^2 \frac{c_W^2}{s_W^2} \left[ \mathrm{Re}\Pi^{\mathrm{fer}}_{Z\gamma}(M_Z^2) \right]^2, \]

where the definitions of the symbols can be read from the codes below, and the last term originates from the \(Z\)- \(\gamma\) mixing (see, e.g., Chapter 6 of [Bardin:1999ak]).

Parameters
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\rho^{\alpha^2}\)

Definition at line 54 of file EWSMTwoLoopEW.cpp.

55{
56 double Mz = cache.getSM().getMz();
57 double Mw = Mw_i;
58 double sW2 = cache.getSM().sW2(Mw);
59 double cW2 = cache.getSM().cW2(Mw);
60
61 double DeltaRho = 0.0;
62
63#ifndef EW_SUBLEADING_ALPHA2
64 /* O(\alpha^2 Mt^4/Mz^4) */
65 DeltaRho += 3.0 * rho_2();
66 DeltaRho *= pow(cache.Xt_alpha(Mw), 2.0);
67#else
68 /* O(\alpha^2 Mt^4/Mz^4 + \alpha^2 Mt^2/Mz^2) */
69 double zt = Mz * Mz / cache.getSM().getMtpole() / cache.getSM().getMtpole();
70 DeltaRho += 3.0 * pow(cache.Xt_alpha(Mw), 2.0)
71 *(DeltaRho2(Mw) + 4.0 * zt * cW2 * DeltaRho2Add(Mw));
72#endif
73
74 /* add O(alpha^2) contribution from the Z-gamma mixing */
75 DeltaRho += -pow(cache.getSM().getAle() / 4.0 / M_PI, 2.0) * cW2 / sW2
76 * pow(myOneLoopEW.PibarZgamma_fer(Mz, Mz*Mz, Mw).real(), 2.0);
77
78 return DeltaRho;
79}
EWSMOneLoopEW::PibarZgamma_fer
gslpp::complex PibarZgamma_fer(const double mu, const double s, const double Mw_i) const
The fermionic contribution to the self-energy of the - mixing in the Unitary gauge,...
Definition: EWSMOneLoopEW.cpp:541
EWSMTwoLoopEW::DeltaRho2Add
double DeltaRho2Add(const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:267
EWSMTwoLoopEW::DeltaRho
double DeltaRho(const double Mw_i) const
Leading two-loop contribution of to , denoted as .
Definition: EWSMTwoLoopEW.cpp:54
EWSMTwoLoopEW::DeltaRho2
double DeltaRho2(const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:203
EWSMTwoLoopEW::rho_2
double rho_2() const
The function .
Definition: EWSMTwoLoopEW.cpp:137

◆ DeltaRho2()

double EWSMTwoLoopEW::DeltaRho2 ( const double  Mw_i) const
private

The auxiliary function \(\Delta\hat{\rho}^{(2)}\).

See [Degrassi:1996mg].

Parameters
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\hat{\rho}^{(2)}\)

Definition at line 203 of file EWSMTwoLoopEW.cpp.

