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EvolDF2 Class Reference

#include <EvolDF2.h>

+ Inheritance diagram for EvolDF2:

Detailed Description

Definition at line 15 of file EvolDF2.h.

Public Member Functions

gslpp::matrix< double > AnomalousDimension (orders order, unsigned int nf, int basis=0) const
 ADM in the basis used in Ciuchini et.al. hep-ph/9711402 (basis = 0, default) or in the basis (QVLL, QLR, QSLL) used in Buras et.al. hep-ph/0005183 (basis = 1) More...
 
gslpp::matrix< double > & Df2Evol (double mu, double M, orders order, schemes scheme=NDR)
 
double etabS0 (double mu) const
 Buras et al, hep-ph/9512380. More...
 
double etacc (double mu) const
 Buras et al, hep-ph/9512380. More...
 
double etact (double mu) const
 Buras et al, hep-ph/9512380. More...
 
double etatt (double mu) const
 Buras et al, hep-ph/9512380. More...
 
 EvolDF2 (unsigned int dim_i, schemes scheme, orders order, const StandardModel &model)
 constructor More...
 
virtual ~EvolDF2 ()
 destructor More...
 
- Public Member Functions inherited from RGEvolutor
gslpp::matrix< double > * Evol (orders order)
 Evolution matrix set at a fixed order of QCD coupling. More...
 
gslpp::matrix< double > * Evol (orders_qed order_qed)
 Evolution matrix set at a fixed order of Electroweak coupling. More...
 
gslpp::matrix< double > ** getEvol () const
 
double getM () const
 Retrieve the upper scale of the Wilson Coefficients. More...
 
 RGEvolutor (unsigned int dim, schemes scheme, orders order)
 constructor More...
 
 RGEvolutor (unsigned int dim, schemes scheme, orders order, orders_qed order_qed)
 constructor More...
 
void setEvol (const gslpp::matrix< double > &m, orders order_i)
 
void setEvol (const gslpp::matrix< double > &m, orders_qed order_qed_i)
 
void setEvol (unsigned int i, unsigned int j, double x, orders order_i)
 
void setEvol (unsigned int i, unsigned int j, double x, orders order_i, orders_qed order_qed)
 
void setM (double M)
 Sets the upper scale for the running of the Wilson Coefficients. More...
 
void setMu (double mu)
 Sets the lower scale for the running of the Wilson Coefficients. More...
 
void setScales (double mu, double M)
 Sets the upper and lower scale for the running of the Wilson Coefficients. More...
 
virtual ~RGEvolutor ()
 destructor More...
 
- Public Member Functions inherited from WilsonTemplate< gslpp::matrix< double > >
double getMu () const
 
orders getOrder () const
 
orders_qed getOrder_qed () const
 
schemes getScheme () const
 
unsigned int getSize () const
 
virtual void resetCoefficient ()
 
void setScheme (schemes scheme)
 
 WilsonTemplate (const WilsonTemplate< gslpp::matrix< double > > &orig)
 
 WilsonTemplate (unsigned int dim, schemes scheme_i, orders order_i, orders_qed order_qed_i=NO_QED)
 
virtual ~WilsonTemplate ()
 

Private Member Functions

void Df2Evol (double mu, double M, double nf, schemes scheme)
 

Private Attributes

double a [5]
 
double alsMZ_cache = 0.
 
double b [5][5][5]
 
double c [3][5][5][5]
 
double d [3][5][5][5]
 
unsigned int dim
 
const StandardModel & model
 
double Mz_cache = 0.
 

Additional Inherited Members

- Protected Member Functions inherited from WilsonTemplate< gslpp::matrix< double > >
gslpp::matrix< double > * Elem (orders order) const
 
gslpp::matrix< double > * Elem (orders_qed order_qed) const
 
void setElem (const gslpp::matrix< double > &v, orders order_i)
 
void setElem (const gslpp::matrix< double > &v, orders_qed order_qed_i)
 
- Protected Attributes inherited from RGEvolutor
double M
 
- Protected Attributes inherited from WilsonTemplate< gslpp::matrix< double > >
gslpp::matrix< double > * elem [MAXORDER_QED+1]
 
double mu
 
orders order
 
orders_qed order_qed
 
schemes scheme
 
unsigned int size
 

Constructor & Destructor Documentation

◆ EvolDF2()

EvolDF2::EvolDF2 ( unsigned int  dim_i,
schemes  scheme,
orders  order,
const StandardModel &  model 
)

constructor

Parameters
dim
scheme
order
model

Definition at line 12 of file EvolDF2.cpp.

