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EvolDF1 Class Reference

#include <EvolDF1.h>

+ Inheritance diagram for EvolDF1:

Detailed Description

Definition at line 23 of file EvolDF1.h.

Public Member Functions

gslpp::matrix< double > AnomalousDimension (indices nm, uint n_u, uint n_d) const
 a method returning the anomalous dimension matrix given in the Misiak basis
 
const Expanded< gslpp::matrix< double > > & DF1Evol (double mu, double M, schemes scheme=NDR)
 a method returning the evolutor related to the high scale \( M \) and the low scale \( \mu \)
 
 EvolDF1 (std::string reqblocks, schemes scheme, const StandardModel &model_i, qcd_orders order_qcd, qed_orders order_qed)
 EvolDF1 constructor.
 
virtual ~EvolDF1 ()
 EvolDF1 destructor.
 
- Public Member Functions inherited from RGEvolutorNew
const gslpp::matrix< double > & Evol (qcd_orders order_qcd, qed_orders order_qed=QED0) const
 Evolution matrix set at a fixed order of Electroweak coupling.
 
const Expanded< gslpp::matrix< double > > & getEvol () const
 
double getM () const
 Retrieve the upper scale of the Wilson Coefficients.
 
 RGEvolutorNew (unsigned int dim, schemes scheme, qcd_orders order_qcd_i, qed_orders order_qed_i=QED0)
 constructor
 
void setEvol (const gslpp::matrix< double > &m, qcd_orders order_qcd_i, qed_orders order_qed_i=QED0)
 
void setEvol (unsigned int i, unsigned int j, double x, qcd_orders order_i, qed_orders order_qed=QED0)
 
void setM (double M)
 Sets the upper scale for the running of the Wilson Coefficients.
 
void setMu (double mu)
 Sets the lower scale for the running of the Wilson Coefficients.
 
void setScales (double mu, double M)
 Sets the upper and lower scale for the running of the Wilson Coefficients.
 
virtual ~RGEvolutorNew ()
 destructor
 
- Public Member Functions inherited from WilsonTemplateNew< gslpp::matrix< double > >
double getMu () const
 
qcd_orders getOrder_QCD () const
 
qed_orders getOrder_QED () const
 
schemes getScheme () const
 
unsigned int getSize () const
 
const gslpp::matrix< double > & getWilson (qcd_orders order_qcd_i, qed_orders order_qed_i=QED0) const
 
void resetWilson ()
 
void setMu (double mu)
 
void setScheme (schemes scheme)
 
 WilsonTemplateNew (unsigned int size_i, schemes scheme_i, qcd_orders order_qcd_i, qed_orders order_qed_i=QED0)
 

Private Member Functions

void CheckNf (indices nm, uint nf) const
 a method returning the anomalous dimension in the Chetyrkin, Misiak and Munz operator basis
 
void DF1Ev (double mu, double M, int nf, schemes scheme)
 a void type method storing properly the magic numbers for the implementation of the evolutor
 
double f_f (uint nf, uint i, uint j, int k, double eta)
 auxiliary function f - eq. (50) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
 
double f_g (uint nf, uint i, uint p, uint j, int k, int l, double eta)
 auxiliary function g - eq. (52) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
 
double f_h (uint nf, uint i, uint p, uint q, uint j, int k, int l, int m, double eta)
 auxiliary function h - eq. (53) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
 
double f_r (uint nf, uint i, uint j, int k, double eta)
 auxiliary function r - eq. (51) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
 
gslpp::matrix< double > GammaBB (indices nm, uint n_u, uint n_d) const
 BB block of the QCD+QED anomalous dimension.
 
gslpp::matrix< double > GammaBL (indices nm, uint n_u, uint n_d) const
 BL block of the QED anomalous dimension.
 
gslpp::matrix< double > GammaBP (indices nm, uint n_u, uint n_d) const
 BP block of the QCD+QED anomalous dimension.
 
gslpp::matrix< double > GammaBQ (indices nm, uint n_u, uint n_d) const
 BQ block of the QED anomalous dimension.
 
gslpp::matrix< double > GammaCC (indices nm, uint n_u, uint n_d) const
 CC block of the QCD+QED anomalous dimension.
 
gslpp::matrix< double > GammaCL (indices nm, uint n_u, uint n_d) const
 CL block of the QED anomalous dimension.
 
gslpp::matrix< double > GammaCM (indices nm, uint n_u, uint n_d) const
 CM block of the QCD+QED anomalous dimension.
 
gslpp::matrix< double > GammaCP (indices nm, uint n_u, uint n_d) const
 CP block of the QCD+QED anomalous dimension.
 
gslpp::matrix< double > GammaCQ (indices nm, uint n_u, uint n_d) const
 CQ block of the QED anomalous dimension.
 
gslpp::matrix< double > GammaLL (indices nm, uint n_u, uint n_d) const
 LL block of the QED anomalous dimension.
 
gslpp::matrix< double > GammaMM (indices nm, uint n_u, uint n_d) const
 MM block of the QCD+QED anomalous dimension.
 
gslpp::matrix< double > GammaPL (indices nm, uint n_u, uint n_d) const
 PL block of the QED anomalous dimension.
 
gslpp::matrix< double > GammaPM (indices nm, uint n_u, uint n_d) const
 PM block of the QCD+QED anomalous dimension.
 
gslpp::matrix< double > GammaPP (indices nm, uint n_u, uint n_d) const
 PP block of the QCD+QED anomalous dimension.
 
gslpp::matrix< double > GammaPQ (indices nm, uint n_u, uint n_d) const
 PQ block of the QED anomalous dimension.
 
gslpp::matrix< double > GammaQL (indices nm, uint n_u, uint n_d) const
 QL block of the QED anomalous dimension.
 
gslpp::matrix< double > GammaQM (indices nm, uint n_u, uint n_d) const
 QM block of the QCD anomalous dimension.
 
gslpp::matrix< double > GammaQP (indices nm, uint n_u, uint n_d) const
 QP block of the QCD+QED anomalous dimension.
 
gslpp::matrix< double > GammaQQ (indices nm, uint n_u, uint n_d) const
 QQ block of the QCD+QED anomalous dimension.
 

Private Attributes

std::map< uint, double > ai [NF]
 
double alsM_cache
 
std::string blocks
 
gslpp::vector< double > eval
 
gslpp::vector< gslpp::complex > evalc
 
gslpp::matrix< double > evec
 
gslpp::matrix< double > evec_i
 
gslpp::matrix< gslpp::complex > evecc
 
int f_f_c [4][F_iCacheSize]
 
double f_f_d [2][F_iCacheSize]
 
gslpp::matrix< double > gg
 
gslpp::matrix< double > h
 
gslpp::matrix< double > js
 
gslpp::matrix< double > jss
 
gslpp::matrix< double > jssv
 
gslpp::matrix< double > jv
 
double MAls_cache
 
const StandardModel & model
 
uint nfmax
 
uint nfmin
 
uint nops
 
gslpp::matrix< double > s_s
 
gslpp::matrix< double > vij
 
std::map< std::vector< uint >, double > vM0vi [NF]
 
std::map< std::vector< uint >, double > vM113vi [NF]
 
std::map< std::vector< uint >, double > vM11vi [NF]
 
std::map< std::vector< uint >, double > vM131vi [NF]
 
std::map< std::vector< uint >, double > vM133vi [NF]
 
std::map< std::vector< uint >, double > vM13vi [NF]
 
std::map< std::vector< uint >, double > vM14vi [NF]
 
std::map< std::vector< uint >, double > vM1vi [NF]
 
std::map< std::vector< uint >, double > vM23vi [NF]
 
std::map< std::vector< uint >, double > vM2vi [NF]
 
std::map< std::vector< uint >, double > vM311vi [NF]
 
std::map< std::vector< uint >, double > vM313vi [NF]
 
std::map< std::vector< uint >, double > vM31vi [NF]
 
std::map< std::vector< uint >, double > vM32vi [NF]
 
std::map< std::vector< uint >, double > vM331vi [NF]
 
std::map< std::vector< uint >, double > vM33vi [NF]
 
std::map< std::vector< uint >, double > vM34vi [NF]
 
std::map< std::vector< uint >, double > vM3vi [NF]
 
std::map< std::vector< uint >, double > vM41vi [NF]
 
std::map< std::vector< uint >, double > vM43vi [NF]
 
std::map< std::vector< uint >, double > vM4vi [NF]
 
std::map< std::vector< uint >, double > vM5vi [NF]
 
std::map< std::vector< uint >, double > vM6vi [NF]
 

Friends

double gslpp_special_functions::zeta (int i)
 

Additional Inherited Members

- Protected Member Functions inherited from WilsonTemplateNew< gslpp::matrix< double > >
Expanded< gslpp::matrix< double > > getWilson () const
 
void setWilson (const gslpp::matrix< double > &v, qcd_orders order_qcd_i, qed_orders order_qed_i=QED0)
 
- Protected Attributes inherited from RGEvolutorNew
double M
 
- Protected Attributes inherited from WilsonTemplateNew< gslpp::matrix< double > >
double mu
 
qcd_orders order_qcd
 
qed_orders order_qed
 
schemes scheme
 
unsigned int size
 
Expanded< gslpp::matrix< double > > wilson
 

Constructor & Destructor Documentation

◆ EvolDF1()

EvolDF1::EvolDF1 ( std::string  reqblocks,
schemes  scheme,
const StandardModel &  model_i,
qcd_orders  order_qcd,
qed_orders  order_qed 
)

EvolDF1 constructor.

Parameters
diman uinteger for the dimension of the evolutor
schemean enum "schemes" for the regularization scheme of the evolutor
orderan enum "orders" for the order \( \alpha_s\) in the evolutor
order_qedan enum "orders_qed" for the order \( \alpha_e\) in the evolutor
modelan object of StandardModel class

Definition at line 29 of file EvolDF1.cpp.