204{
205 double Mt = cache.getSM().getMtpole();
206 double mh = cache.getSM().getMHl();
207 double ht = mh * mh / Mt / Mt;
208
209 double rho2;
210 if (mh < 3.8 * Mt) {
211 rho2 = -15.642 + 0.036382 * Mt + pow(ht, 1.0 / 4.0)*(2.301 - 0.01343 * Mt)
212 + sqrt(ht)*(0.01809 * Mt - 9.953) + ht * (5.687 - 0.01568 * Mt)
213 + pow(ht, 3.0 / 2.0)*(0.005369 * Mt - 1.647)
214 + ht * ht * (0.1852 - 0.000646 * Mt);
215 } else {
216 double Mz = cache.getSM().getMz();
217 double Mw = Mw_i;
218 double Mz2 = Mz*Mz, Mw2 = Mw*Mw, Mt2 = Mt*Mt;
219 double cW2 = cache.getSM().cW2(Mw), sW2 = cache.getSM().sW2(Mw);
220 double cW4 = cW2*cW2, cW6 = cW4*cW2;
221 double zt = Mz * Mz / Mt / Mt;
222 double ht2 = ht*ht, ht3 = ht2*ht, ht4 = ht3*ht, ht5 = ht4*ht, ht6 = ht5*ht;
223 double mu = Mt; // renormalization scale
224
225 double B0_Mt2_Mz2_Mw2_Mw2 = cache.getPV().B0(Mt2, Mz2, Mw2, Mw2).real();
226 double B0_Mt2_Mw2_Mw2_Mz2 = cache.getPV().B0(Mt2, Mw2, Mw2, Mz2).real();
227 double Li21mht = cache.getPolyLog().Li2(1.0 - ht).real();
228
229 return ( 25.0 - 4.0 * ht + (1.0 / 2.0 - 1.0 / ht) * M_PI * M_PI
230 + (ht - 4.0) * sqrt(ht) * g(ht) / 2.0
231 + (-6.0 - 6.0 * ht + ht2 / 2.0) * log(ht)
232 + (6.0 / ht - 15.0 + 12.0 * ht - 3.0 * ht2) * Li21mht
233 + 3.0 / 2.0 * (-10.0 + 6.0 * ht - ht2) * phi(ht / 4.0)
234 + zt * (1.0 / (54.0 * cW2 * (ht - 4.0) * ht)
235 *(-1776.0 * cW4
236 + (72.0 - 6250.0 * cW2 - 3056.0 * cW4 + 3696.0 * cW6) * ht
237 + (-18.0 + 1283.0 * cW2 + 1371.0 * cW4 - 1436.0 * cW6) * ht2
238 + (68.0 * cW2 - 124.0 * cW4 + 128.0 * cW6) * ht3)
239 + (6.0 * cW2 * ht - 37.0 * cW2 - 119.0 * ht2 + 56.0 * cW2 * ht2)
240 * M_PI * M_PI / 27.0 / ht2
241 + (32.0 * cW4 / 3.0 - 2.0 / 3.0 - 12.0 * cW2) * B0_Mt2_Mz2_Mw2_Mw2
242 + (20.0 / 3.0 + 1.0 / 3.0 / cW2 - 8.0 * cW2) * B0_Mt2_Mw2_Mw2_Mz2
243 + (17.0 - 58.0 * cW2 + 32.0 * cW4)*(4.0 - ht) * sqrt(ht) * g(ht) / 27.0
244 - 40.0 * sW2 * (4.0 - ht) * Lambda(ht) / 3.0 / ht
245 + 2.0 * cW2 * (37.0 - 6.0 * ht - 12.0 * ht2 - 22.0 * ht3 + 9.0 * ht4)
246 * Li21mht / 9.0 / ht2
247 - (1.0 + 14.0 * cW2 + 16.0 * cW4) * log(cW2) / 3.0
248 + (11520.0 - 15072.0 * cW2
249 - (7170.0 - 8928.0 * cW2 - 768.0 * cW4) * ht
250 + (3411.0 - 7062.0 * cW2 + 3264.0 * cW4) * ht2
251 - (1259.0 - 3547.0 * cW2 + 2144.0 * cW4) * ht3
252 + (238.0 - 758.0 * cW2 + 448.0 * cW4) * ht4
253 - (17.0 - 58.0 * cW2 + 32.0 * cW4) * ht5)
254 * log(ht) / 27.0 / (ht - 4.0) / (ht - 4.0) / ht
255 + 8.0 / 9.0 * (4.0 - 26.0 * cW2 - 5.0 * cW4) * log(Mt * Mt / mu / mu)
256 + (3.0 + 5.0 * cW2 - 26.0 * cW4 - 48.0 * cW6) * log(zt) / 9.0 / cW2
257 + (3840.0 * sW2 - (4310.0 - 4224.0 * cW2 - 256.0 * cW4) * ht
258 + (1706.0 - 1312.0 * cW2 - 320.0 * cW4) * ht2
259 - (315.0 + 476.0 * cW2 - 64.0 * cW4) * ht3
260 + (24.0 + 454.0 * cW2) * ht4 - 112.0 * cW2 * ht5
261 + 9.0 * cW2 * ht6)
262 * phi(ht / 4.0) / 9.0 / (ht - 4.0) / (ht - 4.0) / ht2));
263 }
264 return rho2;
265}
EWSMcache::getPolyLog
const Polylogarithms getPolyLog() const
A get method to access the member object of type Polylogarithms.
Definition: EWSMcache.h:115
Polylogarithms::Li2
gslpp::complex Li2(const double x) const
The dilogarithm with a real argument, .
Definition: Polylogarithms.cpp:22

◆ DeltaRho2Add()

double EWSMTwoLoopEW::DeltaRho2Add ( const double  Mw_i) const
private

The auxiliary function \(\Delta\bar{\rho}_{\mathrm{add}}^{(2)}\).