13: RGEvolutor(dim_i, scheme, order),
14 model(model),
15 dim(dim_i)
16{
17 //double Nc = model.getNc();
18 int basis = 0; //0: Gabbiani, 1: Buras
19 gslpp::matrix<double> g0t(AnomalousDimension(LO, 3, basis).transpose());
20
21 gslpp::matrix<gslpp::complex>vv(dim, dim, 0.);
22 gslpp::vector<gslpp::complex>ee(dim, 0.);
23
24 g0t.eigensystem(vv, ee);
25
26 gslpp::matrix<double> v(vv.real());
27 gslpp::vector<double> e(ee.real());
28
29 gslpp::matrix<double> vi = v.inverse();
30 for (unsigned int k = 0; k < dim; k++) {
31 a[k] = e(k);
32// std::cout << "a[" << k << "] = " << a[k] << std::endl;
33 for (unsigned int j = 0; j < dim; j++) {
34 for (unsigned int i = 0; i < dim; i++) {
35 b[i][j][k] = v(i, k) * vi(k, j);
36// if (b[i][j][k] != 0.)
37// std::cout << "b[" << i << "][" << j << "][" << k << "] = " << b[i][j][k] << std::endl;
38 }
39 }
40 }
41
42 gslpp::matrix<double> h(dim, dim, 0.);
43 for (int l = 0; l < 3; l++) {
44 gslpp::matrix<double> gg = vi * (AnomalousDimension(NLO, 6 - l, basis).transpose()) * v;
45 double b0 = model.Beta0(6 - l);
46 for (unsigned int i = 0; i < dim; i++)
47 for (unsigned int j = 0; j < dim; j++)
48 h(i, j) = (i == j) * e(i) * model.Beta1(6 - l) / (2. * b0 * b0) -
49 gg(i, j) / (2. * b0 + e(i) - e(j));
50 gslpp::matrix<double> j = v * h * vi;
51 gslpp::matrix<double> jv = j*v;
52 gslpp::matrix<double> vij = vi*j;
53 for (unsigned int i = 0; i < dim; i++)
54 for (unsigned int j = 0; j < dim; j++)
55 for (unsigned int k = 0; k < dim; k++) {
56 c[l][i][j][k] = jv(i, k) * vi(k, j);
57// if (c[l][i][j][k] != 0.)
58// std::cout << "c[" << l << "][" << i << "][" << j << "][" << k << "] = " << c[l][i][j][k] << std::endl;
59 d[l][i][j][k] = -v(i, k) * vij(k, j);
60// if (d[l][i][j][k] != 0.)
61// std::cout << "d[" << l << "][" << i << "][" << j << "][" << k << "] = " << d[l][i][j][k] << std::endl;
62 }
63 }
64}
LO
@ LO
Definition: OrderScheme.h:34
NLO
@ NLO
Definition: OrderScheme.h:35
EvolDF2::d
double d[3][5][5][5]
Definition: EvolDF2.h:96
EvolDF2::dim
unsigned int dim
Definition: EvolDF2.h:98
EvolDF2::b
double b[5][5][5]
Definition: EvolDF2.h:94
EvolDF2::c
double c[3][5][5][5]
Definition: EvolDF2.h:95
EvolDF2::a
double a[5]
Definition: EvolDF2.h:93
EvolDF2::AnomalousDimension
gslpp::matrix< double > AnomalousDimension(orders order, unsigned int nf, int basis=0) const
ADM in the basis used in Ciuchini et.al. hep-ph/9711402 (basis = 0, default) or in the basis (QVLL,...
Definition: EvolDF2.cpp:69
EvolDF2::model
const StandardModel & model
Definition: EvolDF2.h:97
QCD::Beta1
const double Beta1(const double nf) const
The coefficient for a certain number of flavours .
Definition: QCD.cpp:606
QCD::Beta0
const double Beta0(const double nf) const
The coefficient for a certain number of flavours .
Definition: QCD.cpp:601
RGEvolutor::RGEvolutor
RGEvolutor(unsigned int dim, schemes scheme, orders order)
constructor
Definition: RGEvolutor.cpp:10

◆ ~EvolDF2()

EvolDF2::~EvolDF2 ( )
virtual

destructor

Definition at line 66 of file EvolDF2.cpp.