30: RGEvolutorNew(blocks_nops.at(reqblocks), scheme, ord_qcd, ord_qed), model(model_i), blocks(reqblocks),
31evec(blocks_nops.at(reqblocks), 0.), evec_i(blocks_nops.at(reqblocks), 0.), js(blocks_nops.at(reqblocks), 0.),
32h(blocks_nops.at(reqblocks), 0.), gg(blocks_nops.at(reqblocks), 0.), s_s(blocks_nops.at(reqblocks), 0.),
33jssv(blocks_nops.at(reqblocks), 0.), jss(blocks_nops.at(reqblocks), 0.), jv(blocks_nops.at(reqblocks), 0.),
34vij(blocks_nops.at(reqblocks), 0.), eval(blocks_nops.at(reqblocks), 0.), evecc(blocks_nops.at(reqblocks), 0.),
35evalc(blocks_nops.at(reqblocks), 0.)
36{
37 // blocks_ord = {
38 // {"C", NNLO},
39 // {"CP", NNLO},
40 // {"CPM", NNLO},
41 // {"L", NNLO},
42 // {"CPML", NNLO},
43 // {"CPQB", NLO},
44 // {"CPMQB", NLO},
45 // {"CPMLQB", NLO}};
46
47 // if (blocks_nops[blocks] != nops)
48 // throw std::runtime_error("EvolDF1(): number of operators does not match block specification");
49
50 this->nops = blocks_nops.at(reqblocks);
51 uint nf, nnf, nu, nd, a, b, i, j, p, q;
52 double b0, b0e, b1, b2, b3, b4, term;
53
54 alsM_cache = 0.;
55 MAls_cache = 0.;
56
57 gslpp::matrix<double> W10(nops, nops, 0.), W20(nops, nops, 0.), W30(nops, nops, 0.),
58 W01(nops, nops, 0.), W02(nops, nops, 0.), W11(nops, nops, 0.), W21(nops, nops, 0.);
59 gslpp::matrix<double> M1(nops, nops, 0.), M2(nops, nops, 0.), M3(nops, nops, 0.), M4(nops, nops, 0.),
60 M5(nops, nops, 0.), M6(nops, nops, 0.);
61
62 if (order_qed == QED0 && blocks.find("L") == std::string::npos &&
63 blocks.find("Q") == std::string::npos && blocks.find("B") == std::string::npos)
64 {
65 nfmin = 3;
66 nfmax = 6;
67 } else
68 nfmin = nfmax = 5;
69
70
71 for (nf = nfmin; nf <= nfmax; nf++)
72 {
73 nnf = nf - nfmin;
74 nu = nf / 2;
75 nd = nf % 2 == 0 ? nf / 2 : nf / 2 + 1;
76
77 b0 = model.Beta_s(00, nf);
78 b1 = model.Beta_s(10, nf) / 2. / b0 / b0;
79 b2 = model.Beta_s(20, nf) / 4. / b0 / b0 / b0 - b1 * b1;
80
81 W10 = AnomalousDimension(10, nu, nd).transpose() / 2. / b0;
82 W20 = AnomalousDimension(20, nu, nd).transpose() / 4. / b0 / b0;
83 W30 = AnomalousDimension(30, nu, nd).transpose() / 8. / b0 / b0 / b0;
84
85 // std::cout << AnomalousDimension(01, nu, nd).transpose() << std::endl;
86 // std::cout << W10 << std::endl;
87
88 // Misiak-Munz basis, defined as in T. Huber et al., hep-ph/0512066
89 W10.eigensystem(evecc, evalc);
90 for (size_t jj = 0; jj < evalc.size(); jj++)
91 if (fabs(evalc(jj).imag()) > EPS) throw ("check the imaginary part of eigenvalues of W10");
92 eval = evalc.real();
93 evec = evecc.real();
94 evec_i = (evecc.inverse()).real();
95
96 // QCD magic numbers
97 // M2: B(-2), M1: B(-1)_10
98 M2 = evec_i * (W30 - b1 * W20 - b2 * W10) * evec;
99 M1 = evec_i * (W20 - b1 * W10) * evec;
100
101 for (a = 0; a < nops; a++)
102 {
103 ai[nnf].insert(std::pair<uint, double > (a, eval(a)));
104 for (b = 0; b < nops; b++)
105 for (i = 0; i < nops; i++)
106 {
107 if (fabs(term = evec(a, i) * evec_i(i, b)) > EPS)
108 vM0vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i}, term)); // QCD LO evolutor
109 for (j = 0; j < nops; j++)
110 {
111 if (fabs(term = evec(a, i) * M1(i, j) * evec_i(j, b)) > EPS)
112 vM1vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j}, term)); // QCD NLO evolutor
113 if (fabs(term = evec(a, i) * M2(i, j) * evec_i(j, b)) > EPS)
114 vM2vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j}, term)); // QCD NNLO evolutor
115 for (p = 0; p < nops; p++)
116 if (fabs(term = evec(a, i) * M1(i, p) * M1(p, j) * evec_i(j, b)) > EPS)
117 vM11vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term)); // QCD NNLO evolutor
118 }
119 }
120 }
121
122 if (order_qed != QED0)
123 {
124 b0e = model.Beta_e(00, nf);
125 b3 = model.Beta_s(01, nf) / 2. / b0 / b0e;
126 b4 = model.Beta_s(11, nf) / 4. / b0 / b0 / b0e - 2. * b1*b3;
127 W01 = AnomalousDimension(01, nu, nd).transpose() / 2. / b0e;
128 W02 = AnomalousDimension(02, nu, nd).transpose() / 4. / b0e / b0e;
129 W11 = AnomalousDimension(11, nu, nd).transpose() / 4. / b0 / b0e;
130 W21 = AnomalousDimension(21, nu, nd).transpose() / 8. / b0 / b0 / b0e;
131
132 // QED magic numbers
133 // M3: B(1)_01, B(2)_02, B(1)_02, R5_12, M4: B(0)_11, B(0)_12, M5: B(-1)_21, M6: B(1)_12 - proper powers of omega and lambda added in DF1Evol
134 M3 = evec_i * W01 * evec;
135 M4 = evec_i * (W11 - b1 * W01 - b3 * W10) * evec;
136 M5 = evec_i * (W21 - b1 * W11 - b2 * W01 - b3 * W20 - b4 * W10) * evec;
137 M6 = evec_i * (W02 + W11 - (b1 + b3) * W01 - b3 * W10) * evec;
138 for (a = 0; a < nops; a++)
139 for (b = 0; b < nops; b++)
140 for (i = 0; i < nops; i++)
141 for (j = 0; j < nops; j++)
142 {
143 if (fabs(term = evec(a, i) * M3(i, j) * evec_i(j, b)) > EPS)
144 vM3vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j}, term));
145 if (fabs(term = evec(a, i) * M4(i, j) * evec_i(j, b)) > EPS)
146 vM4vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j}, term));
147 if (fabs(term = evec(a, i) * M5(i, j) * evec_i(j, b)) > EPS)
148 vM5vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j}, term));
149 if (fabs(term = evec(a, i) * M6(i, j) * evec_i(j, b)) > EPS)
150 vM6vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j}, term));
151 for (p = 0; p < nops; p++)
152 {
153 if (fabs(term = evec(a, i) * M3(i, p) * M3(p, j) * evec_i(j, b)) > EPS)
154 vM33vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term));
155 if (fabs(term = evec(a, i) * M3(i, p) * M1(p, j) * evec_i(j, b)) > EPS)
156 vM31vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term));
157 if (fabs(term = evec(a, i) * M1(i, p) * M3(p, j) * evec_i(j, b)) > EPS)
158 vM13vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term));
159 if (fabs(term = evec(a, i) * M3(i, p) * M4(p, j) * evec_i(j, b)) > EPS)
160 vM34vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term));
161 if (fabs(term = evec(a, i) * M4(i, p) * M3(p, j) * evec_i(j, b)) > EPS)
162 vM43vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term));
163 if (fabs(term = evec(a, i) * M2(i, p) * M3(p, j) * evec_i(j, b)) > EPS)
164 vM23vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term));
165 if (fabs(term = evec(a, i) * M3(i, p) * M2(p, j) * evec_i(j, b)) > EPS)
166 vM32vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term));
167 if (fabs(term = evec(a, i) * M1(i, p) * M4(p, j) * evec_i(j, b)) > EPS)
168 vM14vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term));
169 if (fabs(term = evec(a, i) * M4(i, p) * M1(p, j) * evec_i(j, b)) > EPS)
170 vM41vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p}, term));
171 for (q = 0; q < nops; q++)
172 {
173 if (fabs(term = evec(a, i) * M1(i, p) * M1(p, q) * M3(q, j) * evec_i(j, b)) > EPS)
174 vM113vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p, q}, term));
175 if (fabs(term = evec(a, i) * M1(i, p) * M3(p, q) * M1(q, j) * evec_i(j, b)) > EPS)
176 vM131vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p, q}, term));
177 if (fabs(term = evec(a, i) * M3(i, p) * M1(p, q) * M1(q, j) * evec_i(j, b)) > EPS)
178 vM311vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p, q}, term));
179 if (fabs(term = evec(a, i) * M3(i, p) * M3(p, q) * M1(q, j) * evec_i(j, b)) > EPS)
180 vM331vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p, q}, term));
181 if (fabs(term = evec(a, i) * M3(i, p) * M1(p, q) * M3(q, j) * evec_i(j, b)) > EPS)
182 vM313vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p, q}, term));
183 if (fabs(term = evec(a, i) * M1(i, p) * M3(p, q) * M3(q, j) * evec_i(j, b)) > EPS)
184 vM133vi[nnf].insert(std::pair<std::vector<uint>, double > ({a, b, i, j, p, q}, term));
185 }
186 }
187 }
188 }
189 }
190}
blocks_nops
std::map< std::string, uint > blocks_nops
Definition EvolDF1.cpp:16
uint
unsigned int uint
Definition EvolDF1.h:20
QED0
@ QED0
Definition OrderScheme.h:91
EvolDF1::gg
gslpp::matrix< double > gg
Definition EvolDF1.h:339
EvolDF1::vM131vi
std::map< std::vector< uint >, double > vM131vi[NF]
Definition EvolDF1.h:331
EvolDF1::vM14vi
std::map< std::vector< uint >, double > vM14vi[NF]
Definition EvolDF1.h:331
EvolDF1::vM34vi
std::map< std::vector< uint >, double > vM34vi[NF]
Definition EvolDF1.h:330
EvolDF1::vM2vi
std::map< std::vector< uint >, double > vM2vi[NF]
Definition EvolDF1.h:329
EvolDF1::nfmin
uint nfmin
Definition EvolDF1.h:336
EvolDF1::vM3vi
std::map< std::vector< uint >, double > vM3vi[NF]
Definition EvolDF1.h:329
EvolDF1::vM5vi
std::map< std::vector< uint >, double > vM5vi[NF]
Definition EvolDF1.h:329
EvolDF1::jv
gslpp::matrix< double > jv
Definition EvolDF1.h:339
EvolDF1::vM311vi
std::map< std::vector< uint >, double > vM311vi[NF]
Definition EvolDF1.h:331
EvolDF1::evec
gslpp::matrix< double > evec
Definition EvolDF1.h:339
EvolDF1::vM133vi
std::map< std::vector< uint >, double > vM133vi[NF]
Definition EvolDF1.h:331
EvolDF1::js
gslpp::matrix< double > js
Definition EvolDF1.h:339
EvolDF1::vM331vi
std::map< std::vector< uint >, double > vM331vi[NF]
Definition EvolDF1.h:331
EvolDF1::nops
uint nops
Definition EvolDF1.h:336
EvolDF1::MAls_cache
double MAls_cache
Definition EvolDF1.h:343
EvolDF1::evecc
gslpp::matrix< gslpp::complex > evecc
Definition EvolDF1.h:341
EvolDF1::AnomalousDimension
gslpp::matrix< double > AnomalousDimension(indices nm, uint n_u, uint n_d) const
a method returning the anomalous dimension matrix given in the Misiak basis
Definition EvolDF1.cpp:1251
EvolDF1::alsM_cache
double alsM_cache
Definition EvolDF1.h:343
EvolDF1::vM33vi
std::map< std::vector< uint >, double > vM33vi[NF]
Definition EvolDF1.h:330
EvolDF1::vM43vi
std::map< std::vector< uint >, double > vM43vi[NF]
Definition EvolDF1.h:330
EvolDF1::jssv
gslpp::matrix< double > jssv
Definition EvolDF1.h:339
EvolDF1::evalc
gslpp::vector< gslpp::complex > evalc
Definition EvolDF1.h:342
EvolDF1::jss
gslpp::matrix< double > jss
Definition EvolDF1.h:339
EvolDF1::vM11vi
std::map< std::vector< uint >, double > vM11vi[NF]
Definition EvolDF1.h:330
EvolDF1::model
const StandardModel & model
Definition EvolDF1.h:333
EvolDF1::vM13vi
std::map< std::vector< uint >, double > vM13vi[NF]
Definition EvolDF1.h:330
EvolDF1::vM313vi
std::map< std::vector< uint >, double > vM313vi[NF]
Definition EvolDF1.h:331
EvolDF1::vM1vi
std::map< std::vector< uint >, double > vM1vi[NF]
Definition EvolDF1.h:329
EvolDF1::vM32vi
std::map< std::vector< uint >, double > vM32vi[NF]
Definition EvolDF1.h:330
EvolDF1::vij
gslpp::matrix< double > vij
Definition EvolDF1.h:339
EvolDF1::h
gslpp::matrix< double > h
Definition EvolDF1.h:339
EvolDF1::vM41vi
std::map< std::vector< uint >, double > vM41vi[NF]
Definition EvolDF1.h:331
EvolDF1::blocks
std::string blocks
Definition EvolDF1.h:337
EvolDF1::vM6vi
std::map< std::vector< uint >, double > vM6vi[NF]
Definition EvolDF1.h:330
EvolDF1::vM0vi
std::map< std::vector< uint >, double > vM0vi[NF]
Definition EvolDF1.h:329
EvolDF1::vM23vi
std::map< std::vector< uint >, double > vM23vi[NF]
Definition EvolDF1.h:330
EvolDF1::nfmax
uint nfmax
Definition EvolDF1.h:336
EvolDF1::vM4vi
std::map< std::vector< uint >, double > vM4vi[NF]
Definition EvolDF1.h:329
EvolDF1::vM113vi
std::map< std::vector< uint >, double > vM113vi[NF]
Definition EvolDF1.h:331
EvolDF1::s_s
gslpp::matrix< double > s_s
Definition EvolDF1.h:339
EvolDF1::evec_i
gslpp::matrix< double > evec_i
Definition EvolDF1.h:339
EvolDF1::vM31vi
std::map< std::vector< uint >, double > vM31vi[NF]
Definition EvolDF1.h:330
EvolDF1::ai
std::map< uint, double > ai[NF]
Definition EvolDF1.h:328
EvolDF1::eval
gslpp::vector< double > eval
Definition EvolDF1.h:340
StandardModel::Beta_s
const double Beta_s(int nm, unsigned int nf) const
QCD beta function coefficients including QED corrections - eq. (36) hep-ph/0512066.
Definition StandardModel/src/StandardModel.cpp:632
StandardModel::Beta_e
const double Beta_e(int nm, unsigned int nf) const
QED beta function coefficients - eq. (36) hep-ph/0512066.
Definition StandardModel/src/StandardModel.cpp:660

◆ ~EvolDF1()

EvolDF1::~EvolDF1 ( )
virtual

EvolDF1 destructor.

Definition at line 192 of file EvolDF1.cpp.

193{
194}

Member Function Documentation

◆ AnomalousDimension()

gslpp::matrix< double > EvolDF1::AnomalousDimension ( indices  nm,
uint  n_u,
uint  n_d 
) const

a method returning the anomalous dimension matrix given in the Misiak basis

Parameters
nmindices nm corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM in the Misiak basis

Definition at line 1251 of file EvolDF1.cpp.

1252{
1253 gslpp::matrix<double> gammaDF1(nops, nops, 0.);
1254
1255 // assign blocks according to user request: "C", "CP", "CPM", "L", "CPML", "CPQB", "CPMQB", "CPMLQB"
1256
1257 if (blocks.compare("C") == 0)
1258 gammaDF1.assign(0, 0, GammaCC(nm, n_u, n_d));
1259 else if (blocks.compare("CP") == 0)
1260 {
1261 gammaDF1.assign(0, 0, GammaCC(nm, n_u, n_d));
1262 gammaDF1.assign(0, 2, GammaCP(nm, n_u, n_d));
1263 gammaDF1.assign(2, 2, GammaPP(nm, n_u, n_d));
1264 } else if (blocks.compare("CPM") == 0)
1265 {
1266 gammaDF1.assign(0, 0, GammaCC(nm, n_u, n_d));
1267 gammaDF1.assign(0, 2, GammaCP(nm, n_u, n_d));
1268 gammaDF1.assign(2, 2, GammaPP(nm, n_u, n_d));
1269 gammaDF1.assign(0, 6, GammaCM(nm, n_u, n_d));
1270 gammaDF1.assign(2, 6, GammaPM(nm, n_u, n_d));
1271 gammaDF1.assign(6, 6, GammaMM(nm, n_u, n_d));
1272 } else if (blocks.compare("CPQ") == 0)
1273 {
1274 gammaDF1.assign(0, 0, GammaCC(nm, n_u, n_d));
1275 gammaDF1.assign(0, 2, GammaCP(nm, n_u, n_d));
1276 gammaDF1.assign(2, 2, GammaPP(nm, n_u, n_d));
1277 gammaDF1.assign(0, 6, GammaCQ(nm, n_u, n_d));
1278 gammaDF1.assign(2, 6, GammaPQ(nm, n_u, n_d));
1279 gammaDF1.assign(6, 2, GammaQP(nm, n_u, n_d));
1280 gammaDF1.assign(6, 6, GammaQQ(nm, n_u, n_d));
1281 } else if (blocks.compare("L") == 0)
1282 {
1283 gammaDF1.assign(0, 0, GammaLL(nm, n_u, n_d));
1284 } else if (blocks.compare("CPL") == 0)
1285 {
1286 gammaDF1.assign(0, 0, GammaCC(nm, n_u, n_d));
1287 gammaDF1.assign(0, 2, GammaCP(nm, n_u, n_d));
1288 gammaDF1.assign(2, 2, GammaPP(nm, n_u, n_d));
1289 gammaDF1.assign(0, 6, GammaCL(nm, n_u, n_d));
1290 gammaDF1.assign(2, 6, GammaPL(nm, n_u, n_d));
1291 gammaDF1.assign(6, 6, GammaLL(nm, n_u, n_d));
1292 } else if (blocks.compare("CPML") == 0)
1293 {
1294 gammaDF1.assign(0, 0, GammaCC(nm, n_u, n_d));
1295 gammaDF1.assign(0, 2, GammaCP(nm, n_u, n_d));
1296 gammaDF1.assign(2, 2, GammaPP(nm, n_u, n_d));
1297 gammaDF1.assign(0, 6, GammaCM(nm, n_u, n_d));
1298 gammaDF1.assign(2, 6, GammaPM(nm, n_u, n_d));
1299 gammaDF1.assign(6, 6, GammaMM(nm, n_u, n_d));
1300 gammaDF1.assign(0, 8, GammaCL(nm, n_u, n_d));
1301 gammaDF1.assign(2, 8, GammaPL(nm, n_u, n_d));
1302 gammaDF1.assign(8, 8, GammaLL(nm, n_u, n_d));
1303 } else if (blocks.compare("CPQB") == 0)
1304 {
1305 gammaDF1.assign(0, 0, GammaCC(nm, n_u, n_d));
1306 gammaDF1.assign(0, 2, GammaCP(nm, n_u, n_d));
1307 gammaDF1.assign(2, 2, GammaPP(nm, n_u, n_d));
1308 gammaDF1.assign(0, 6, GammaCQ(nm, n_u, n_d));
1309 gammaDF1.assign(2, 6, GammaPQ(nm, n_u, n_d));
1310 gammaDF1.assign(6, 2, GammaQP(nm, n_u, n_d));
1311 gammaDF1.assign(6, 6, GammaQQ(nm, n_u, n_d));
1312 gammaDF1.assign(10, 2, GammaBP(nm, n_u, n_d));
1313 gammaDF1.assign(10, 6, GammaBQ(nm, n_u, n_d));
1314 gammaDF1.assign(10, 10, GammaBB(nm, n_u, n_d));
1315 } else if (blocks.compare("CPMQB") == 0)
1316 {
1317 gammaDF1.assign(0, 0, GammaCC(nm, n_u, n_d));
1318 gammaDF1.assign(0, 2, GammaCP(nm, n_u, n_d));
1319 gammaDF1.assign(2, 2, GammaPP(nm, n_u, n_d));
1320 gammaDF1.assign(0, 6, GammaCM(nm, n_u, n_d));
1321 gammaDF1.assign(2, 6, GammaPM(nm, n_u, n_d));
1322 gammaDF1.assign(6, 6, GammaMM(nm, n_u, n_d));
1323 gammaDF1.assign(0, 8, GammaCQ(nm, n_u, n_d));
1324 gammaDF1.assign(2, 8, GammaPQ(nm, n_u, n_d));
1325 gammaDF1.assign(8, 2, GammaQP(nm, n_u, n_d));
1326 gammaDF1.assign(8, 6, GammaQM(nm, n_u, n_d));
1327 gammaDF1.assign(8, 8, GammaQQ(nm, n_u, n_d));
1328 gammaDF1.assign(12, 2, GammaBP(nm, n_u, n_d));
1329 gammaDF1.assign(12, 8, GammaBQ(nm, n_u, n_d));
1330 gammaDF1.assign(12, 12, GammaBB(nm, n_u, n_d)); // *** does BM exists?
1331 } else if (blocks.compare("CPMLQB") == 0)
1332 {
1333 gammaDF1.assign(0, 0, GammaCC(nm, n_u, n_d));
1334 gammaDF1.assign(0, 2, GammaCP(nm, n_u, n_d));
1335 gammaDF1.assign(2, 2, GammaPP(nm, n_u, n_d));
1336 gammaDF1.assign(0, 6, GammaCM(nm, n_u, n_d));
1337 gammaDF1.assign(2, 6, GammaPM(nm, n_u, n_d));
1338 gammaDF1.assign(6, 6, GammaMM(nm, n_u, n_d));
1339 gammaDF1.assign(0, 8, GammaCL(nm, n_u, n_d));
1340 gammaDF1.assign(2, 8, GammaPL(nm, n_u, n_d));
1341 gammaDF1.assign(8, 8, GammaLL(nm, n_u, n_d));
1342
1343 gammaDF1.assign(0, 10, GammaCQ(nm, n_u, n_d));
1344 gammaDF1.assign(2, 10, GammaPQ(nm, n_u, n_d));
1345 gammaDF1.assign(10, 2, GammaQP(nm, n_u, n_d));
1346 gammaDF1.assign(10, 6, GammaQM(nm, n_u, n_d));
1347 gammaDF1.assign(10, 8, GammaQL(nm, n_u, n_d));
1348 gammaDF1.assign(10, 10, GammaQQ(nm, n_u, n_d));
1349 gammaDF1.assign(14, 2, GammaBP(nm, n_u, n_d));
1350 gammaDF1.assign(14, 8, GammaBL(nm, n_u, n_d));
1351 gammaDF1.assign(14, 10, GammaBQ(nm, n_u, n_d));
1352 gammaDF1.assign(14, 14, GammaBB(nm, n_u, n_d)); // *** does BM exists?
1353 } else
1354 throw std::runtime_error("EvolDF1::AnomalousDimension(): block not implemented");
1355
1356 return (gammaDF1);
1357}
EvolDF1::GammaQQ
gslpp::matrix< double > GammaQQ(indices nm, uint n_u, uint n_d) const
QQ block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:1030
EvolDF1::GammaCP
gslpp::matrix< double > GammaCP(indices nm, uint n_u, uint n_d) const
CP block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:330
EvolDF1::GammaBL
gslpp::matrix< double > GammaBL(indices nm, uint n_u, uint n_d) const
BL block of the QED anomalous dimension.
Definition EvolDF1.cpp:1154
EvolDF1::GammaBB
gslpp::matrix< double > GammaBB(indices nm, uint n_u, uint n_d) const
BB block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:1215
EvolDF1::GammaBP
gslpp::matrix< double > GammaBP(indices nm, uint n_u, uint n_d) const
BP block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:1116
EvolDF1::GammaMM
gslpp::matrix< double > GammaMM(indices nm, uint n_u, uint n_d) const
MM block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:796
EvolDF1::GammaQL
gslpp::matrix< double > GammaQL(indices nm, uint n_u, uint n_d) const
QL block of the QED anomalous dimension.
Definition EvolDF1.cpp:994
EvolDF1::GammaCL
gslpp::matrix< double > GammaCL(indices nm, uint n_u, uint n_d) const
CL block of the QED anomalous dimension.
Definition EvolDF1.cpp:442
EvolDF1::GammaBQ
gslpp::matrix< double > GammaBQ(indices nm, uint n_u, uint n_d) const
BQ block of the QED anomalous dimension.
Definition EvolDF1.cpp:1184
EvolDF1::GammaPL
gslpp::matrix< double > GammaPL(indices nm, uint n_u, uint n_d) const
PL block of the QED anomalous dimension.
Definition EvolDF1.cpp:689
EvolDF1::GammaPP
gslpp::matrix< double > GammaPP(indices nm, uint n_u, uint n_d) const
PP block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:521
EvolDF1::GammaPM
gslpp::matrix< double > GammaPM(indices nm, uint n_u, uint n_d) const
PM block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:611
EvolDF1::GammaPQ
gslpp::matrix< double > GammaPQ(indices nm, uint n_u, uint n_d) const
PQ block of the QED anomalous dimension.
Definition EvolDF1.cpp:742
EvolDF1::GammaCM
gslpp::matrix< double > GammaCM(indices nm, uint n_u, uint n_d) const
CM block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:384
EvolDF1::GammaCQ
gslpp::matrix< double > GammaCQ(indices nm, uint n_u, uint n_d) const
CQ block of the QED anomalous dimension.
Definition EvolDF1.cpp:484
EvolDF1::GammaCC
gslpp::matrix< double > GammaCC(indices nm, uint n_u, uint n_d) const
CC block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:279
EvolDF1::GammaQP
gslpp::matrix< double > GammaQP(indices nm, uint n_u, uint n_d) const
QP block of the QCD+QED anomalous dimension.
Definition EvolDF1.cpp:883
EvolDF1::GammaLL
gslpp::matrix< double > GammaLL(indices nm, uint n_u, uint n_d) const
LL block of the QED anomalous dimension.
Definition EvolDF1.cpp:850
EvolDF1::GammaQM
gslpp::matrix< double > GammaQM(indices nm, uint n_u, uint n_d) const
QM block of the QCD anomalous dimension.
Definition EvolDF1.cpp:959