See [Degrassi:1996ps].

Parameters
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta\bar{\rho}_{\mathrm{add}}^{(2)}\)

Definition at line 267 of file EWSMTwoLoopEW.cpp.

268{
269 double Mz = cache.getSM().getMz(), Mz2 = Mz*Mz;
270 double Mw = Mw_i, Mw2 = Mw*Mw;
271 double cW2 = cache.getSM().cW2(Mw);
272 double cW4 = cW2*cW2, cW6 = cW4*cW2;
273 double Mt = cache.getSM().getMtpole(), Mt2 = Mt*Mt;
274 double zt = Mz2 / Mt2;
275 double mu = Mt; // renormalization scale
276
277 double B0_Mt2_Mz2_Mw2_Mw2 = cache.getPV().B0(Mt2, Mz2, Mw2, Mw2).real();
278 double B0_Mt2_Mw2_0_Mw2 = cache.getPV().B0(Mt2, Mw2, 0.0, Mw2).real();
279 double B0_Mt2_Mw2_Mw2_Mz2 = cache.getPV().B0(Mt2, Mw2, Mw2, Mz2).real();
280
281 double dRho2add = 542.0 / 27.0 - 2.0 / 3.0 / cW2 - 800.0 * cW2 / 27.0
282 + 1.0 / 3.0 * (1.0 + 26.0 * cW2 + 24.0 * cW4) * B0_Mt2_Mz2_Mw2_Mw2
283 + 4.0 * cW2 * B0_Mt2_Mw2_0_Mw2
284 - (11.0 / 3.0 + 1.0 / 3.0 / cW2 + 4.0 * cW2) * B0_Mt2_Mw2_Mw2_Mz2
285 - (2.0 / 3.0 + 4.0 * cW2 / 3.0 - 8.0 * cW4) * log(cW2)
286 + (1.0 / cW2 - 38.0 / 3.0 + 34.0 * cW2 / 3.0) * log(Mt2 / mu / mu)
287 + 2.0 * (3.0 - 62.0 * cW2 + 74.0 * cW4 + 36.0 * cW6) * log(zt) / 9.0 / cW2;
288 return dRho2add;
289}

◆ deltaRho_rem_f()

gslpp::complex EWSMTwoLoopEW::deltaRho_rem_f ( const Particle  f,
const double  Mw_i 
) const

Remainder contribution of \(O(\alpha^2)\) to the effective couplings \(\rho_Z^f\), denoted as \(\delta\rho_{\mathrm{rem}}^{f,\, \alpha^2}\).

This function handles the \(O(\alpha^2)\) remainder contribution to \(\rho_{Z}^{f}\) in the on-shell scheme, which was calculated in [Degrassi:1999jd] :

\[ \delta\rho_{\rm rem}^{f,\, \alpha^2} = 3 (X_t^{\alpha})^2 \left[ 16\, {\it zt}\,c_W^2\, \Delta\hat{\eta}^{(2)} + 4\, {\it zt}\,c_W^2\, \Delta\bar{\eta}_{\rm add}^{(2)} \right], \]

where the definitions of the symbols can be read from the codes below.

Parameters
[in]fa lepton or quark
[in]Mw_ithe \(W\)-boson mass
Returns
\(\delta\rho_{\mathrm{rem}}^{f,\, \alpha^2}\)

Definition at line 96 of file EWSMTwoLoopEW.cpp.

97{
98 if (f.is("TOP")) return ( gslpp::complex(0.0, 0.0, false));
99
100 gslpp::complex dRho = gslpp::complex(0.0, 0.0, false);
101
102#ifdef EW_SUBLEADING_ALPHA2
103 /* O(\alpha^2 Mt^4/Mz^4 + \alpha^2 Mt^2/Mz^2) */
104 double Mz = cache.getSM().getMz();
105 double Mw = Mw_i;
106 double cW2 = cache.getSM().cW2(Mw);
107 double zt = Mz * Mz / cache.getSM().getMtpole() / cache.getSM().getMtpole();
108 dRho += 3.0 * pow(cache.Xt_alpha(Mw), 2.0)
109 *(16.0 * zt * cW2 * DeltaEta2(Mw) + 4.0 * zt * cW2 * DeltaEta2Add_f(f, Mw));
110#endif
111
112 return dRho;
113}
EWSMTwoLoopEW::DeltaEta2Add_f
gslpp::complex DeltaEta2Add_f(const Particle f, const double Mw_i) const
The auxiliary function for .
Definition: EWSMTwoLoopEW.cpp:461
EWSMTwoLoopEW::DeltaEta2
double DeltaEta2(const double Mw_i) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:383

◆ DeltaRw2()

double EWSMTwoLoopEW::DeltaRw2 ( const double  Mw_i) const
private

The auxiliary function \(\Delta \hat{r}_W^{(2)}\).