67{}

Member Function Documentation

◆ AnomalousDimension()

gslpp::matrix< double > EvolDF2::AnomalousDimension ( orders  order,
unsigned int  nf,
int  basis = 0 
) const

ADM in the basis used in Ciuchini et.al. hep-ph/9711402 (basis = 0, default) or in the basis (QVLL, QLR, QSLL) used in Buras et.al. hep-ph/0005183 (basis = 1)

Parameters
order
nfnumber of active flavours
basisbasis identifier (0: ciuchini, 1: buras)
Returns
Anomalous dimension for DeltaF=2 processes

Definition at line 69 of file EvolDF2.cpp.

70{
71 gslpp::matrix<double> ad(dim, dim, 0.);
72 double Nc = model.getNc();
73 switch (basis) {
74 case 0:
75 switch (order) {
76 case LO:
77 ad(0, 0) = (6. * Nc - 6.) / Nc;
78 ad(1, 1) = -(6. * Nc * Nc - 8. * Nc - 2.) / Nc;
79 ad(1, 2) = (4. * Nc - 8.) / Nc;
80 ad(2, 1) = (4. * Nc * Nc - 4. * Nc - 8.) / Nc;
81 ad(2, 2) = (2. * Nc * Nc + 4. * Nc + 2.) / Nc;
82 ad(3, 3) = -(6. * Nc * Nc - 6.) / Nc;
83 ad(4, 3) = -6.;
84 ad(4, 4) = 6. / Nc;
85 break;
86 case NLO:
87
88 // MSbar-NDR scheme with evanescent operators of Buras, Misiak & Urban
89
90 if (!(nf == 3 || nf == 4 || nf == 5 || nf == 6))
91 throw std::runtime_error("EvolDF2::AnomalousDimension(): wrong number of flavours");
92 ad(0, 0) = -(-1. + Nc)*(-171. + 19. * Nc * Nc + Nc * (63. - 4. * nf)) / (6. * Nc * Nc);
93 ad(1, 1) = (-1251. - 609. * Nc * Nc * Nc * Nc + Nc * (432. - 52. * nf) - 8. * Nc * Nc * (-71 + 2. * nf) +
94 20. * Nc * Nc * Nc * (32. + 3. * nf)) / (18. * Nc * Nc);
95 ad(1, 2) = -(2. * (-2. + Nc)*(-72. + Nc * Nc + 2. * Nc * (63. + nf))) / (9. * Nc * Nc);
96 ad(2, 1) = 2. * (119. * Nc * Nc * Nc + 8. * (-9. + 5. * nf) + 2. * Nc * (-125. + 7. * nf) -
97 Nc * Nc * (101. + 14. * nf)) / (9. * Nc);
98 ad(2, 2) = (477. + 343. * Nc * Nc * Nc * Nc + Nc * Nc * Nc * (380. - 52. * nf) - 4. * Nc * (-36. + nf) -
99 8. * Nc * Nc * (16. + 13. * nf)) / (18. * Nc * Nc);
100 ad(3, 3) = (45. + 479. * Nc * Nc - 203. * Nc * Nc * Nc * Nc - 44. * Nc * nf + 20. * Nc * Nc * Nc * nf) /
101 (6. * Nc * Nc);
102 ad(3, 4) = -(18. / Nc)-(71. * Nc) / 2. + 4. * nf;
103 ad(4, 3) = 3. / Nc - (100. * Nc) / 3. + (22. * nf) / 3.;
104 ad(4, 4) = (45. + 137. * Nc * Nc - 44. * Nc * nf) / (6. * Nc * Nc);
105 break;
106 default:
107 throw std::runtime_error("EvolDF2::AnomalousDimension(): order not implemented");
108 }
109 break;
110 case 1:
111 switch (order) {
112 case LO:
113 ad(0, 0) = 6. - 6. / Nc;
114 ad(1, 1) = 6. / Nc;
115 ad(1, 2) = 12.;
116 ad(2, 2) = 6. / Nc - 6. * Nc;
117 ad(3, 3) = 6. + 6. / Nc - 6. * Nc;
118 ad(3, 4) = 1. / 2. - 1. / Nc;
119 ad(4, 3) = -24. - 48. / Nc;
120 ad(4, 4) = 6. - 2. / Nc + 2. * Nc;
121 break;
122 case NLO:
123
124 // MSbar-NDR scheme with evanescent operators of Buras, Misiak & Urban
125
126 if (!(nf == 3 || nf == 4 || nf == 5 || nf == 6))
127 throw std::runtime_error("EvolDF2::AnomalousDimension(): wrong number of flavours");
128 ad(0, 0) = -22. / 3. - 57. / (2. * Nc * Nc) + 39. / Nc - (19. * Nc) / 6. + (2. * nf) / 3. - (2. * nf) / 3. / Nc;
129 ad(1, 1) = 137. / 6. + 15. / (2 * Nc * Nc) - (22 * nf) / (3 * Nc);
130 ad(1, 2) = -(6. / Nc) + (200. * Nc) / 3. - (44 * nf) / 3.;
131 ad(2, 1) = 9. / Nc + (71. * Nc) / 4. - 2. * nf;
132 ad(2, 2) = 479. / 6. + 15. / (2. * Nc * Nc) - (203. * Nc * Nc) / 6. - (22. * nf) / (3. * Nc) + (10. * Nc * nf) / 3.;
133 ad(3, 3) = 136. / 3. - 107. / (2. * Nc * Nc) - 12. / Nc + (107. * Nc) / 3. - (203. * Nc * Nc) / 6. - (2. * nf) / 3. - (10. * nf) / (3. * Nc) + (10. * Nc * nf) / 3.;
134 ad(3, 4) = -31. / 9. - 4. / (Nc * Nc) + 9. / Nc - Nc / 36. - nf / 18. + nf / (9 * Nc);
135 ad(4, 3) = -704. / 3. - 320. / (Nc * Nc) - 208. / Nc - (364. * Nc) / 3. + (136. * nf) / 3. + (176. * nf) / (3. * Nc);
136 ad(4, 4) = -188. / 9. + 21. / (2. * Nc * Nc) + 44. / Nc + 21. * Nc + (343. * Nc * Nc) / 18. - 6. * nf + (2. * nf) / (9. * Nc) - (26. * Nc * nf) / 9.;
137 break;
138 default:
139 throw std::runtime_error("EvolDF2::AnomalousDimension(): order not implemented");
140 }
141 break;
142 default:
143 throw std::runtime_error("EvolDF2::AnomalousDimension(): basis not implemented");
144 }
145 return (ad);
146}
QCD::getNc
const double getNc() const
A get method to access the number of colours .
Definition: QCD.h:507