◆ CheckNf()

void EvolDF1::CheckNf ( indices  nm,
uint  nf 
) const
private

a method returning the anomalous dimension in the Chetyrkin, Misiak and Munz operator basis

Parameters
orderan enum "orders" for the order of perturbation theory of the evolutor
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM at the order LO/NLO in the Chetyrkin, Misiak and Munz basis

a method returning the anomalous dimension for the evolution of the effective Wilson coefficients

Parameters
mata temporary variable of gslpp::matrix type
Returns
the ADM at the order LO/NLO for the effective Wilson coefficients
Parameters
aarray of double for the magic numbers of the evolutor ( LO evolution )
barray of double for the magic numbers of the evolutor ( LO evolution )
carray of double for the magic numbers of the evolutor ( NLO evolution, associated to \( \alpha_{strong}(\mu) \) )
darray of double for the magic numbers of the evolutor ( NLO evolution, associated to \( \alpha_{strong}(M) \) )

Check if anomalous dimension indices and Nf match

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
nfnumber of active flavours

Definition at line 269 of file EvolDF1.cpp.

270{
271 if (nm % 10 == 0)
272 {
273 if (!(nf == 3 || nf == 4 || nf == 5 || nf == 6))
274 throw std::runtime_error("EvolDF1::CheckNf(): Wrong number of flavours in anoumalous dimensions");
275 } else if (nf != 5)
276 throw std::runtime_error("EvolDF1::CheckNf(): Wrong number of flavours in anoumalous dimensions");
277}

◆ DF1Ev()

void EvolDF1::DF1Ev ( double  mu,
double  M,
int  nf,
schemes  scheme 
)
private

a void type method storing properly the magic numbers for the implementation of the evolutor

Parameters
mua double for the low scale of the evolution
Ma double for the high scale of the evolution
nfa double for the active number of flavors
schemean enum "schemes" for the regularization scheme of the evolutor

Definition at line 1453 of file EvolDF1.cpp.