See [Degrassi:1996mg].

Parameters
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta \hat{r}_W^{(2)}\)

Definition at line 291 of file EWSMTwoLoopEW.cpp.

292{
293 double Mz = cache.getSM().getMz(), Mz2 = Mz*Mz;
294 double Mw = Mw_i, Mw2 = Mw*Mw;
295 double cW2 = cache.getSM().cW2(Mw), sW2 = cache.getSM().sW2(Mw);
296 double cW4 = cW2*cW2, cW6 = cW4*cW2;
297 double Mt = cache.getSM().getMtpole(), Mt2 = Mt*Mt;
298 double mh = cache.getSM().getMHl(), mh2 = mh*mh;
299 double zt = Mz2 / Mt2;
300 double zt2 = zt*zt;
301 double ht = mh2 / Mt2;
302 double ht2 = ht*ht, ht3 = ht2*ht, ht4 = ht3*ht, ht5 = ht4*ht;
303 double mu = Mt; // renormalization scale
304
305 double dRw2;
306 if (mh < 0.3 * Mt) {
307 double B0_Mt2_Mw2_mh2_Mw2 = cache.getPV().B0(Mt2, Mw2, mh2, Mw2).real();
308 double B0_Mt2_Mw2_Mw2_Mz2 = cache.getPV().B0(Mt2, Mw2, Mw2, Mz2).real();
309 dRw2 = -13.0 / 144.0 - 1.0 / 48.0 / cW4 - 41.0 / 96.0 / cW2 + 61.0 * cW2 / 72.0
310 + (7.0 - 16.0 * cW2) / 27.0 * M_PI * sqrt(ht) - M_PI * M_PI / 36.0
311 - 5.0 * ht2 / 144.0 / cW4 / zt2 + 35.0 * ht / 288.0 / cW2 / zt
312 + 5.0 / 12.0 * (1.0 + ht2 / 12.0 / cW4 / zt2 - ht / 3.0 / cW2 / zt) * B0_Mt2_Mw2_mh2_Mw2
313 + (1.0 + 20.0 * cW2 - 24.0 * cW4) / 48.0 / cW4 * B0_Mt2_Mw2_Mw2_Mz2
314 - (5.0 * sW2 * ht2 + 3.0 * ht * zt + 48.0 * cW2 * ht * zt - 60.0 * cW4 * ht * zt
315 - 3.0 * cW2 * zt2 - 8.0 * cW4 * zt2 + 20.0 * cW6 * zt2) * log(cW2)
316 / 144.0 / cW2 / sW2 / zt / (ht - cW2 * zt)
317 + 5.0 * ht * (ht2 - 4.0 * cW2 * ht * zt + 12.0 * cW4 * zt2) * log(ht)
318 / 144.0 / cW4 / zt2 / (ht - cW2 * zt)
319 + (17.0 / 36.0 - 13.0 * cW2 / 18.0) * log(Mt2 / mu / mu)
320 - (5.0 * cW2 * ht2 - 3.0 * ht * zt - 60.0 * cW2 * ht * zt + 60.0 * cW4 * ht * zt
321 + (3.0 * cW2 + 60.0 * cW4 - 20.0 * cW6) * zt2) * log(zt)
322 / 144.0 / cW4 / zt / (ht - cW2 * zt);
323 } else {
324 double B0_Mt2_Mw2_Mw2_Mz2 = cache.getPV().B0(Mt2, Mw2, Mw2, Mz2).real();
325 dRw2 = -121.0 / 288.0 - 1.0 / 48.0 / cW4 - 41.0 / 96.0 / cW2 + 77.0 * cW2 / 12.0
326 + 19.0 / 72.0 / ht + (41.0 / 216.0 - 4.0 * cW2 / 27.0) * ht
327 - (19.0 + 21.0 * ht) * M_PI * M_PI / 432.0 / ht2
328 - (1.0 / 2.0 - 1.0 / 48.0 / cW4 - 5.0 / 12.0 / cW2) * B0_Mt2_Mw2_Mw2_Mz2
329 + (16.0 * cW2 - 7.0) / 216.0 * (ht - 4.0) * sqrt(ht) * g(ht)
330 - (1.0 / 12.0 - 1.0 / 3.0 / ht) * Lambda(ht)
331 + (19.0 + 21.0 * ht - 12.0 * ht2 - 31.0 * ht3 + 9.0 * ht4) / 72.0 / ht2
332 * cache.getPolyLog().Li2(1.0 - ht).real()
333 - (1.0 + 21.0 * cW2 - 25.0 * cW4) * log(cW2) / 48.0 / cW2 / sW2
334 + (17.0 / 36.0 - 13.0 * cW2 / 18.0) * log(Mt2 / mu / mu)
335 + (1.0 + 20.0 * cW2 - 25.0 * cW4) * log(zt) / 48.0 / cW4
336 + (372.0 + (96.0 * cW2 - 213.0) * ht + (432.0 * cW2 - 318.0) * ht2
337 + (97.0 - 160.0 * cW2) * ht3 - (7.0 - 16.0 * cW2) * ht4)
338 / 216.0 / (ht - 4.0) / ht * log(ht)
339 + (96.0 - (384.0 - 64.0 * cW2) * ht - (2.0 + 64.0 * cW2) * ht2 + 231.0 * ht3
340 - 85.0 * ht4 + 9.0 * ht5) / 144.0 / (ht - 4.0) / ht2 * phi(ht / 4.0);
341 }
342 return dRw2;
343}