◆ Df2Evol() [1/2]

void EvolDF2::Df2Evol ( double  mu,
double  M,
double  nf,
schemes  scheme 
)
private

Definition at line 193 of file EvolDF2.cpp.

194{
195
196 gslpp::matrix<double> resLO(dim, 0.), resNLO(dim, 0.), resNNLO(dim, 0.);
197
198 int l = 6 - (int) nf;
199 double alsM = model.Als(M, FULLNLO) / 4. / M_PI;
200 double alsmu = model.Als(mu, FULLNLO) / 4. / M_PI;
201
202 double eta = alsM / alsmu;
203
204 for (unsigned int k = 0; k < dim; k++) {
205 double etap = pow(eta, a[k] / 2. / model.Beta0(nf));
206 for (unsigned int i = 0; i < dim; i++)
207 for (unsigned int j = 0; j < dim; j++) {
208 resNNLO(i, j) += 0.;
209 resNLO(i, j) += c[l][i][j][k] * etap * alsmu;
210 resNLO(i, j) += d[l][i][j][k] * etap * alsM;
211 resLO(i, j) += b[i][j][k] * etap;
212 }
213 }
214 switch (order) {
215 case NNLO:
216 *elem[NNLO] = 0.; // Marco can implement it if he wishes to!
217 case NLO:
218 *elem[NLO] = (*elem[LO]) * resNLO + (*elem[NLO]) * resLO;
219 case LO:
220 *elem[LO] = (*elem[LO]) * resLO;
221 break;
222 case FULLNNLO:
223 case FULLNLO:
224 default:
225 throw std::runtime_error("Error in EvolDF2::Df2Evol()");
226 }
227}
NNLO
@ NNLO
Definition: OrderScheme.h:36
FULLNNLO
@ FULLNNLO
Definition: OrderScheme.h:39
FULLNLO
@ FULLNLO
Definition: OrderScheme.h:38
RGEvolutor::M
double M
Definition: RGEvolutor.h:142
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:1088
WilsonTemplate< gslpp::matrix< double > >::elem
gslpp::matrix< double > * elem[MAXORDER_QED+1]
Definition: WilsonTemplate.h:114

◆ Df2Evol() [2/2]

gslpp::matrix< double > & EvolDF2::Df2Evol ( double  mu,
double  M,
orders  order,
schemes  scheme = NDR 
)
Parameters
mulow energy scale
Mmatching scale
order
scheme
Returns
the Wilson coefficients evolved from the scale M to the scale mu

Definition at line 148 of file EvolDF2.cpp.