1454{
1455 gslpp::matrix<double> mtmp(nops, 0.);
1456 std::vector<std::vector<gslpp::matrix<double> > > vtmp2;
1457 std::vector<gslpp::matrix<double> > vtmp;
1458 for (int j = 0; j <= order_qed; j++)
1459 vtmp.push_back(mtmp);
1460 for (int i = 0; i <= order_qcd; i++)
1461 vtmp2.push_back(vtmp);
1462 Expanded<gslpp::matrix<double> > res(vtmp2);
1463 // gslpp::matrix<double> res01(nops, 0.), res02(nops, 0.), res11(nops, 0.), res12(nops, 0.),
1464 // res21(nops, 0.), resLO(nops, 0.), resNLO(nops, 0.), resNNLO(nops, 0.);
1465
1466 // uint a, b, i, j, p, q
1467 uint nnf = nf - nfmin;
1468 double b0, b0e, b5, alsM, eta, omega, lambda; //, term;
1469 std::map< std::vector<uint>, double >::iterator itr;
1470 // std::vector<uint> v;
1471
1472
1473 // alsM = model.Als(M) / 4. / M_PI;
1474 // double alsmu = model.Als(mu) / 4. / M_PI;
1475 b0 = model.Beta_s(00, nf);
1476 alsM = model.Als(M, FULLNNNLO, true, order_qed == QED0 ? false : true);
1477 eta = alsM / model.Als(mu, FULLNNNLO, true, order_qed == QED0 ? false : true);
1478 // eta = alsM / model.Als(mu);
1479 omega = 2. * b0 * alsM / 4. / M_PI;
1480
1481 for (itr = vM0vi[nnf].begin(); itr != vM0vi[nnf].end(); ++itr)
1482 {
1483 const std::vector<uint> &v = itr->first;
1484 const uint &a = v[0];
1485 const uint &b = v[1];
1486 const uint &i = v[2];
1487
1488 res.setMatrixElement(QCD0, QED0, a, b, res.getOrd(QCD0, QED0)(a, b) + itr->second * pow(eta, ai[nnf].at(i)));
1489 }
1490
1491 for (itr = vM1vi[nnf].begin(); itr != vM1vi[nnf].end(); ++itr)
1492 {
1493 const std::vector<uint> &v = itr->first;
1494 const uint &a = v[0];
1495 const uint &b = v[1];
1496 const uint &i = v[2];
1497 const uint &j = v[3];
1498
1499 res.setMatrixElement(QCD1, QED0, a, b, res.getOrd(QCD1, QED0)(a, b) + omega * itr->second * f_f(nnf, i, j, -1, eta));
1500 }
1501
1502 for (itr = vM2vi[nnf].begin(); itr != vM2vi[nnf].end(); ++itr)
1503 {
1504 const std::vector<uint> &v = itr->first;
1505 const uint &a = v[0];
1506 const uint &b = v[1];
1507 const uint &i = v[2];
1508 const uint &j = v[3];
1509
1510 res.setMatrixElement(QCD2, QED0, a, b, res.getOrd(QCD2, QED0)(a, b) + omega * omega * itr->second * f_f(nnf, i, j, -2, eta));
1511 }
1512
1513 for (itr = vM11vi[nnf].begin(); itr != vM11vi[nnf].end(); ++itr)
1514 {
1515 const std::vector<uint> &v = itr->first;
1516 const uint &a = v[0];
1517 const uint &b = v[1];
1518 const uint &i = v[2];
1519 const uint &j = v[3];
1520 const uint &p = v[4];
1521
1522 res.setMatrixElement(QCD2, QED0, a, b, res.getOrd(QCD2, QED0)(a, b) + omega * omega * itr->second * f_g(nnf, i, p, j, -1, -1, eta));
1523 }
1524
1525 if (order_qed != QED0)
1526 {
1527 b0e = model.Beta_e(00, nf);
1528 b5 = model.Beta_e(01, nf) / 2. / b0 / b0e - model.Beta_s(10, nf) / 2. / b0 / b0;
1529 lambda = b0e * model.Ale(M, FULLNLO) / b0 / model.Als(M, FULLNNNLO, true, true); // WARNING: CHANGE ME!!!
1530
1531 for (itr = vM3vi[nnf].begin(); itr != vM3vi[nnf].end(); ++itr)
1532 {
1533 const std::vector<uint> &v = itr->first;
1534 const uint &a = v[0];
1535 const uint &b = v[1];
1536 const uint &i = v[2];
1537 const uint &j = v[3];
1538 const double &term = itr->second;
1539
1540 res.setMatrixElement(QCD0, QED1, a, b, res.getOrd(QCD0, QED1)(a, b) + lambda * term * f_f(nnf, i, j, 1, eta));
1541 res.setMatrixElement(QCD0, QED2, a, b, res.getOrd(QCD0, QED2)(a, b) + lambda * lambda * term * (f_f(nnf, i, j, 2, eta) - f_f(nnf, i, j, 1, eta)));
1542 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) + omega * lambda * lambda * b5 * term * f_r(nnf, i, j, 1, eta));
1543 }
1544
1545 for (itr = vM4vi[nnf].begin(); itr != vM4vi[nnf].end(); ++itr)
1546 {
1547 const std::vector<uint> &v = itr->first;
1548 const uint &a = v[0];
1549 const uint &b = v[1];
1550 const uint &i = v[2];
1551 const uint &j = v[3];
1552 const double &term = itr->second;
1553
1554 res.setMatrixElement(QCD1, QED1, a, b, res.getOrd(QCD1, QED1)(a, b) + omega * lambda * term * f_f(nnf, i, j, 0, eta));
1555 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) - omega * lambda * lambda * term * f_f(nnf, i, j, 0, eta));
1556 }
1557
1558 for (itr = vM5vi[nnf].begin(); itr != vM5vi[nnf].end(); ++itr)
1559 {
1560 const std::vector<uint> &v = itr->first;
1561 const uint &a = v[0];
1562 const uint &b = v[1];
1563 const uint &i = v[2];
1564 const uint &j = v[3];
1565
1566 res.setMatrixElement(QCD2, QED1, a, b, res.getOrd(QCD2, QED1)(a, b) + omega * omega * lambda * itr->second * f_f(nnf, i, j, -1, eta));
1567 }
1568
1569 for (itr = vM6vi[nnf].begin(); itr != vM6vi[nnf].end(); ++itr)
1570 {
1571 const std::vector<uint> &v = itr->first;
1572 const uint &a = v[0];
1573 const uint &b = v[1];
1574 const uint &i = v[2];
1575 const uint &j = v[3];
1576
1577 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) + omega * lambda * lambda * itr->second * f_f(nnf, i, j, 1, eta));
1578 }
1579
1580 for (itr = vM33vi[nnf].begin(); itr != vM33vi[nnf].end(); ++itr)
1581 {
1582 const std::vector<uint> &v = itr->first;
1583 const uint &a = v[0];
1584 const uint &b = v[1];
1585 const uint &i = v[2];
1586 const uint &j = v[3];
1587 const uint &p = v[4];
1588
1589 res.setMatrixElement(QCD0, QED2, a, b, res.getOrd(QCD0, QED2)(a, b) + lambda * lambda * itr->second * f_g(nnf, i, p, j, 1, 1, eta));
1590 }
1591
1592 for (itr = vM13vi[nnf].begin(); itr != vM13vi[nnf].end(); ++itr)
1593 {
1594 const std::vector<uint> &v = itr->first;
1595 const uint &a = v[0];
1596 const uint &b = v[1];
1597 const uint &i = v[2];
1598 const uint &j = v[3];
1599 const uint &p = v[4];
1600 const double &term = itr->second;
1601
1602 res.setMatrixElement(QCD1, QED1, a, b, res.getOrd(QCD1, QED1)(a, b) + omega * lambda * term * f_g(nnf, i, p, j, -1, 1, eta));
1603 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) + omega * lambda * lambda * term * (f_g(nnf, i, p, j, -1, 2, eta) - f_g(nnf, i, p, j, -1, 1, eta)));
1604 }
1605
1606 for (itr = vM31vi[nnf].begin(); itr != vM31vi[nnf].end(); ++itr)
1607 {
1608 const std::vector<uint> &v = itr->first;
1609 const uint &a = v[0];
1610 const uint &b = v[1];
1611 const uint &i = v[2];
1612 const uint &j = v[3];
1613 const uint &p = v[4];
1614 const double &term = itr->second;
1615
1616 res.setMatrixElement(QCD1, QED1, a, b, res.getOrd(QCD1, QED1)(a, b) + omega * lambda * term * f_g(nnf, i, p, j, 1, -1, eta));
1617 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) + omega * lambda * lambda * term * (f_g(nnf, i, p, j, 2, -1, eta) - f_g(nnf, i, p, j, 1, -1, eta)));
1618 }
1619
1620 for (itr = vM34vi[nnf].begin(); itr != vM34vi[nnf].end(); ++itr)
1621 {
1622 const std::vector<uint> &v = itr->first;
1623 const uint &a = v[0];
1624 const uint &b = v[1];
1625 const uint &i = v[2];
1626 const uint &j = v[3];
1627 const uint &p = v[4];
1628
1629 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) + omega * lambda * lambda * itr->second * f_g(nnf, i, p, j, 1, 0, eta));
1630 }
1631
1632 for (itr = vM43vi[nnf].begin(); itr != vM43vi[nnf].end(); ++itr)
1633 {
1634 const std::vector<uint> &v = itr->first;
1635 const uint &a = v[0];
1636 const uint &b = v[1];
1637 const uint &i = v[2];
1638 const uint &j = v[3];
1639 const uint &p = v[4];
1640
1641 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) + omega * lambda * lambda * itr->second * f_g(nnf, i, p, j, 0, 1, eta));
1642 }
1643
1644 for (itr = vM23vi[nnf].begin(); itr != vM23vi[nnf].end(); ++itr)
1645 {
1646 const std::vector<uint> &v = itr->first;
1647 const uint &a = v[0];
1648 const uint &b = v[1];
1649 const uint &i = v[2];
1650 const uint &j = v[3];
1651 const uint &p = v[4];
1652
1653 res.setMatrixElement(QCD2, QED1, a, b, res.getOrd(QCD2, QED1)(a, b) + omega * omega * lambda * itr->second * f_g(nnf, i, p, j, -2, 1, eta));
1654 }
1655
1656 for (itr = vM32vi[nnf].begin(); itr != vM32vi[nnf].end(); ++itr)
1657 {
1658 const std::vector<uint> &v = itr->first;
1659 const uint &a = v[0];
1660 const uint &b = v[1];
1661 const uint &i = v[2];
1662 const uint &j = v[3];
1663 const uint &p = v[4];
1664
1665 res.setMatrixElement(QCD2, QED1, a, b, res.getOrd(QCD2, QED1)(a, b) + omega * omega * lambda * itr->second * f_g(nnf, i, p, j, 1, -2, eta));
1666 }
1667
1668 for (itr = vM14vi[nnf].begin(); itr != vM14vi[nnf].end(); ++itr)
1669 {
1670 const std::vector<uint> &v = itr->first;
1671 const uint &a = v[0];
1672 const uint &b = v[1];
1673 const uint &i = v[2];
1674 const uint &j = v[3];
1675 const uint &p = v[4];
1676
1677 res.setMatrixElement(QCD2, QED1, a, b, res.getOrd(QCD2, QED1)(a, b) + omega * omega * lambda * itr->second * f_g(nnf, i, p, j, -1, 0, eta));
1678 }
1679
1680 for (itr = vM41vi[nnf].begin(); itr != vM41vi[nnf].end(); ++itr)
1681 {
1682 const std::vector<uint> &v = itr->first;
1683 const uint &a = v[0];
1684 const uint &b = v[1];
1685 const uint &i = v[2];
1686 const uint &j = v[3];
1687 const uint &p = v[4];
1688
1689 res.setMatrixElement(QCD2, QED1, a, b, res.getOrd(QCD2, QED1)(a, b) + omega * omega * lambda * itr->second * f_g(nnf, i, p, j, 0, -1, eta));
1690 }
1691
1692 for (itr = vM113vi[nnf].begin(); itr != vM113vi[nnf].end(); ++itr)
1693 {
1694 const std::vector<uint> &v = itr->first;
1695 const uint &a = v[0];
1696 const uint &b = v[1];
1697 const uint &i = v[2];
1698 const uint &j = v[3];
1699 const uint &p = v[4];
1700 const uint &q = v[5];
1701
1702 res.setMatrixElement(QCD2, QED1, a, b, res.getOrd(QCD2, QED1)(a, b) + omega * omega * lambda * itr->second * f_h(nnf, i, p, q, j, -1, -1, 1, eta));
1703 }
1704
1705 for (itr = vM131vi[nnf].begin(); itr != vM131vi[nnf].end(); ++itr)
1706 {
1707 const std::vector<uint> &v = itr->first;
1708 const uint &a = v[0];
1709 const uint &b = v[1];
1710 const uint &i = v[2];
1711 const uint &j = v[3];
1712 const uint &p = v[4];
1713 const uint &q = v[5];
1714
1715 res.setMatrixElement(QCD2, QED1, a, b, res.getOrd(QCD2, QED1)(a, b) + omega * omega * lambda * itr->second * f_h(nnf, i, p, q, j, -1, 1, -1, eta));
1716 }
1717
1718 for (itr = vM311vi[nnf].begin(); itr != vM311vi[nnf].end(); ++itr)
1719 {
1720 const std::vector<uint> &v = itr->first;
1721 const uint &a = v[0];
1722 const uint &b = v[1];
1723 const uint &i = v[2];
1724 const uint &j = v[3];
1725 const uint &p = v[4];
1726 const uint &q = v[5];
1727
1728 res.setMatrixElement(QCD2, QED1, a, b, res.getOrd(QCD2, QED1)(a, b) + omega * omega * lambda * itr->second * f_h(nnf, i, p, q, j, 1, -1, -1, eta));
1729 }
1730
1731 for (itr = vM133vi[nnf].begin(); itr != vM133vi[nnf].end(); ++itr)
1732 {
1733 const std::vector<uint> &v = itr->first;
1734 const uint &a = v[0];
1735 const uint &b = v[1];
1736 const uint &i = v[2];
1737 const uint &j = v[3];
1738 const uint &p = v[4];
1739 const uint &q = v[5];
1740
1741 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) + omega * lambda * lambda * itr->second * f_h(nnf, i, p, q, j, -1, 1, 1, eta));
1742 }
1743
1744 for (itr = vM313vi[nnf].begin(); itr != vM313vi[nnf].end(); ++itr)
1745 {
1746 const std::vector<uint> &v = itr->first;
1747 const uint &a = v[0];
1748 const uint &b = v[1];
1749 const uint &i = v[2];
1750 const uint &j = v[3];
1751 const uint &p = v[4];
1752 const uint &q = v[5];
1753
1754 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) + omega * lambda * lambda * itr->second * f_h(nnf, i, p, q, j, 1, -1, 1, eta));
1755 }
1756
1757 for (itr = vM331vi[nnf].begin(); itr != vM331vi[nnf].end(); ++itr)
1758 {
1759 const std::vector<uint> &v = itr->first;
1760 const uint &a = v[0];
1761 const uint &b = v[1];
1762 const uint &i = v[2];
1763 const uint &j = v[3];
1764 const uint &p = v[4];
1765 const uint &q = v[5];
1766
1767 res.setMatrixElement(QCD1, QED2, a, b, res.getOrd(QCD1, QED2)(a, b) + omega * lambda * lambda * itr->second * f_h(nnf, i, p, q, j, 1, 1, -1, eta));
1768 }
1769 /*
1770 for (a = 0; a < nops; a++)
1771 for (b = 0; b < nops; b++)
1772 {
1773 for (i = 0; i < nops; i++)
1774 for (j = 0; j < nops; j++)
1775 {
1776 res01(a, b) += (lambda * vM3vi.at(idx(nf, a, b, i, j)) * f_f(nf, i, j, 1, eta)).real();
1777 res02(a, b) += (lambda * lambda * vM3vi.at(idx(nf, a, b, i, j)) * (f_f(nf, i, j, 2, eta) - f_f(nf, i, j, 1, eta))).real();
1778 res11(a, b) += (omega * lambda * vM4vi.at(idx(nf, a, b, i, j)) * f_f(nf, i, j, 0, eta)).real();
1779 res12(a, b) += (omega * lambda * lambda * (-vM4vi.at(idx(nf, a, b, i, j)) * f_f(nf, i, j, 0, eta) + vM6vi.at(idx(nf, a, b, i, j)) * f_f(nf, i, j, 1, eta)) +
1780 b5 * vM3vi.at(idx(nf, a, b, i, j)) * f_r(nf, i, j, 1, eta)).real();
1781 res21(a, b) += (omega * omega * lambda * vM5vi.at(idx(nf, a, b, i, j)) * f_f(nf, i, j, -1, eta)).real();
1782 for (p = 0; p < nops; p++)
1783 {
1784 res02(a, b) += (lambda * lambda * vM33vi.at(idx(nf, a, b, i, j, p)) * f_g(nf, i, p, j, 1, 1, eta)).real();
1785 res11(a, b) += (omega * lambda * (vM13vi.at(idx(nf, a, b, i, j, p)) * f_g(nf, i, p, j, -1, 1, eta) + vM31vi.at(idx(nf, a, b, i, j, p)) * f_g(nf, i, p, j, 1, -1, eta))).real();
1786 res12(a, b) += (omega * lambda * lambda * (vM13vi.at(idx(nf, a, b, i, j, p)) * (f_g(nf, i, p, j, -1, 2, eta) - f_g(nf, i, p, j, -1, 1, eta)) +
1787 vM31vi.at(idx(nf, a, b, i, j, p)) * (f_g(nf, i, p, j, 2, -1, eta) - f_g(nf, i, p, j, 1, -1, eta)) + vM34vi.at(idx(nf, a, b, i, j, p)) * f_g(nf, i, p, j, 1, 0, eta) +
1788 vM43vi.at(idx(nf, a, b, i, j, p)) * f_g(nf, i, p, j, 0, 1, eta))).real();
1789 res21(a, b) += (omega * omega * lambda * (vM14vi.at(idx(nf, a, b, i, j, p)) * f_g(nf, i, p, j, -1, 0, eta) + vM41vi.at(idx(nf, a, b, i, j, p)) * f_g(nf, i, p, j, 0, -1, eta) +
1790 vM23vi.at(idx(nf, a, b, i, j, p)) * f_g(nf, i, p, j, -2, 1, eta) + vM32vi.at(idx(nf, a, b, i, j, p)) * f_g(nf, i, p, j, 1, -2, eta))).real();
1791
1792 for (q = 0; q < nops; q++)
1793 {
1794 res12(a, b) += (omega * lambda * lambda * (vM133vi.at(idx(nf, a, b, i, j, p, q)) * f_h(nf, i, p, q, j, -1, 1, 1, eta) + vM313vi.at(idx(nf, a, b, i, j, p, q)) *
1795 f_h(nf, i, p, q, j, 1, -1, 1, eta) + vM331vi.at(idx(nf, a, b, i, j, p, q)) * f_h(nf, i, p, q, j, 1, 1, -1, eta))).real();
1796 res21(a, b) += (omega * omega * lambda * (vM113vi.at(idx(nf, a, b, i, j, p, q)) * f_h(nf, i, p, q, j, -1, -1, 1, eta) + vM131vi.at(idx(nf, a, b, i, j, p, q)) *
1797 f_h(nf, i, p, q, j, -1, 1, -1, eta) + vM311vi.at(idx(nf, a, b, i, j, p, q)) * f_h(nf, i, p, q, j, 1, -1, -1, eta))).real();
1798 }
1799 }
1800 }
1801 if (fabs(res01(a, b)) < EPS) res01(a, b) = 0.;
1802 if (fabs(res02(a, b)) < EPS) res02(a, b) = 0.;
1803 if (fabs(res11(a, b)) < EPS) res11(a, b) = 0.;
1804 if (fabs(res12(a, b)) < EPS) res12(a, b) = 0.;
1805 if (fabs(res21(a, b)) < EPS) res21(a, b) = 0.;
1806 }
1807 */
1808 for (uint a = 0; a < nops; a++)
1809 for (uint b = 0; b < nops; b++)
1810 {
1811 if (fabs(res.getOrd(QCD0, QED0)(a, b)) < EPS) res.setMatrixElement(QCD0, QED0, a, b, 0.);
1812 if (fabs(res.getOrd(QCD1, QED0)(a, b)) < EPS) res.setMatrixElement(QCD1, QED0, a, b, 0.);
1813 if (fabs(res.getOrd(QCD2, QED0)(a, b)) < EPS) res.setMatrixElement(QCD2, QED0, a, b, 0.);
1814 if (fabs(res.getOrd(QCD0, QED1)(a, b)) < EPS) res.setMatrixElement(QCD0, QED1, a, b, 0.);
1815 if (fabs(res.getOrd(QCD0, QED2)(a, b)) < EPS) res.setMatrixElement(QCD0, QED2, a, b, 0.);
1816 if (fabs(res.getOrd(QCD1, QED1)(a, b)) < EPS) res.setMatrixElement(QCD1, QED1, a, b, 0.);
1817 if (fabs(res.getOrd(QCD1, QED2)(a, b)) < EPS) res.setMatrixElement(QCD1, QED2, a, b, 0.);
1818 if (fabs(res.getOrd(QCD2, QED1)(a, b)) < EPS) res.setMatrixElement(QCD2, QED1, a, b, 0.);
1819 }
1820 } else
1821 for (uint a = 0; a < nops; a++)
1822 for (uint b = 0; b < nops; b++)
1823 {
1824 if (fabs(res.getOrd(QCD0, QED0)(a, b)) < EPS) res.setMatrixElement(QCD0, QED0, a, b, 0.);
1825 if (fabs(res.getOrd(QCD1, QED0)(a, b)) < EPS) res.setMatrixElement(QCD1, QED0, a, b, 0.);
1826 if (fabs(res.getOrd(QCD2, QED0)(a, b)) < EPS) res.setMatrixElement(QCD2, QED0, a, b, 0.);
1827 }
1828
1829 wilson = res * wilson;
1830}
FULLNNNLO
@ FULLNNNLO
Definition OrderScheme.h:40
FULLNLO
@ FULLNLO
Definition OrderScheme.h:38
QED1
@ QED1
Definition OrderScheme.h:92
QED2
@ QED2
Definition OrderScheme.h:93
QCD1
@ QCD1
Definition OrderScheme.h:76
QCD0
@ QCD0
Definition OrderScheme.h:75
QCD2
@ QCD2
Definition OrderScheme.h:77
EvolDF1::f_h
double f_h(uint nf, uint i, uint p, uint q, uint j, int k, int l, int m, double eta)
auxiliary function h - eq. (53) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
Definition EvolDF1.cpp:253
EvolDF1::f_f
double f_f(uint nf, uint i, uint j, int k, double eta)
auxiliary function f - eq. (50) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
Definition EvolDF1.cpp:206
EvolDF1::f_r
double f_r(uint nf, uint i, uint j, int k, double eta)
auxiliary function r - eq. (51) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
Definition EvolDF1.cpp:233
EvolDF1::f_g
double f_g(uint nf, uint i, uint p, uint j, int k, int l, double eta)
auxiliary function g - eq. (52) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
Definition EvolDF1.cpp:243
StandardModel::Ale
const double Ale(double mu, orders order, bool Nf_thr=true) const
The running electromagnetic coupling in the scheme.
Definition StandardModel/src/StandardModel.cpp:783
StandardModel::Als
const double Als(const double mu, const orders order, const bool Nf_thr, const bool qed_flag) const
The running QCD coupling in the scheme including QED corrections.
Definition StandardModel.h:1120
WilsonTemplateNew< gslpp::matrix< double > >::wilson
Expanded< gslpp::matrix< double > > wilson
Definition WilsonTemplateNew.h:118

◆ DF1Evol()

const Expanded< gslpp::matrix< double > > & EvolDF1::DF1Evol ( double  mu,
double  M,
schemes  scheme = NDR 
)

a method returning the evolutor related to the high scale \( M \) and the low scale \( \mu \)

Parameters
mua double for the low scale of the evolution
Ma double for the high scale of the evolution
orderan enum "orders" for the order of perturbation theory of the evolutor
schemean enum "schemes" for the regularization scheme of the evolutor
Returns
the evolutor \( U (\mu , M) \)

Definition at line 1359 of file EvolDF1.cpp.