◆ f0()

double EWSMTwoLoopEW::f0 ( const double  a) const
private

The auxiliary function \(f(a,0)\).

See [Fleischer:1993ub] and [Fleischer:1994cb].

Parameters
[in]athe ratio \(a=(m_h/m_t)^2\)
Returns
\(f(a,0)\)

Definition at line 180 of file EWSMTwoLoopEW.cpp.

181{
182 if (a >= 0.0)
183 return ( cache.getPolyLog().Li2(1.0 - a).real()); // 1-a<1
184 else
185 throw std::runtime_error("Out of range in EWSMTwoLoopEW::f0()");
186}

◆ f1()

double EWSMTwoLoopEW::f1 ( const double  a) const
private

The auxiliary function \(f(a,1)\).

See [Fleischer:1993ub] and [Fleischer:1994cb].

Parameters
[in]athe ratio \(a=(m_h/m_t)^2\)
Returns
\(f(a,1)\)

Definition at line 188 of file EWSMTwoLoopEW.cpp.

189{
190 if (a >= 0.0 && a <= 4.0) {
191 double y = 4.0 / a;
192 double phi = 2.0 * asin(sqrt(a / 4.0));
193 return ( -2.0 / sqrt(y - 1.0) * cache.getClausen().Cl2(phi));
194 } else if (a > 4.0) {
195 double y = 4.0 / a; // 0<y<1
196 double xi = (sqrt(1.0 - y) - 1.0) / (sqrt(1.0 - y) + 1.0); // -1<xi<0
197 return ( -1.0 / sqrt(1.0 - y)*(cache.getPolyLog().Li2(xi).real()
198 - cache.getPolyLog().Li2(1.0 / xi).real()));
199 } else
200 throw std::runtime_error("Out of range in EWSMTwoLoopEW::f1()");
201}
ClausenFunctions::Cl2
double Cl2(const double phi) const
The Clausen function of index 2, .
Definition: ClausenFunctions.cpp:21
EWSMcache::getClausen
const ClausenFunctions getClausen() const
A get method to access the member object of type ClausenFunctions.
Definition: EWSMcache.h:124
xi
A class for , relevant for mesons mixing in the Standard Model.
Definition: xi.h:23

◆ f2Add()

double EWSMTwoLoopEW::f2Add ( const double  Mw_i) const
private

The auxiliary function \(\bar{f}_{\rm add}^{(2)}\).

See [Degrassi:1996ps].

Parameters
[in]Mw_ithe \(W\)-boson mass
Returns
\(\bar{f}_{\rm add}^{(2)}\)

Definition at line 365 of file EWSMTwoLoopEW.cpp.

366{
367 double Mz = cache.getSM().getMz(), Mz2 = Mz*Mz;
368 double Mw = Mw_i, Mw2 = Mw*Mw;
369 double cW2 = cache.getSM().cW2(Mw), sW2 = cache.getSM().sW2(Mw);
370 double Mt = cache.getSM().getMtpole(), Mt2 = Mt*Mt;
371 double zt = Mz2 / Mt2;
372
373 double B0_Mt2_Mw2_0_Mw2 = cache.getPV().B0(Mt2, Mw2, 0.0, Mw2).real();
374 double B0_Mt2_Mw2_Mw2_Mz2 = cache.getPV().B0(Mt2, Mw2, Mw2, Mz2).real();
375
376 double f2a = 10.0 / 3.0 + 1.0 / 3.0 / cW2 + 4.0 * cW2 * B0_Mt2_Mw2_0_Mw2
377 - (11.0 / 3.0 + 1.0 / 3.0 / cW2 + 4.0 * cW2) * B0_Mt2_Mw2_Mw2_Mz2
378 + (11.0 - 8.0 * cW2) * log(cW2) / 6.0 / sW2
379 - (11.0 / 3.0 + 1.0 / 3.0 / cW2) * log(zt);
380 return f2a;
381}

◆ FV()

gslpp::complex EWSMTwoLoopEW::FV ( const double  x) const
private

The auxiliary function \(f(x)\).

This function is used in Vadd() and Vfi(). See [Degrassi:1990ec].

Parameters
[in]xa real variable
Returns
\(f(x)\)
Attention
This function is valid for \(x>0\).

Definition at line 607 of file EWSMTwoLoopEW.cpp.

608{
609 if (x <= 0.0)
610 throw std::runtime_error("Out of range in EWSMTwoLoopEW::FV()");
611
612 gslpp::complex i = gslpp::complex::i();
613
614 return ( i * M_PI * (2.0 / x + 3.0 - 2.0 * (1.0 + 1.0 / x)*(1.0 + 1.0 / x) * log(1.0 + x))
615 + 2.0 / x + 7.0 / 2.0 - (3.0 + 2.0 / x) * log(x)
616 + (1.0 + 1.0 / x)*(1.0 + 1.0 / x)
617 *(2.0 * cache.getPolyLog().Li2(1.0 / (1.0 + x))
618 - M_PI * M_PI / 3.0 + pow(log(1.0 + x), 2.0)));
619}

◆ g()

double EWSMTwoLoopEW::g ( const double  a) const
private

The auxiliary function \(g(a)\).

See [Fleischer:1993ub] and [Fleischer:1994cb].

Parameters
[in]athe ratio \(a=(m_h/m_t)^2\)
Returns
\(g(a)\)

Definition at line 167 of file EWSMTwoLoopEW.cpp.

168{
169 if (a >= 0.0 && a <= 4.0) {
170 double phi = 2.0 * asin(sqrt(a / 4.0));
171 return ( sqrt(4.0 - a)*(M_PI - phi));
172 } else if (a > 4.0) {
173 double y = 4.0 / a;
174 double xi = (sqrt(1.0 - y) - 1.0) / (sqrt(1.0 - y) + 1.0);
175 return ( sqrt(a - 4.0) * log(-xi));
176 } else
177 throw std::runtime_error("Out of range in EWSMTwoLoopEW::g()");
178}

◆ GV()

gslpp::complex EWSMTwoLoopEW::GV ( const double  x) const
private

The auxiliary function \(g(x)\).

This function is used in Vadd() and Vfi(). See [Degrassi:1990ec].

Parameters
[in]xa real variable
Returns
\(g(x)\)
Attention
This function is valid for \(0<x<4\).

Definition at line 621 of file EWSMTwoLoopEW.cpp.

622{
623 if (x <= 0.0 || x >= 4.0)
624 throw std::runtime_error("Out of range in EWSMTwoLoopEW::GV()");
625
626 double atanX = atan(sqrt(x / (4.0 - x)));
627
628 return ( (sqrt((4.0 - x) / x) * atanX - 1.0)*(1.0 / x + 1.0 / 2.0) + 9.0 / 8.0
629 + 1.0 / 2.0 / x - (1.0 + 1.0 / 2.0 / x)*4.0 / x * atanX * atanX);
630}

◆ Lambda()

double EWSMTwoLoopEW::Lambda ( const double  x) const
private

The auxiliary function \(\Lambda(x)\).

This functions is used in DeltaRho2(), DeltaRw2() and DeltaEta2(). See [Degrassi:1996mg] and [Degrassi:1999jd].

Parameters
[in]xa real variable
Returns
\(\Lambda(x)\)
Attention
This function is valid for \(x\geq 0\).

Definition at line 584 of file EWSMTwoLoopEW.cpp.