1360{
1361 if (nfmin == 5 && nfmax == 5 && (model.Nf(mu) != 5. || model.Nf(M) != 5.))
1362 throw std::runtime_error("EvolDF1::Df1Evol(): only nf = 5 available.");
1363
1364 switch (scheme)
1365 {
1366 case NDR:
1367 break;
1368 case LRI:
1369 case HV:
1370 default:
1371 std::stringstream out;
1372 out << scheme;
1373 throw std::runtime_error("EvolDF1::Df1Evol(): scheme " + out.str() + " not implemented ");
1374 }
1375
1376 double alsM = model.getAlsM();
1377 double MAls = model.getMAls();
1378 if (alsM == alsM_cache && MAls == MAls_cache)
1379 {
1380 if (mu == this->mu && M == this->M && scheme == this->scheme)
1381 return (getEvol());
1382 }
1383 alsM_cache = alsM;
1384 MAls_cache = MAls;
1385
1386 if (M < mu)
1387 {
1388 std::stringstream out;
1389 out << "M = " << M << " < mu = " << mu;
1390 throw std::runtime_error("EvolDF1::Df1Evol(): " + out.str() + ".");
1391 }
1392
1393 setScales(mu, M); // also assign evol to identity
1394
1395 double m_down = mu;
1396 double m_up = model.AboveTh(m_down);
1397 double nf = model.Nf(m_down);
1398
1399 while (m_up < M)
1400 { // where are the nf thresholds? ???? <<<<<<<<<<
1401 DF1Ev(m_down, m_up, (int) nf, scheme);
1402 m_down = m_up;
1403 m_up = model.AboveTh(m_down);
1404 nf += 1.;
1405 }
1406 DF1Ev(m_down, M, (int) nf, scheme);
1407
1408 return (getEvol());
1409}
HV
@ HV
Definition OrderScheme.h:22
LRI
@ LRI
Definition OrderScheme.h:23
NDR
@ NDR
Definition OrderScheme.h:21
EvolDF1::DF1Ev
void DF1Ev(double mu, double M, int nf, schemes scheme)
a void type method storing properly the magic numbers for the implementation of the evolutor
Definition EvolDF1.cpp:1453
QCD::getAlsM
const double getAlsM() const
A get method to access the value of .
Definition QCD.h:555
QCD::AboveTh
const double AboveTh(const double mu) const
The active flavour threshold above the scale as defined in QCD::Thresholds().
Definition QCD.cpp:547
QCD::Nf
const double Nf(const double mu) const
The number of active flavour at scale .
Definition QCD.cpp:571
QCD::getMAls
const double getMAls() const
A get method to access the mass scale at which the strong coupling constant measurement is provided.
Definition QCD.h:564
RGEvolutorNew::getEvol
const Expanded< gslpp::matrix< double > > & getEvol() const
Definition RGEvolutorNew.cpp:37
RGEvolutorNew::setScales
void setScales(double mu, double M)
Sets the upper and lower scale for the running of the Wilson Coefficients.
Definition RGEvolutorNew.cpp:47

◆ f_f()

double EvolDF1::f_f ( uint  nf,
uint  i,
uint  j,
int  k,
double  eta 
)
private

auxiliary function f - eq. (50) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066

Parameters
imatrix index
jmatrix index
korder index
etaals(M)/als(mu)
Returns
function value

Definition at line 206 of file EvolDF1.cpp.

207{
208 for (int il = 0; il < F_iCacheSize; il++)
209 if (f_f_c[0][il] == (int) nnf && f_f_c[1][il] == (int) i && f_f_c[2][il] == (int) j &&
210 f_f_c[3][il] == k && f_f_d[0][il] == eta)
211 return f_f_d[1][il];
212
213 double aii = ai[nnf].at(i), aij = ai[nnf].at(j);
214 double den = aij + k - aii, ret;
215
216 if (fabs(den) < EPS)
217 ret = pow(eta, aii) * log(eta);
218 else
219 ret = (pow(eta, aij + k) - pow(eta, aii)) / den;
220
221 model.CacheShift(f_f_c, 4);
222 model.CacheShift(f_f_d, 2);
223 f_f_c[0][0] = (int) nnf;
224 f_f_c[1][0] = (int) i;
225 f_f_c[2][0] = (int) j;
226 f_f_c[3][0] = k;
227 f_f_d[0][0] = eta;
228 f_f_d[1][0] = ret;
229
230 return ret;
231}
EvolDF1::f_f_d
double f_f_d[2][F_iCacheSize]
Definition EvolDF1.h:348
EvolDF1::f_f_c
int f_f_c[4][F_iCacheSize]
Definition EvolDF1.h:347
QCD::CacheShift
void CacheShift(double cache[][5], int n) const
A member used to manage the caching for this class.

◆ f_g()

double EvolDF1::f_g ( uint  nf,
uint  i,
uint  p,
uint  j,
int  k,
int  l,
double  eta 
)
private

auxiliary function g - eq. (52) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066

Parameters
imatrix index
pmatrix index
jmatrix index
korder index
lorder index
etaals(M)/als(mu)
Returns
function value

Definition at line 243 of file EvolDF1.cpp.

244{
245 double den = ai[nnf].at(j) + l - ai[nnf].at(p);
246
247 if (fabs(den) < EPS)
248 return (f_r(nnf, i, p, k, eta));
249 else
250 return ((f_f(nnf, i, j, k + l, eta) - f_f(nnf, i, p, k, eta)) / den);
251}

◆ f_h()

double EvolDF1::f_h ( uint  nf,
uint  i,
uint  p,
uint  q,
uint  j,
int  k,
int  l,
int  m,
double  eta 
)
private

auxiliary function h - eq. (53) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066

Parameters
imatrix index
pmatrix index
qmatrix index
jmatrix index
korder index
lorder index
morder index
etaals(M)/als(mu)
Returns
function value

Definition at line 253 of file EvolDF1.cpp.

254{
255 double ll = log(eta), den1 = ai[nnf].at(j) + m - ai[nnf].at(q),
256 den2 = ai[nnf].at(q) + l - ai[nnf].at(p),
257 den3 = ai[nnf].at(p) + k - ai[nnf].at(i);
258
259 if (fabs(den1) < EPS && fabs(den2) < EPS && fabs(den3) < EPS)
260 return (pow(eta, ai[nnf].at(i)) * ll * ll * ll / 6.);
261 else if (fabs(den1) < EPS && fabs(den2) < EPS)
262 return ((0.5 * pow(eta, ai[nnf].at(p) + k) * ll * ll - f_r(nnf, i, p, k, eta)) / den3);
263 else if (fabs(den1) < EPS)
264 return ((f_r(nnf, i, q, k + l, eta) - f_g(nnf, i, p, q, k, l, eta)) / den2);
265 else
266 return ((f_g(nnf, i, p, j, k, l + m, eta) - f_g(nnf, i, p, q, k, l, eta)) / den1);
267}

◆ f_r()

double EvolDF1::f_r ( uint  nf,
uint  i,
uint  j,
int  k,
double  eta 
)
private

auxiliary function r - eq. (51) of Huber, Lunghi, Misiak, Wyler, hep-ph/0512066

Parameters
imatrix index
jmatrix index
korder index
etaals(M)/als(mu)
Returns
function value

Definition at line 233 of file EvolDF1.cpp.

234{
235 double ll = log(eta), den = ai[nnf].at(j) + k - ai[nnf].at(i);
236
237 if (fabs(den) < EPS)
238 return (0.5 * pow(eta, ai[nnf].at(i)) * ll * ll);
239 else
240 return ((pow(eta, ai[nnf].at(j) + k) * ll - f_f(nnf, i, j, k, eta)) / den);
241}

◆ GammaBB()

gslpp::matrix< double > EvolDF1::GammaBB ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

BB block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM BB block in the Misiak basis

Definition at line 1215 of file EvolDF1.cpp.

1216{
1217 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
1218 if (nf != 5)
1219 throw std::runtime_error("EvolDF1::GammaBB(): Wrong number of flavours in anoumalous dimensions");
1220
1221 gslpp::matrix<double> gammaDF1(1, 1, 0.);
1222
1223 switch (nm)
1224 {
1225 // QCD
1226 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
1227 case 10:
1228 gammaDF1(0, 0) = 4.;
1229 break;
1230 case 20:
1231 gammaDF1(0, 0) = 325. / 9.;
1232 break;
1233 // QED
1234 // ref.: Bobeth, Gambino, Gorbahn, Haisch, JHEP 0404, 071, hep-ph/0312090
1235 case 01:
1236 gammaDF1(0, 0) = 4. / 3.;
1237 break;
1238 case 11:
1239 gammaDF1(0, 0) = -388. / 9.;
1240 break;
1241 case 30:
1242 case 21:
1243 case 02:
1244 break;
1245 default:
1246 throw std::runtime_error("EvolDF1::GammaBB(): order not implemented");
1247 }
1248 return (gammaDF1);
1249}

◆ GammaBL()

gslpp::matrix< double > EvolDF1::GammaBL ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

BL block of the QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM BL block in the Misiak basis

Definition at line 1154 of file EvolDF1.cpp.

1155{
1156 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
1157 if (nf != 5)
1158 throw std::runtime_error("EvolDF1::GammaBL(): Wrong number of flavours in anoumalous dimensions");
1159
1160 gslpp::matrix<double> gammaDF1(1, 2, 0.);
1161
1162 switch (nm)
1163 {
1164 // QED
1165 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
1166 case 01:
1167 gammaDF1(0, 0) = 16. / 9.;
1168 break;
1169 case 11:
1170 gammaDF1(0, 0) = -8. / 9.;
1171 break;
1172 case 10:
1173 case 20:
1174 case 30:
1175 case 21:
1176 case 02:
1177 break;
1178 default:
1179 throw std::runtime_error("EvolDF1::GammaBL(): order not implemented");
1180 }
1181 return (gammaDF1);
1182}

◆ GammaBP()

gslpp::matrix< double > EvolDF1::GammaBP ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

BP block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM BP block in the Misiak basis

Definition at line 1116 of file EvolDF1.cpp.

1117{
1118 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
1119 if (nf != 5)
1120 throw std::runtime_error("EvolDF1::GammaBP(): Wrong number of flavours in anoumalous dimensions");
1121
1122 gslpp::matrix<double> gammaDF1(1, 4, 0.);
1123
1124 switch (nm)
1125 {
1126 // QCD
1127 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
1128 case 10:
1129 gammaDF1(0, 1) = 4. / 3.;
1130 break;
1131 case 20:
1132 gammaDF1(0, 0) = -1576. / 81.;
1133 gammaDF1(0, 1) = 446. / 27.;
1134 gammaDF1(0, 2) = 172. / 81.;
1135 gammaDF1(0, 3) = 40. / 27.;
1136 break;
1137 // QED
1138 // ref.: Bobeth, Gambino, Gorbahn, Haisch, JHEP 0404, 071, hep-ph/0312090
1139 case 01:
1140 break;
1141 case 11:
1142 gammaDF1(0, 1) = -232. / 81.;
1143 break;
1144 case 30:
1145 case 21:
1146 case 02:
1147 break;
1148 default:
1149 throw std::runtime_error("EvolDF1::GammaBP(): order not implemented");
1150 }
1151 return (gammaDF1);
1152}

◆ GammaBQ()

gslpp::matrix< double > EvolDF1::GammaBQ ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

BQ block of the QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM BQ block in the Misiak basis

Definition at line 1184 of file EvolDF1.cpp.

1185{
1186 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
1187 if (nf != 5)
1188 throw std::runtime_error("EvolDF1::GammaBQ(): Wrong number of flavours in anoumalous dimensions");
1189
1190 gslpp::matrix<double> gammaDF1(1, 4, 0.);
1191
1192 switch (nm)
1193 {
1194 // QED
1195 // ref.: Bobeth, Gambino, Gorbahn, Haisch, JHEP 0404, 071, hep-ph/0312090
1196 case 01:
1197 gammaDF1(0, 0) = -16. / 9.;
1198 break;
1199 case 11:
1200 gammaDF1(0, 1) = 580. / 27.;
1201 gammaDF1(0, 3) = -94. / 27.;
1202 break;
1203 case 10:
1204 case 20:
1205 case 30:
1206 case 21:
1207 case 02:
1208 break;
1209 default:
1210 throw std::runtime_error("EvolDF1::GammaBQ(): order not implemented");
1211 }
1212 return (gammaDF1);
1213}

◆ GammaCC()

gslpp::matrix< double > EvolDF1::GammaCC ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

CC block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM CC block in the Misiak basis

Definition at line 279 of file EvolDF1.cpp.

280{
281 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
282 CheckNf(nm, nf);
283
284 gslpp::matrix<double> gammaDF1(2, 2, 0.);
285 double z3 = gslpp_special_functions::zeta(3);
286
287 switch (nm)
288 {
289 // QCD
290 // ref.: Gorbahn, Haisch, Nucl. Phys. B 713, 291, hep-ph/0411071
291 case 10:
292 gammaDF1(0, 0) = -4.;
293 gammaDF1(0, 1) = 8. / 3.;
294 gammaDF1(1, 0) = 12.;
295 break;
296 case 20:
297 gammaDF1(0, 0) = -145. / 3. + nf * 16. / 9.; // -355./9.
298 gammaDF1(0, 1) = -26. + nf * 40. / 27.; // -502./27.
299 gammaDF1(1, 0) = -45. + nf * 20. / 3.; // -35./3.
300 gammaDF1(1, 1) = -28. / 3.;
301 break;
302 case 30:
303 gammaDF1(0, 0) = -1927. / 2. + nf * 257. / 9. + nf * nf * 40. / 9. + z3 * (224. + nf * 160. / 3.); // -12773./18. + z3*1472./3.
304 gammaDF1(0, 1) = 475. / 9. + nf * 362. / 27. - nf * nf * 40. / 27. - z3 * (896. / 3. + nf * 320. / 9.); // 745./9. - z3*4288./9.
305 gammaDF1(1, 0) = 307. / 2. + nf * 361. / 3. - nf * nf * 20. / 3. - z3 * (1344. + nf * 160.); // 1177./2. - z3*2144.
306 gammaDF1(1, 1) = 1298. / 3. - nf * 76. / 3. - z3 * 224.; // 306. + z3*224.
307 break;
308 // QED
309 // only available for nf = 5
310 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
311 case 01:
312 gammaDF1(0, 0) = -8. / 3.;
313 gammaDF1(1, 1) = -8. / 3.;
314 break;
315 case 11:
316 gammaDF1(0, 0) = 169. / 9.;
317 gammaDF1(0, 1) = 100. / 27.;
318 gammaDF1(1, 0) = 50. / 3.;
319 gammaDF1(1, 1) = -8. / 3.;
320 break;
321 case 21:
322 case 02:
323 break;
324 default:
325 throw std::runtime_error("EvolDF1::GammaCC(): order not implemented");
326 }
327 return (gammaDF1);
328}
EvolDF1::CheckNf
void CheckNf(indices nm, uint nf) const
a method returning the anomalous dimension in the Chetyrkin, Misiak and Munz operator basis
Definition EvolDF1.cpp:269
EvolDF1::zeta
friend double gslpp_special_functions::zeta(int i)

◆ GammaCL()

gslpp::matrix< double > EvolDF1::GammaCL ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

CL block of the QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM CL block in the Misiak basis

Definition at line 442 of file EvolDF1.cpp.

443{
444 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
445 if (nf != 5)
446 throw std::runtime_error("EvolDF1::GammaCL(): Wrong number of flavours in anoumalous dimensions");
447
448
449 gslpp::matrix<double> gammaDF1(2, 2, 0.);
450 double z3 = gslpp_special_functions::zeta(3);
451
452 switch (nm)
453 {
454 // QED
455 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
456 case 01:
457 gammaDF1(0, 0) = -32. / 27.;
458 gammaDF1(1, 0) = -8. / 9.;
459 break;
460 case 11:
461 gammaDF1(0, 0) = -2272. / 729.;
462 gammaDF1(1, 0) = 1952. / 243.;
463 break;
464 case 21:
465 gammaDF1(0, 0) = -1359190. / 19683. + z3 * 6976. / 243.;
466 gammaDF1(1, 0) = -229696. / 6561. - z3 * 3584. / 81.;
467 break;
468 case 02:
469 gammaDF1(0, 0) = -11680. / 2187.;
470 gammaDF1(1, 0) = -2920. / 729.;
471 gammaDF1(0, 1) = -416. / 81.;
472 gammaDF1(1, 1) = -104. / 27.;
473 break;
474 case 10:
475 case 20:
476 case 30:
477 break;
478 default:
479 throw std::runtime_error("EvolDF1::GammaCL(): order not implemented");
480 }
481 return (gammaDF1);
482}

◆ GammaCM()

gslpp::matrix< double > EvolDF1::GammaCM ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

CM block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM CM block in the Misiak basis

Definition at line 384 of file EvolDF1.cpp.