585{
586 if (x >= 0.0 && x <= 4.0) {
587 return ( -1.0 / 2.0 / sqrt(x) * g(x) + M_PI / 2.0 * sqrt(4.0 / x - 1.0));
588 } else if (x > 4.0) {
589 return ( -1.0 / 2.0 / sqrt(x) * g(x));
590 } else
591 throw std::runtime_error("Out of range in EWSMTwoLoopEW::Lambda()");
592}

◆ phi()

double EWSMTwoLoopEW::phi ( const double  x) const
private

The auxiliary function \(\phi(x)\).

This functions is used in DeltaRho2(), DeltaRw2(), deltaEoverE2(), DeltaEta2() and DeltaKappa2(). See [Degrassi:1996mg] and [Degrassi:1999jd].

Parameters
[in]xa real variable
Returns
\(\phi(x)\)
Attention
This function is valid for \(x\geq 0\).

Definition at line 594 of file EWSMTwoLoopEW.cpp.

595{
596 if (x >= 0.0 && x <= 1.0) {
597 return ( 4.0 * sqrt(x / (1.0 - x)) * cache.getClausen().Cl2(2.0 * asin(sqrt(x))));
598 } else if (x > 1.0) {
599 double lambda = sqrt(1.0 - 1.0 / x);
600 return ( 1.0 / lambda * (-4.0 * cache.getPolyLog().Li2((1.0 - lambda) / 2.0).real()
601 + 2.0 * pow(log((1.0 - lambda) / 2.0), 2.0)
602 - pow(log(4.0 * x), 2.0) + M_PI * M_PI / 3.0));
603 } else
604 throw std::runtime_error("Out of range in EWSMTwoLoopEW::phi()");
605}

◆ rho_2()

double EWSMTwoLoopEW::rho_2 ( ) const

The function \(\rho^{(2)}\).

This function parameterize the \(O(\alpha^2 m_t^4/M_Z^4)\) contribution to \(\Delta\rho\):

\[ \Delta\rho^{\alpha^2} = 3 (X_t^{\alpha})^2\rho^{(2)}, \]

where the expression of \(\rho^{(2)}\) can be found in [Fleischer:1993ub] and [Fleischer:1994cb] (see also [Barbieri:1992nz] and [Barbieri:1992dq]).

Returns
\(\rho^{(2)}\)

Definition at line 137 of file EWSMTwoLoopEW.cpp.

138{
139 double a = cache.getSM().getMHl() * cache.getSM().getMHl() / cache.getSM().getMtpole() / cache.getSM().getMtpole();
140 if (a <= 0.0) throw std::runtime_error("a is out of range in EWSMTwoLoopEW::rho_2");
141 double g_a = g(a);
142 double f_a_0 = f0(a); // f(a,0)
143 double f_a_1 = f1(a); // f(a,1)
144 double log_a = -2.0 * cache.logMTOPtoMH();
145 return ( 25.0 - 4.0 * a + 0.5 * (a * a - 12.0 * a - 12.0) * log_a
146 + (a - 2.0) / 2.0 / a * M_PI * M_PI + 0.5 * (a - 4.0) * sqrt(a) * g_a
147 - 3.0 / a * (a - 1.0)*(a - 1.0)*(a - 2.0) * f_a_0
148 + 3.0 * (a * a - 6.0 * a + 10.0) * f_a_1);
149}
EWSMTwoLoopEW::f1
double f1(const double a) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:188
EWSMTwoLoopEW::f0
double f0(const double a) const
The auxiliary function .
Definition: EWSMTwoLoopEW.cpp:180
EWSMcache::logMTOPtoMH
double logMTOPtoMH() const
A cache method.
Definition: EWSMcache.cpp:134

◆ tau_2()

double EWSMTwoLoopEW::tau_2 ( ) const

The function \(\tau^{(2)}\).

This function parmeterize the \(O(\alpha^2 m_t^4/M_Z^4)\) contribution to the \(Zb\bar{b}\) vertex (see EWSM::taub()), where the expression of \(\tau^{(2)}\) can be found in [Fleischer:1993ub] and [Fleischer:1994cb] (see also [Barbieri:1992nz] and [Barbieri:1992dq]).

Returns
\(\tau^{(2)}\)

Definition at line 151 of file EWSMTwoLoopEW.cpp.