385{
386 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
387 CheckNf(nm, nf);
388
389 gslpp::matrix<double> gammaDF1(2, 2, 0.);
390 double Qu = 2. / 3.;
391 double Qd = -1. / 3.;
392 double Qbar = n_u * Qu + n_d*Qd;
393 double z3 = gslpp_special_functions::zeta(3);
394
395 switch (nm)
396 {
397 // QCD
398 // ref.: Czakon, Haisch, Misiak, JHEP 0703, 008, hep-ph/0612329
399 case 10:
400 gammaDF1(0, 0) = 8. / 243. - Qu * 4. / 3.;
401 gammaDF1(0, 1) = 173. / 162.;
402 gammaDF1(1, 0) = -16. / 81. + Qu * 8.;
403 gammaDF1(1, 1) = 70. / 27.;
404 break;
405 case 20:
406 gammaDF1(0, 0) = 12614. / 2187. - nf * 64. / 2187. - Qu * 374. / 27. + nf * Qu * 2. / 27.;
407 gammaDF1(0, 1) = 65867. / 5832. + nf * 431. / 5832.;
408 gammaDF1(1, 0) = -2332. / 729. + nf * 128. / 729. + Qu * 136. / 9. - nf * Qu * 4. / 9.;
409 gammaDF1(1, 1) = 10577. / 486. - nf * 917. / 972.;
410 break;
411 case 30:
412 gammaDF1(0, 0) = 77506102. / 531441. - nf * 875374. / 177147. + nf * nf * 560. / 19683. - Qu * 9731. / 162. +
413 nf * Qu * 11045. / 729. + nf * nf * Qu * 316. / 729. + Qbar * 3695. / 486. + z3 * (-112216. / 6561. + nf * 728. / 729. +
414 Qu * 25508. / 81. - nf * Qu * 64. / 81. - Qbar * 100. / 27.);
415 gammaDF1(0, 1) = -421272953. / 1417176. - nf * 8210077. / 472392. - nf * nf * 1955. / 6561. + z3 * (-953042. / 2187. -
416 nf * 10381. / 486.);
417 gammaDF1(1, 0) = -15463055. / 177147. + nf * 242204. / 59049. - nf * nf * 1120. / 6561. + Qu * 55748. / 27. -
418 nf * Qu * 33970. / 243. - nf * nf * Qu * 632. / 243. - Qbar * 3695. / 81. + z3 * (365696. / 2187. - nf * 1168. / 243. -
419 Qu * 51232. / 27. - nf * Qu * 1024. / 27. + Qbar * 200. / 9.);
420 gammaDF1(1, 1) = 98548513. / 472392. - nf * 5615165. / 78732. - nf * nf * 2489. / 2187. + z3 * (-607103. / 729. -
421 nf * 1679. / 81.);
422 break;
423 // QED
424 // only available for nf = 5
425 // ref.: Baranowski, Misiak, Phys. Lett. B 483, 410, hep-ph/9907427
426 case 01:
427 gammaDF1(0, 0) = -832. / 729.;
428 gammaDF1(0, 1) = 22. / 243.;
429 gammaDF1(1, 0) = -208. / 243.;
430 gammaDF1(1, 1) = -116. / 81.;
431 break;
432 case 11:
433 case 21:
434 case 02:
435 break;
436 default:
437 throw std::runtime_error("EvolDF1::GammaCM(): order not implemented");
438 }
439 return (gammaDF1);
440}

◆ GammaCP()

gslpp::matrix< double > EvolDF1::GammaCP ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

CP block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM CP block in the Misiak basis

Definition at line 330 of file EvolDF1.cpp.

331{
332 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
333 CheckNf(nm, nf);
334
335 gslpp::matrix<double> gammaDF1(2, 4, 0.);
336 double z3 = gslpp_special_functions::zeta(3);
337
338 switch (nm)
339 {
340 // QCD
341 // ref.: Gorbahn, Haisch, Nucl. Phys. B 713, 291, hep-ph/0411071
342 case 10:
343 gammaDF1(0, 1) = -2. / 9.;
344 gammaDF1(1, 1) = 4. / 3.;
345 break;
346 case 20:
347 gammaDF1(0, 0) = -1412. / 243.;
348 gammaDF1(0, 1) = -1369. / 243.;
349 gammaDF1(0, 2) = 134. / 243.;
350 gammaDF1(0, 3) = -35. / 162.;
351 gammaDF1(1, 0) = -416. / 81.;
352 gammaDF1(1, 1) = 1280. / 81.;
353 gammaDF1(1, 2) = 56. / 81.;
354 gammaDF1(1, 3) = 35. / 27.;
355 break;
356 case 30:
357 gammaDF1(0, 0) = 269107. / 13122. - nf * 2288. / 729. - z3 * 1360. / 81.; // 63187./13122. - z3*1360./81.
358 gammaDF1(0, 1) = -2425817. / 13122. + nf * 30815. / 4374. - z3 * 776. / 81.; // -981796./6561. - z3*776./81.
359 gammaDF1(0, 2) = -343783. / 52488. + nf * 392. / 729. + z3 * 124. / 81.; // -202663./52488. + z3*124./81.
360 gammaDF1(0, 3) = -37573. / 69984. + nf * 35. / 972. + z3 * 100. / 27.; // -24973./69984. + z3*100./27.
361 gammaDF1(1, 0) = 69797. / 2187. + nf * 904. / 243. + z3 * 2720. / 27.; // 110477./2187. + z3*2720./.27.
362 gammaDF1(1, 1) = 1457549. / 8748. - nf * 22067. / 729. - z3 * 2768. / 27.; // 133529./8748. - z3*2768./27.
363 gammaDF1(1, 2) = -37889. / 8748. - nf * 28. / 243. - z3 * 248. / 27.; // -42929./8748. - z3*248./27.
364 gammaDF1(1, 3) = 366919. / 11664. - nf * 35. / 162. - z3 * 110. / 9.; // 354319./11664. - z3*110./9.
365 break;
366 // QED
367 // only available for nf = 5
368 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
369 case 01:
370 break;
371 case 11:
372 gammaDF1(0, 1) = 254. / 729.;
373 gammaDF1(1, 1) = 1076. / 243.;
374 break;
375 case 21:
376 case 02:
377 break;
378 default:
379 throw std::runtime_error("EvolDF1::GammaCP(): order not implemented");
380 }
381 return (gammaDF1);
382}

◆ GammaCQ()

gslpp::matrix< double > EvolDF1::GammaCQ ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

CQ block of the QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM CQ block in the Misiak basis

Definition at line 484 of file EvolDF1.cpp.

485{
486 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
487 if (nf != 5)
488 throw std::runtime_error("EvolDF1::GammaCQ(): Wrong number of flavours in anoumalous dimensions");
489
490
491 gslpp::matrix<double> gammaDF1(2, 4, 0.);
492
493 switch (nm)
494 {
495 // QED
496 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
497 case 01:
498 gammaDF1(0, 0) = 32. / 27.;
499 gammaDF1(1, 0) = 8. / 9.;
500 break;
501 case 11:
502 gammaDF1(0, 0) = 2272. / 729.;
503 gammaDF1(0, 1) = 122. / 81.;
504 gammaDF1(0, 3) = 49. / 81.;
505 gammaDF1(1, 0) = -1952. / 243.;
506 gammaDF1(1, 1) = -748. / 27.;
507 gammaDF1(1, 3) = 82. / 27.;
508 break;
509 case 10:
510 case 20:
511 case 30:
512 case 21:
513 case 02:
514 break;
515 default:
516 throw std::runtime_error("EvolDF1::GammaCQ(): order not implemented");
517 }
518 return (gammaDF1);
519}

◆ GammaLL()

gslpp::matrix< double > EvolDF1::GammaLL ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

LL block of the QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM LL block in the Misiak basis

Definition at line 850 of file EvolDF1.cpp.

851{
852 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
853 if (nf != 5)
854 throw std::runtime_error("EvolDF1::GammaLL(): Wrong number of flavours in anoumalous dimensions");
855
856 gslpp::matrix<double> gammaDF1(2, 2, 0.);
857
858 switch (nm)
859 {
860 // QED
861 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
862 case 01:
863 gammaDF1(0, 0) = 8.;
864 gammaDF1(0, 1) = -4.;
865 gammaDF1(1, 0) = -4.;
866 break;
867 case 11:
868 gammaDF1(0, 1) = 16.;
869 gammaDF1(1, 0) = 16.;
870 break;
871 case 10:
872 case 20:
873 case 30:
874 case 21:
875 case 02:
876 break;
877 default:
878 throw std::runtime_error("EvolDF1::GammaLL(): order not implemented");
879 }
880 return (gammaDF1);
881}

◆ GammaMM()

gslpp::matrix< double > EvolDF1::GammaMM ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

MM block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM MM block in the Misiak basis

Definition at line 796 of file EvolDF1.cpp.

797{
798 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
799 CheckNf(nm, nf);
800
801 gslpp::matrix<double> gammaDF1(2, 2, 0.);
802 double Qu = 2. / 3.;
803 double Qd = -1. / 3.;
804 double Qbar = n_u * Qu + n_d*Qd;
805 double z3 = gslpp_special_functions::zeta(3);
806
807 switch (nm)
808 {
809 // QCD
810 //ref.: Gorbahn, Haisch, Misiak, Phys. Rev. Lett. 95, 102004, hep-ph/0504194
811 case 10:
812 gammaDF1(0, 0) = 32. / 3.;
813 gammaDF1(1, 0) = Qd * 32. / 3.;
814 gammaDF1(1, 1) = 28. / 3.;
815 break;
816 case 20:
817 gammaDF1(0, 0) = 1936. / 9. - nf * 224. / 27.;
818 gammaDF1(1, 0) = Qd * 368. / 3. - nf * Qd * 224. / 27.;
819 gammaDF1(1, 1) = 1456. / 9. - nf * 61. / 27.;
820 break;
821 case 30:
822 gammaDF1(0, 0) = 307448. / 81. - nf * 23776. / 81. - nf * nf * 352. / 81. + z3 * (-1856. / 27. - nf * 1280. / 9.);
823 gammaDF1(1, 0) = -Qbar * 1600. / 27. + Qd * 159872. / 81. - nf * Qd * 17108. / 81. - nf * nf * Qd * 352. / 81. + z3 * (Qbar * 640. / 9. -
824 Qd * 1856. / 27. - nf * Qd * 1280. / 9.);
825 gammaDF1(1, 1) = 268807. / 81. - nf * 4343. / 27. - nf * nf * 461. / 81. + z3 * (-28624. / 27. - nf * 1312. / 9.);
826 break;
827 // QED
828 // only available for nf = 5
829 // ref.: Bobeth, Gambino, Gorbahn, Haisch, JHEP 0404, 071, hep-ph/0312090
830 case 01:
831 gammaDF1(0, 0) = 16. / 9.;
832 gammaDF1(0, 1) = -8. / 3.;
833 gammaDF1(1, 1) = 8. / 9.;
834 break;
835 case 11:
836 gammaDF1(0, 0) = -256. / 27.;
837 gammaDF1(0, 1) = -52. / 9.;
838 gammaDF1(1, 0) = 128. / 81.;
839 gammaDF1(1, 1) = -40. / 27.;
840 break;
841 case 21:
842 case 02:
843 break;
844 default:
845 throw std::runtime_error("EvolDF1::GammaMM(): order not implemented");
846 }
847 return (gammaDF1);
848}

◆ GammaPL()

gslpp::matrix< double > EvolDF1::GammaPL ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

PL block of the QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM PL block in the Misiak basis

Definition at line 689 of file EvolDF1.cpp.

690{
691 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
692 if (nf != 5)
693 throw std::runtime_error("EvolDF1::GammaPL(): Wrong number of flavours in anoumalous dimensions");
694
695
696 gslpp::matrix<double> gammaDF1(4, 2, 0.);
697 double z3 = gslpp_special_functions::zeta(3);
698
699 switch (nm)
700 {
701 // QED
702 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
703
704 case 01:
705 gammaDF1(0, 0) = -16. / 9.;
706 gammaDF1(1, 0) = 32. / 27.;
707 gammaDF1(2, 0) = -112. / 9.;
708 gammaDF1(3, 0) = 512. / 27.;
709 break;
710 case 11:
711 gammaDF1(0, 0) = -6752. / 243.;
712 gammaDF1(1, 0) = -2192. / 729.;
713 gammaDF1(2, 0) = -84032. / 243.;
714 gammaDF1(3, 0) = -37856. / 729.;
715 break;
716 case 21:
717 gammaDF1(0, 0) = -1290092. / 6561. + z3 * 3200. / 81.;
718 gammaDF1(1, 0) = -819971. / 19683. - z3 * 19936. / 243.;
719 gammaDF1(2, 0) = -16821944. / 6561. + z3 * 30464. / 81.;
720 gammaDF1(3, 0) = -17787368. / 19683. - z3 * 286720. / 243.;
721 break;
722 case 02:
723 gammaDF1(0, 0) = -39752. / 729.;
724 gammaDF1(1, 0) = 1024. / 2187.;
725 gammaDF1(2, 0) = -381344. / 729.;
726 gammaDF1(3, 0) = 24832. / 2187.;
727 gammaDF1(0, 1) = -136. / 27.;
728 gammaDF1(1, 1) = -448. / 81.;
729 gammaDF1(2, 1) = -15616. / 27.;
730 gammaDF1(3, 1) = -7936. / 81.;
731 break;
732 case 10:
733 case 20:
734 case 30:
735 break;
736 default:
737 throw std::runtime_error("EvolDF1::GammaPL(): order not implemented");
738 }
739 return (gammaDF1);
740}

◆ GammaPM()

gslpp::matrix< double > EvolDF1::GammaPM ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

PM block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM PM block in the Misiak basis

Definition at line 611 of file EvolDF1.cpp.