152{
153 double a = cache.getSM().getMHl() * cache.getSM().getMHl() / cache.getSM().getMtpole() / cache.getSM().getMtpole();
154 if (a <= 0.0) throw std::runtime_error("a is out of range in EWSMTwoLoopEW::tau_2");
155 double g_a = g(a);
156 double f_a_0 = f0(a); // f(a,0)
157 double f_a_1 = f1(a); // f(a,1)
158 double log_a = -2.0 * cache.logMTOPtoMH();
159 return ( 9.0 - 13.0 / 4.0 * a - 2.0 * a * a - a / 4.0 * (19.0 + 6.0 * a) * log_a
160 - a * a / 4.0 * (7.0 - 6.0 * a) * log_a * log_a
161 - (1.0 / 4.0 + 7.0 / 2.0 * a * a - 3.0 * a * a * a) * M_PI * M_PI / 6.0
162 + (a / 2.0 - 2.0) * sqrt(a) * g_a
163 + (a - 1.0)*(a - 1.0)*(4.0 * a - 7.0 / 4.0) * f_a_0
164 - (a * a * a - 33.0 / 4.0 * a * a + 18.0 * a - 7.0) * f_a_1);
165}

◆ Vadd()

gslpp::complex EWSMTwoLoopEW::Vadd ( const double  I3f,
const double  Qf,
const double  Mw_i 
) const
private

The auxiliary function \(V_{\rm add}\).

This functions is used in DeltaEta2Add_tmp(). See [Degrassi:1999jd].

Parameters
[in]I3fthe isospin of a final-state fermion
[in]Qfthe electric charge of a final-state fermion
[in]Mw_ithe \(W\)-boson mass
Returns
\(V_{\rm add}\)

Definition at line 536 of file EWSMTwoLoopEW.cpp.

538{
539 double Mw = Mw_i, Mw2 = Mw*Mw;
540 double cW2 = cache.getSM().cW2(Mw), sW2 = cache.getSM().sW2(Mw);
541 double Mt = cache.getSM().getMtpole();
542 double mu = Mt; // renormalization scale
543
544 gslpp::complex V = 8.0 * cW2 * log(Mw2 / mu / mu)
545 + 3.0 * (2.0 * I3f * Qf - 4.0 * sW2 * Qf * Qf) * FV(1.0)
546 - 16.0 * cW2 * GV(1.0 / cW2)
547 + (1.0 - 4.0 * cW2 - 4.0 * (1.0 - 2.0 * cW2) * I3f * Qf) * FV(1.0 / cW2);
548 return V;
549}

◆ Vfi()

gslpp::complex EWSMTwoLoopEW::Vfi ( const double  I3f,
const double  Qf,
const double  q2,
const double  Mw_i 
) const
private

The auxiliary function \({\cal V}_{fi}(q^2)\).

This function is used in DeltaEtaf1(). See [Degrassi:1990ec].

Parameters
[in]I3fthe isospin of a final-state fermion
[in]Qfthe electric charge of a final-state fermion
[in]q2invariant mass squared
[in]Mw_ithe \(W\)-boson mass
Returns
\({\cal V}_{fi}(q^2)\)

Definition at line 566 of file EWSMTwoLoopEW.cpp.

568{
569 double I3i = cache.I3_f(cache.getSM().getLeptons(StandardModel::ELECTRON));
570 double Qi = cache.Q_f(cache.getSM().getLeptons(StandardModel::ELECTRON));
571 double I3aQaQa = I3i * Qi * Qi + I3f * Qf*Qf;
572 double I3aQa = I3i * Qi + I3f*Qf;
573 double QaQa = Qi * Qi + Qf*Qf;
574 double Mz = cache.getSM().getMz(), Mz2 = Mz*Mz;
575 double Mw = Mw_i, Mw2 = Mw*Mw;
576 double cW2 = cache.getSM().cW2(Mw), sW2 = cache.getSM().sW2(Mw);
577
578 gslpp::complex V = (1.0 - sW2 * (2.0 - 2.0 * I3aQaQa)) * FV(q2 / Mw2)
579 + 8.0 * cW2 * GV(q2 / Mw2)
580 - (1.0 - 6.0 * sW2 * I3aQa + 6.0 * sW2 * QaQa) / 2.0 / cW2 * FV(q2 / Mz2);
581 return V;
582}

Member Data Documentation

◆ cache

const EWSMcache& EWSMTwoLoopEW::cache
private

A reference to an object of type EWSMcache.

Definition at line 207 of file EWSMTwoLoopEW.h.

◆ myOneLoopEW

const EWSMOneLoopEW EWSMTwoLoopEW::myOneLoopEW
private

An object of type EWSMOneLoopEW.

Definition at line 208 of file EWSMTwoLoopEW.h.

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