612{
613 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
614 CheckNf(nm, nf);
615
616 gslpp::matrix<double> gammaDF1(4, 2, 0.);
617 double Qu = 2. / 3.;
618 double Qd = -1. / 3.;
619 double Qbar = n_u * Qu + n_d*Qd;
620 double z3 = gslpp_special_functions::zeta(3);
621
622 switch (nm)
623 {
624 // QCD
625 // ref.: Czakon, Haisch, Misiak, JHEP 0703, 008, hep-ph/0612329
626 case 10:
627 gammaDF1(0, 0) = -176. / 81.;
628 gammaDF1(0, 1) = 14. / 27.;
629 gammaDF1(1, 0) = 88. / 243. - nf * 16. / 81.;
630 gammaDF1(1, 1) = 74. / 81. - nf * 49. / 54.;
631 gammaDF1(2, 0) = -6272. / 81.;
632 gammaDF1(2, 1) = 1736. / 27. + nf * 36.;
633 gammaDF1(3, 0) = 3136. / 243. - nf * 160. / 81. + Qbar * 48.;
634 gammaDF1(3, 1) = 2372. / 81. + nf * 160. / 27.;
635 break;
636 case 20:
637 gammaDF1(0, 0) = 97876. / 729. - nf * 4352. / 729. - Qbar * 112. / 3.;
638 gammaDF1(0, 1) = 42524. / 243. - nf * 2398. / 243.;
639 gammaDF1(1, 0) = -70376. / 2187. - nf * 15788. / 2187. + nf * nf * 32. / 729. - Qbar * 140. / 9.;
640 gammaDF1(1, 1) = -159718. / 729. - nf * 39719. / 5832. - nf * nf * 253. / 486.;
641 gammaDF1(2, 0) = 1764752. / 729. - nf * 65408. / 729. - Qbar * 3136. / 3.;
642 gammaDF1(2, 1) = 2281576. / 243. + nf * 140954. / 243. - nf * nf * 14.;
643 gammaDF1(3, 0) = 4193840. / 2187. - nf * 324128. / 2187. + nf * nf * 896. / 729. - Qbar * 1136. / 9. - nf * Qbar * 56. / 3.;
644 gammaDF1(3, 1) = -3031517. / 729. - nf * 15431. / 1458. - nf * nf * 6031. / 486.;
645 break;
646 case 30:
647 gammaDF1(0, 0) = 102439553. / 177147. - nf * 12273398 / 59049. + nf * nf * 5824. / 6561. + Qbar * 26639. / 81. - nf * Qbar * 8. / 27. +
648 z3 * (3508864. / 2187. - nf * 1904. / 243. - Qbar * 1984. / 9. - nf * Qbar * 64. / 9.);
649 gammaDF1(0, 1) = 3205172129. / 472392. - nf * 108963529. / 314928. + nf * nf * 58903. / 4374. + z3 * (-1597588. / 729. +
650 nf * 13028. / 81. - nf * nf * 20. / 9.);
651 gammaDF1(1, 0) = -2493414077. / 1062882. - nf * 9901031. / 354294. + nf * nf * 243872. / 59049. - nf * nf * nf * 1184. / 6561. -
652 Qbar * 49993. / 972. + nf * Qbar * 305. / 27. + z3 * (-1922264. / 6561. + nf * 308648. / 2187. - nf * nf * 1280. / 243. +
653 Qbar * 1010. / 9. - nf * Qbar * 200. / 27.);
654 gammaDF1(1, 1) = -6678822461. / 2834352. + nf * 127999025. / 1889568. + nf * nf * 1699073. / 157464. + nf * nf * nf * 505. / 4374. +
655 z3 * (2312684. / 2187. + nf * 128347. / 729. + nf * nf * 920. / 81.);
656 gammaDF1(2, 0) = 8808397748. / 177147. - nf * 174839456. / 59049. + nf * nf * 1600. / 729. - Qbar * 669694. / 81. + nf * Qbar * 10672. / 27. +
657 z3 * (123543040. / 2187. - nf * 207712. / 243. + nf * nf * 128. / 27. - Qbar * 24880. / 9. - nf * Qbar * 640. / 9.);
658 gammaDF1(2, 1) = 29013624461. / 118098. - nf * 64260772. / 19683. - nf * nf * 230962. / 243. - nf * nf * nf * 148. / 27. +
659 z3 * (-69359224. / 729. - nf * 885356. / 81. - nf * nf * 5080. / 9.);
660 gammaDF1(3, 0) = 7684242746. / 531441. - nf * 351775414. / 177147. - nf * nf * 479776. / 59049. - nf * nf * nf * 11456. / 6561. +
661 Qbar * 3950201. / 243. - nf * Qbar * 130538. / 81. - nf * nf * Qbar * 592. / 81. + z3 * (7699264. / 6561. + nf * 2854976. / 2187. -
662 nf * nf * 12320. / 243. - Qbar * 108584. / 9. - nf * Qbar * 1136. / 27.);
663 gammaDF1(3, 1) = -72810260309. / 708588. + nf * 2545824851. / 472392. - nf * nf * 33778271. / 78732. - nf * nf * nf * 3988. / 2187. +
664 z3 * (-61384768. / 2187. - nf * 685472. / 729. + nf * nf * 350. / 81.);
665 break;
666 // QED
667 // only available for nf = 5
668 // ref.: Baranowski, Misiak, Phys. Lett. B 483, 410, hep-ph/9907427
669 case 01:
670 gammaDF1(0, 0) = -20. / 243.;
671 gammaDF1(0, 1) = 20. / 81.;
672 gammaDF1(1, 0) = -176. / 729.;
673 gammaDF1(1, 1) = 14. / 243.;
674 gammaDF1(2, 0) = -22712. / 243.;
675 gammaDF1(2, 1) = 1328. / 81.;
676 gammaDF1(3, 0) = -6272. / 729.;
677 gammaDF1(3, 1) = -1180. / 243.;
678 break;
679 case 11:
680 case 21:
681 case 02:
682 break;
683 default:
684 throw std::runtime_error("EvolDF1::GammaPM(): order not implemented");
685 }
686 return (gammaDF1);
687}

◆ GammaPP()

gslpp::matrix< double > EvolDF1::GammaPP ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

PP block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM PP block in the Misiak basis

Definition at line 521 of file EvolDF1.cpp.

522{
523 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
524 CheckNf(nm, nf);
525
526 gslpp::matrix<double> gammaDF1(4, 4, 0.);
527 double z3 = gslpp_special_functions::zeta(3);
528
529 switch (nm)
530 {
531 // QCD
532 // ref.: Gorbahn, Haisch, Nucl. Phys. B 713, 291, hep-ph/0411071
533 case 10:
534 gammaDF1(0, 1) = -52. / 3.;
535 gammaDF1(0, 3) = 2.;
536 gammaDF1(1, 0) = -40. / 9.;
537 gammaDF1(1, 1) = -160. / 9. + (double) nf * 4. / 3.; // -100./9.
538 gammaDF1(1, 2) = 4. / 9.;
539 gammaDF1(1, 3) = 5. / 6.;
540 gammaDF1(2, 1) = -256. / 3.;
541 gammaDF1(2, 3) = 20.;
542 gammaDF1(3, 0) = -256. / 9.;
543 gammaDF1(3, 1) = -544. / 9. + (double) nf * 40. / 3.; // 56./9.
544 gammaDF1(3, 2) = 40. / 9.;
545 gammaDF1(3, 3) = -2. / 3.;
546 break;
547 case 20:
548 gammaDF1(0, 0) = -4468. / 81.;
549 gammaDF1(0, 1) = -29129. / 81. - nf * 52. / 9.; // -31469./81.
550 gammaDF1(0, 2) = 400. / 81.;
551 gammaDF1(0, 3) = 3493. / 108. - nf * 2. / 9.; // 3373./108.
552 gammaDF1(1, 0) = -13678. / 243. + nf * 368. / 81.; // -8158./243.
553 gammaDF1(1, 1) = -79409. / 243. + nf * 1334. / 81.; // -59399./243.
554 gammaDF1(1, 2) = 509. / 486. - nf * 8. / 81.; // 269./486.
555 gammaDF1(1, 3) = 13499. / 648. - nf * 5. / 27.; // 12899./648.
556 gammaDF1(2, 0) = -244480. / 81. - nf * 160. / 9.; // -251680./81.
557 gammaDF1(2, 1) = -29648. / 81. - nf * 2200. / 9.; // -128648./81.
558 gammaDF1(2, 2) = 23116. / 81. + nf * 16. / 9.; // 23836./81.
559 gammaDF1(2, 3) = 3886. / 27. + nf * 148. / 9.; // 6106./27.
560 gammaDF1(3, 0) = 77600. / 243. - nf * 1264. / 81.; // 58640./243.
561 gammaDF1(3, 1) = -28808. / 243. + nf * 164. / 81.; // -26348./243.
562 gammaDF1(3, 2) = -20324. / 243. + nf * 400. / 81.; // -14324./243.
563 gammaDF1(3, 3) = -21211. / 162. + nf * 622. / 27.; // -2551./162.
564 break;
565 case 30:
566 gammaDF1(0, 0) = -4203068. / 2187. + nf * 14012. / 243. - z3 * 608. / 27.; // -3572528./2187. - z3*608./27.
567 gammaDF1(0, 1) = -18422762. / 2187. + nf * 888605. / 2916. + nf * nf * 272. / 27. + z3 * (39824. / 27. + nf * 160.); // -58158773./8748. + z3*61424./27.
568 gammaDF1(0, 2) = 674281. / 4374. - nf * 1352. / 243. - z3 * 496. / 27.; // 552601./4374. - z3*496./27.
569 gammaDF1(0, 3) = 9284531. / 11664. - nf * 2798. / 81. - nf * nf * 26. / 27. - z3 * (1921. / 9. + nf * 20.); // 6989171./11664. - z3*2821./9.
570 gammaDF1(1, 0) = -5875184. / 6561. + nf * 217892. / 2187. + nf * nf * 472. / 81. + z3 * (27520. / 81. + nf * 1360. / 9.); // -1651004./6561. + z3*88720./81.
571 gammaDF1(1, 1) = -70274587. / 13122. + nf * 8860733. / 17496. - nf * nf * 4010. / 729. + z3 * (16592. / 81. + nf * 2512. / 27.); // -155405353./52488. + z3*54272./81.
572 gammaDF1(1, 2) = 2951809. / 52488. - nf * 31175. / 8748. - nf * nf * 52. / 81. - z3 * (3154. / 81. + nf * 136. / 9.); // 1174159./52488. - z3*9274./81.
573 gammaDF1(1, 3) = 3227801. / 8748. - nf * 105293. / 11664. - nf * nf * 65. / 54. + z3 * (200. / 27. - nf * 220. / 9.); // 10278809./34992. - z3*3100./27.
574 gammaDF1(2, 0) = -194951552. / 2187. + nf * 358672. / 81. - nf * nf * 2144. / 81. + z3 * 87040. / 27.; // -147978032./2187. + z3*87040./27.
575 gammaDF1(2, 1) = -130500332. / 2187. - nf * 2949616. / 729. + nf * nf * 3088. / 27. + z3 * (238016. / 27. + nf * 640.); // -168491372./2187. + z3*324416./27.
576 gammaDF1(2, 2) = 14732222. / 2187. - nf * 27428. / 81. + nf * nf * 272. / 81. - z3 * 13984. / 27.; // 11213042./2187. - z3*13984./27.
577 gammaDF1(2, 3) = 16521659. / 2916. + nf * 8081. / 54. - nf * nf * 316. / 27. - z3 * (22420. / 9. + nf * 200.); // 17850329./2916. - z3*31420./9.
578 gammaDF1(3, 0) = 162733912. / 6561. - nf * 2535466. / 2187. + nf * nf * 17920. / 243. + z3 * (174208. / 81. + nf * 12160. / 9.); // 136797922./6561. + z3*721408./81.
579 gammaDF1(3, 1) = 13286236. / 6561. - nf * 1826023. / 4374. - nf * nf * 159548. / 729. - z3 * (24832. / 81. + nf * 9440. / 27.); // -72614473./13122. - z3*166432./81.
580 gammaDF1(3, 2) = -22191107. / 13122. + nf * 395783. / 4374. - nf * nf * 1720. / 243. - z3 * (33832. / 81. + nf * 1360. / 9.); // -9288181./6561. - z3*95032./81.
581 gammaDF1(3, 3) = -32043361. / 8748. + nf * 3353393. / 5832. - nf * nf * 533. / 81. + z3 * (9248. / 27. - nf * 1120. / 9.); // -16664027./17496. - z3*7552./27.
582 break;
583 // QED
584 // only available for nf = 5
585 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
586 case 01:
587 break;
588 case 11:
589 gammaDF1(0, 1) = 11116. / 243.;
590 gammaDF1(0, 3) = -14. / 3.;
591 gammaDF1(1, 0) = 280. / 27.;
592 gammaDF1(1, 1) = 18763. / 729.;
593 gammaDF1(1, 2) = -28. / 27.;
594 gammaDF1(1, 3) = -35. / 18.;
595 gammaDF1(2, 1) = 111136. / 243.;
596 gammaDF1(2, 3) = -140. / 3.;
597 gammaDF1(3, 0) = 2944. / 27.;
598 gammaDF1(3, 1) = 193312. / 729.;
599 gammaDF1(3, 2) = -280. / 27.;
600 gammaDF1(3, 3) = -175. / 9.;
601 break;
602 case 21:
603 case 02:
604 break;
605 default:
606 throw std::runtime_error("EvolDF1::GammaPP(): order not implemented");
607 }
608 return (gammaDF1);
609}

◆ GammaPQ()

gslpp::matrix< double > EvolDF1::GammaPQ ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

PQ block of the QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM PQ block in the Misiak basis

Definition at line 742 of file EvolDF1.cpp.

743{
744 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
745 if (nf != 5)
746 throw std::runtime_error("EvolDF1::GammaPQ(): Wrong number of flavours in anoumalous dimensions");
747
748 gslpp::matrix<double> gammaDF1(4, 4, 0.);
749
750 switch (nm)
751 {
752 // QED
753 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
754 case 01:
755 gammaDF1(0, 0) = 76. / 9.;
756 gammaDF1(0, 2) = -2. / 3.;
757 gammaDF1(1, 0) = -32. / 27.;
758 gammaDF1(1, 1) = 20. / 3.;
759 gammaDF1(1, 3) = -2. / 3.;
760 gammaDF1(2, 0) = 496. / 9.;
761 gammaDF1(2, 2) = -20. / 3.;
762 gammaDF1(3, 0) = -512. / 27.;
763 gammaDF1(3, 1) = 128. / 3.;
764 gammaDF1(3, 3) = -20. / 3.;
765 break;
766 case 11:
767 gammaDF1(0, 0) = -23488. / 243.;
768 gammaDF1(0, 1) = 6280. / 27.;
769 gammaDF1(0, 2) = 112. / 9.;
770 gammaDF1(0, 3) = -538. / 27.;
771 gammaDF1(1, 0) = 31568. / 729.;
772 gammaDF1(1, 1) = 9481. / 81.;
773 gammaDF1(1, 2) = -92. / 27.;
774 gammaDF1(1, 3) = -1012. / 81.;
775 gammaDF1(2, 0) = -233920. / 243.;
776 gammaDF1(2, 1) = 68848. / 27.;
777 gammaDF1(2, 2) = 1120. / 9.;
778 gammaDF1(2, 3) = -5056. / 27.;
779 gammaDF1(3, 0) = 352352. / 729.;
780 gammaDF1(3, 1) = 116680. / 81.;
781 gammaDF1(3, 2) = -752. / 27.;
782 gammaDF1(3, 3) = -10147. / 81.;
783 break;
784 case 10:
785 case 20:
786 case 30:
787 case 21:
788 case 02:
789 break;
790 default:
791 throw std::runtime_error("EvolDF1::GammaPQ(): order not implemented");
792 }
793 return (gammaDF1);
794}

◆ GammaQL()

gslpp::matrix< double > EvolDF1::GammaQL ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

QL block of the QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM QL block in the Misiak basis

Definition at line 994 of file EvolDF1.cpp.

995{
996 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
997 if (nf != 5)
998 throw std::runtime_error("EvolDF1::GammaQL(): Wrong number of flavours in anoumalous dimensions");
999
1000 gslpp::matrix<double> gammaDF1(4, 2, 0.);
1001
1002 switch (nm)
1003 {
1004 // QED
1005 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
1006 case 01:
1007 gammaDF1(0, 0) = -272. / 27.;
1008 gammaDF1(1, 0) = -32. / 81.;
1009 gammaDF1(2, 0) = -2768. / 27.;
1010 gammaDF1(3, 0) = -512. / 81.;
1011 break;
1012 case 11:
1013 gammaDF1(0, 0) = -24352. / 729.;
1014 gammaDF1(1, 0) = 54608. / 2187.;
1015 gammaDF1(2, 0) = -227008. / 729.;
1016 gammaDF1(3, 0) = 551648. / 2187.;
1017 break;
1018 case 10:
1019 case 20:
1020 case 30:
1021 case 21:
1022 case 02:
1023 break;
1024 default:
1025 throw std::runtime_error("EvolDF1::GammaQL(): order not implemented");
1026 }
1027 return (gammaDF1);
1028}

◆ GammaQM()

gslpp::matrix< double > EvolDF1::GammaQM ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

QM block of the QCD anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM QM block in the Misiak basis

Definition at line 959 of file EvolDF1.cpp.

960{
961 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
962 if (nf != 5)
963 throw std::runtime_error("EvolDF1::GammaQM(): Wrong number of flavours in anoumalous dimensions");
964
965 gslpp::matrix<double> gammaDF1(4, 2, 0.);
966
967 switch (nm)
968 {
969 // QCD
970 // ref.: Baranowski, Misiak, Phys. Lett. B 483, 410, hep-ph/9907427
971 case 10:
972 gammaDF1(0, 0) = 176. / 243.;
973 gammaDF1(0, 1) = -14. / 81.;
974 gammaDF1(1, 0) = -136. / 729.;
975 gammaDF1(1, 1) = -295. / 486.;
976 gammaDF1(2, 0) = 6272. / 243.;
977 gammaDF1(2, 1) = -764. / 81.;
978 gammaDF1(3, 0) = 39152. / 729.;
979 gammaDF1(3, 1) = -1892. / 243.;
980 break;
981 case 20:
982 case 30:
983 case 01:
984 case 11:
985 case 21:
986 case 02:
987 break;
988 default:
989 throw std::runtime_error("EvolDF1::GammaQM(): order not implemented");
990 }
991 return (gammaDF1);
992}

◆ GammaQP()

gslpp::matrix< double > EvolDF1::GammaQP ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

QP block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM QP block in the Misiak basis

Definition at line 883 of file EvolDF1.cpp.

884{
885 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
886 if (nf != 5)
887 throw std::runtime_error("EvolDF1::GammaQP(): Wrong number of flavours in anoumalous dimensions");
888
889 gslpp::matrix<double> gammaDF1(4, 4, 0.);
890
891 switch (nm)
892 {
893 // QCD
894 //ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
895 case 10:
896 gammaDF1(0, 1) = -8. / 9.;
897 gammaDF1(1, 1) = 16. / 27.;
898 gammaDF1(2, 1) = -128. / 9.;
899 gammaDF1(3, 1) = 184. / 27.;
900 break;
901 case 20:
902 gammaDF1(0, 0) = 832. / 243.;
903 gammaDF1(0, 1) = -4000. / 243.;
904 gammaDF1(0, 2) = -112. / 243.;
905 gammaDF1(0, 3) = -70. / 81.;
906 gammaDF1(1, 0) = 3376. / 729.;
907 gammaDF1(1, 1) = 6344. / 729.;
908 gammaDF1(1, 2) = -280. / 729.;
909 gammaDF1(1, 3) = 55. / 486.;
910 gammaDF1(2, 0) = 2272. / 243.;
911 gammaDF1(2, 1) = -72088. / 243.;
912 gammaDF1(2, 2) = -688. / 243.;
913 gammaDF1(2, 3) = -1240. / 81.;
914 gammaDF1(3, 0) = 45424. / 729.;
915 gammaDF1(3, 1) = 84236. / 729.;
916 gammaDF1(3, 2) = -3880. / 729.;
917 gammaDF1(3, 3) = 1220. / 243.;
918 break;
919 // QED
920 // ref.: Bobeth, Gambino, Gorbahn, Haisch, JHEP 0404, 071, hep-ph/0312090
921 case 01:
922 gammaDF1(0, 0) = 40. / 27.;
923 gammaDF1(0, 2) = -4. / 27.;
924 gammaDF1(1, 1) = 40. / 27.;
925 gammaDF1(1, 3) = -4. / 27.;
926 gammaDF1(2, 0) = 256. / 27.;
927 gammaDF1(2, 2) = -40. / 27.;
928 gammaDF1(3, 1) = 256. / 27.;
929 gammaDF1(3, 3) = -40. / 27.;
930 break;
931 case 11:
932 gammaDF1(0, 0) = -2240. / 81.;
933 gammaDF1(0, 1) = 39392. / 729.;
934 gammaDF1(0, 2) = 224. / 81.;
935 gammaDF1(0, 3) = -92. / 27.;
936 gammaDF1(1, 0) = 2176. / 243.;
937 gammaDF1(1, 1) = 84890. / 2187.;
938 gammaDF1(1, 2) = -184. / 243.;
939 gammaDF1(1, 3) = -224. / 81.;
940 gammaDF1(2, 0) = -23552. / 81.;
941 gammaDF1(2, 1) = 399776. / 729.;
942 gammaDF1(2, 2) = 2240. / 81.;
943 gammaDF1(2, 3) = -752. / 27.;
944 gammaDF1(3, 0) = 23296. / 243.;
945 gammaDF1(3, 1) = 933776. / 2187.;
946 gammaDF1(3, 2) = -1504. / 243.;
947 gammaDF1(3, 3) = -2030. / 81.;
948 break;
949 case 30:
950 case 21:
951 case 02:
952 break;
953 default:
954 throw std::runtime_error("EvolDF1::GammaQP(): order not implemented");
955 }
956 return (gammaDF1);
957}

◆ GammaQQ()

gslpp::matrix< double > EvolDF1::GammaQQ ( indices  nm,
uint  n_u,
uint  n_d 
) const
private

QQ block of the QCD+QED anomalous dimension.

Parameters
nmindices corresponding to powers of alpha_s and alpha_em as in Huber, Lunghi, Misiak, Wyler, hep-ph/0512066
n_uan uinteger for the up-type number of d.o.f.
n_dan uinteger for the down-type number of d.o.f.
Returns
the ADM QQ block in the Misiak basis

Definition at line 1030 of file EvolDF1.cpp.

1031{
1032 uint nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
1033 if (nf != 5)
1034 throw std::runtime_error("EvolDF1::GammaQQ(): Wrong number of flavours in anoumalous dimensions");
1035
1036 gslpp::matrix<double> gammaDF1(4, 4, 0.);
1037
1038 switch (nm)
1039 {
1040 // QCD
1041 // ref.: Huber, Lunghi, Misiak, Wyler, Nucl. Phys. B 740, 105, hep-ph/0512066
1042 case 10:
1043 gammaDF1(0, 1) = -20.;
1044 gammaDF1(0, 3) = 2.;
1045 gammaDF1(1, 0) = -40. / 9.;
1046 gammaDF1(1, 1) = -52. / 3.;
1047 gammaDF1(1, 2) = 4. / 9.;
1048 gammaDF1(1, 3) = 5. / 6.;
1049 gammaDF1(2, 1) = -128.;
1050 gammaDF1(2, 3) = 20.;
1051 gammaDF1(3, 0) = -256. / 9.;
1052 gammaDF1(3, 1) = -160. / 3.;
1053 gammaDF1(3, 2) = 40. / 9.;
1054 gammaDF1(3, 3) = -2. / 3.;
1055 break;
1056 case 20:
1057 gammaDF1(0, 0) = -404. / 9.;
1058 gammaDF1(0, 1) = -3077. / 9.;
1059 gammaDF1(0, 2) = 32. / 9.;
1060 gammaDF1(0, 3) = 1031. / 36.;
1061 gammaDF1(1, 0) = -2698. / 81.;
1062 gammaDF1(1, 1) = -8035. / 27.;
1063 gammaDF1(1, 2) = -49. / 162.;
1064 gammaDF1(1, 3) = 4493. / 216.;
1065 gammaDF1(2, 0) = -19072. / 9.;
1066 gammaDF1(2, 1) = -14096. / 9.;
1067 gammaDF1(2, 2) = 1708. / 9.;
1068 gammaDF1(2, 3) = 1622. / 9.;
1069 gammaDF1(3, 0) = 32288. / 81.;
1070 gammaDF1(3, 1) = -15976. / 27.;
1071 gammaDF1(3, 2) = -6692. / 81.;
1072 gammaDF1(3, 3) = -2437. / 54.;
1073 break;
1074 // QED
1075 // ref.: Bobeth, Gambino, Gorbahn, Haisch, JHEP 0404, 071, hep-ph/0312090
1076 case 01:
1077 gammaDF1(0, 0) = 332. / 27.;
1078 gammaDF1(0, 2) = -2. / 9.;
1079 gammaDF1(1, 0) = 32. / 81.;
1080 gammaDF1(1, 1) = 20. / 9.;
1081 gammaDF1(1, 3) = -2. / 9.;
1082 gammaDF1(2, 0) = 3152. / 27.;
1083 gammaDF1(2, 2) = -20. / 9.;
1084 gammaDF1(3, 0) = 512. / 81.;
1085 gammaDF1(3, 1) = 128. / 9.;
1086 gammaDF1(3, 3) = -20. / 9.;
1087 break;
1088 case 11:
1089 gammaDF1(0, 0) = -5888. / 729.;
1090 gammaDF1(0, 1) = 13916. / 81.;
1091 gammaDF1(0, 2) = 112. / 27.;
1092 gammaDF1(0, 3) = -812. / 81.;
1093 gammaDF1(1, 0) = -2552. / 2187.;
1094 gammaDF1(1, 1) = 15638. / 243.;
1095 gammaDF1(1, 2) = -176. / 81.;
1096 gammaDF1(1, 3) = -2881. / 486.;
1097 gammaDF1(2, 0) = -90944. / 729.;
1098 gammaDF1(2, 1) = 90128. / 81.;
1099 gammaDF1(2, 2) = 1120. / 27.;
1100 gammaDF1(2, 3) = -1748. / 81.;
1101 gammaDF1(3, 0) = 1312. / 2187.;
1102 gammaDF1(3, 1) = 102488. / 243.;
1103 gammaDF1(3, 2) = -1592. / 81.;
1104 gammaDF1(3, 3) = -6008. / 243.;
1105 break;
1106 case 30:
1107 case 21:
1108 case 02:
1109 break;
1110 default:
1111 throw std::runtime_error("EvolDF1::GammaQQ(): order not implemented");
1112 }
1113 return (gammaDF1);
1114}

Friends And Related Symbol Documentation

◆ gslpp_special_functions::zeta

double gslpp_special_functions::zeta ( int  i)
friend

Member Data Documentation

◆ ai

std::map< uint, double > EvolDF1::ai[NF]
private

Definition at line 328 of file EvolDF1.h.

◆ alsM_cache

double EvolDF1::alsM_cache
private

Definition at line 343 of file EvolDF1.h.

◆ blocks

std::string EvolDF1::blocks
private

Definition at line 337 of file EvolDF1.h.

◆ eval

gslpp::vector<double> EvolDF1::eval
private

Definition at line 340 of file EvolDF1.h.

◆ evalc

gslpp::vector<gslpp::complex> EvolDF1::evalc
private

Definition at line 342 of file EvolDF1.h.

◆ evec

gslpp::matrix<double> EvolDF1::evec
private

Definition at line 339 of file EvolDF1.h.

◆ evec_i

gslpp::matrix<double> EvolDF1::evec_i
private

Definition at line 339 of file EvolDF1.h.

◆ evecc

gslpp::matrix<gslpp::complex> EvolDF1::evecc
private

Definition at line 341 of file EvolDF1.h.

◆ f_f_c

int EvolDF1::f_f_c[4][F_iCacheSize]
private

Definition at line 347 of file EvolDF1.h.

◆ f_f_d

double EvolDF1::f_f_d[2][F_iCacheSize]
private

Definition at line 348 of file EvolDF1.h.

◆ gg

gslpp::matrix<double> EvolDF1::gg
private

Definition at line 339 of file EvolDF1.h.

◆ h

gslpp::matrix<double> EvolDF1::h
private

Definition at line 339 of file EvolDF1.h.

◆ js

gslpp::matrix<double> EvolDF1::js
private

Definition at line 339 of file EvolDF1.h.

◆ jss

gslpp::matrix<double> EvolDF1::jss
private

Definition at line 339 of file EvolDF1.h.

◆ jssv

gslpp::matrix<double> EvolDF1::jssv
private

Definition at line 339 of file EvolDF1.h.

◆ jv

gslpp::matrix<double> EvolDF1::jv
private

Definition at line 339 of file EvolDF1.h.

◆ MAls_cache

double EvolDF1::MAls_cache
private

Definition at line 343 of file EvolDF1.h.

◆ model

const StandardModel& EvolDF1::model
private

Definition at line 333 of file EvolDF1.h.

◆ nfmax

uint EvolDF1::nfmax
private

Definition at line 336 of file EvolDF1.h.

◆ nfmin

uint EvolDF1::nfmin
private

Definition at line 336 of file EvolDF1.h.

◆ nops

uint EvolDF1::nops
private

Definition at line 336 of file EvolDF1.h.

◆ s_s

gslpp::matrix<double> EvolDF1::s_s
private

Definition at line 339 of file EvolDF1.h.

◆ vij

gslpp::matrix<double> EvolDF1::vij
private

Definition at line 339 of file EvolDF1.h.

◆ vM0vi

std::map< std::vector<uint>, double > EvolDF1::vM0vi[NF]
private

Definition at line 329 of file EvolDF1.h.

◆ vM113vi

std::map< std::vector<uint>, double > EvolDF1::vM113vi[NF]
private

Definition at line 331 of file EvolDF1.h.

◆ vM11vi

std::map< std::vector<uint>, double > EvolDF1::vM11vi[NF]
private

Definition at line 330 of file EvolDF1.h.

◆ vM131vi

std::map< std::vector<uint>, double > EvolDF1::vM131vi[NF]
private

Definition at line 331 of file EvolDF1.h.

◆ vM133vi

std::map< std::vector<uint>, double > EvolDF1::vM133vi[NF]
private

Definition at line 331 of file EvolDF1.h.

◆ vM13vi

std::map< std::vector<uint>, double > EvolDF1::vM13vi[NF]
private

Definition at line 330 of file EvolDF1.h.

◆ vM14vi

std::map< std::vector<uint>, double > EvolDF1::vM14vi[NF]
private

Definition at line 331 of file EvolDF1.h.

◆ vM1vi

std::map< std::vector<uint>, double > EvolDF1::vM1vi[NF]
private

Definition at line 329 of file EvolDF1.h.

◆ vM23vi

std::map< std::vector<uint>, double > EvolDF1::vM23vi[NF]
private

Definition at line 330 of file EvolDF1.h.

◆ vM2vi

std::map< std::vector<uint>, double > EvolDF1::vM2vi[NF]
private

Definition at line 329 of file EvolDF1.h.

◆ vM311vi

std::map< std::vector<uint>, double > EvolDF1::vM311vi[NF]
private

Definition at line 331 of file EvolDF1.h.

◆ vM313vi

std::map< std::vector<uint>, double > EvolDF1::vM313vi[NF]
private

Definition at line 331 of file EvolDF1.h.

◆ vM31vi

std::map< std::vector<uint>, double > EvolDF1::vM31vi[NF]
private

Definition at line 330 of file EvolDF1.h.

◆ vM32vi

std::map< std::vector<uint>, double > EvolDF1::vM32vi[NF]
private

Definition at line 330 of file EvolDF1.h.

◆ vM331vi

std::map< std::vector<uint>, double > EvolDF1::vM331vi[NF]
private

Definition at line 331 of file EvolDF1.h.

◆ vM33vi

std::map< std::vector<uint>, double > EvolDF1::vM33vi[NF]
private

Definition at line 330 of file EvolDF1.h.

◆ vM34vi

std::map< std::vector<uint>, double > EvolDF1::vM34vi[NF]
private

Definition at line 330 of file EvolDF1.h.

◆ vM3vi

std::map< std::vector<uint>, double > EvolDF1::vM3vi[NF]
private

Definition at line 329 of file EvolDF1.h.

◆ vM41vi

std::map< std::vector<uint>, double > EvolDF1::vM41vi[NF]
private

Definition at line 331 of file EvolDF1.h.

◆ vM43vi

std::map< std::vector<uint>, double > EvolDF1::vM43vi[NF]
private

Definition at line 330 of file EvolDF1.h.

◆ vM4vi

std::map< std::vector<uint>, double > EvolDF1::vM4vi[NF]
private

Definition at line 329 of file EvolDF1.h.

◆ vM5vi

std::map< std::vector<uint>, double > EvolDF1::vM5vi[NF]
private

Definition at line 329 of file EvolDF1.h.

◆ vM6vi

std::map< std::vector<uint>, double > EvolDF1::vM6vi[NF]
private

Definition at line 330 of file EvolDF1.h.

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