149{
150 switch (scheme) {
151 case NDR:
152 break;
153 case LRI:
154 case HV:
155 default:
156 std::stringstream out;
157 out << scheme;
158 throw std::runtime_error("EvolDF2::Df2Evol(): scheme " + out.str() + " not implemented ");
159 }
160
161 double alsMZ = model.getAlsMz();
162 double Mz = model.getMz();
163 if(alsMZ == alsMZ_cache && Mz == Mz_cache) {
164 if (mu == this->mu && M == this->M && scheme == this->scheme)
165 return (*Evol(order));
166 }
167 alsMZ_cache = alsMZ;
168 Mz_cache = Mz;
169
170 if (M < mu) {
171 std::stringstream out;
172 out << "M = " << M << " < mu = " << mu;
173 throw out.str();
174 }
175
176 setScales(mu, M); // also assign evol to identity
177 if (M != mu) {
178 double m_down = mu;
179 double m_up = model.AboveTh(m_down);
180 double nf = model.Nf(m_down);
181
182 while (m_up < M) {
183 Df2Evol(m_down, m_up, nf, scheme);
184 m_down = m_up;
185 m_up = model.AboveTh(m_down);
186 nf += 1.;
187 }
188 Df2Evol(m_down, M, nf, scheme);
189 }
190 return (*Evol(order));
191}
HV
@ HV
Definition: OrderScheme.h:22
LRI
@ LRI
Definition: OrderScheme.h:23
NDR
@ NDR
Definition: OrderScheme.h:21
EvolDF2::Df2Evol
gslpp::matrix< double > & Df2Evol(double mu, double M, orders order, schemes scheme=NDR)
Definition: EvolDF2.cpp:148
EvolDF2::alsMZ_cache
double alsMZ_cache
Definition: EvolDF2.h:99
EvolDF2::Mz_cache
double Mz_cache
Definition: EvolDF2.h:100
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
RGEvolutor::setScales
void setScales(double mu, double M)
Sets the upper and lower scale for the running of the Wilson Coefficients.
Definition: RGEvolutor.cpp:85
RGEvolutor::Evol
gslpp::matrix< double > * Evol(orders order)
Evolution matrix set at a fixed order of QCD coupling.
Definition: RGEvolutor.cpp:103
StandardModel::getMz
const double getMz() const
A get method to access the mass of the boson .
Definition: StandardModel.h:753
StandardModel::getAlsMz
const double getAlsMz() const
A get method to access the value of .
Definition: StandardModel.h:771

◆ etabS0()

double EvolDF2::etabS0 ( double  mu) const

Buras et al, hep-ph/9512380.

Parameters
mu
Returns
the NLO corrective factor for the top-top contribution to the bottom oscillations times the LO matching

Definition at line 419 of file EvolDF2.cpp.

420{
421 double N = model.getNc();
422 double x = model.getMatching().x_t(model.getMut());
423 double x2 = x * x;
424 double x3 = x2 * x;
425 double x4 = x3 * x;
426 double xm2 = (1 - x) * (1 - x);
427 double xm3 = xm2 * (1 - x);
428 //double xm4 = xm3 * (1 - x);
429 double logx = log(x);
430 //double Li2 = gsl_sf_dilog(1-x);
431
432 double S0tt = (4. * x - 11. * x2 + x3) / 4. / xm2 -
433 3. * x3 / (2. * xm3) * logx;
434
435 double Bt = 5. * (N - 1.) / 2. / N + 3. * (N * N - 1.) / 2. / N;
436
437 double gamma0 = 6. * (N - 1.) / N;
438
439 double gamma1[4] = {0.}, J[4] = {0.};
440
441 for (int i = 0; i < 4; ++i) {
442 gamma1[i] = (N - 1.) / (2. * N) * (-21. + 57. / N - 19. / 3. * N + 4. / 3. * (i + 3.));
443 J[i] = gamma0 * model.Beta1(3 + i) / 2. / model.Beta0(3 + i) / model.Beta0(3 + i)
444 - gamma1[i] / 2. / model.Beta0(3 + i);
445 }
446
447 double b = (4. - 22. * x + 15. * x2 + 2. * x3 + x4 - 18. * x2 * logx)
448 / ((-1. + x) * (-4. + 15. * x - 12. * x2 + x3 + 6. * x2 * logx));
449
450 double AlsT = model.Als(model.getMut());
451 double Alsm = model.Als(m);
452 double eta =
453 pow(AlsT / Alsm, 6. / 23.) *
454 (1.
455 + AlsT / 4. / M_PI * (model.getMatching().S1(x) / S0tt
456 + Bt - J[2] + gamma0 * log(model.getMut() / model.getMuw())
457 + 6 * (N * N - 1) / N * log(model.getMut() / model.getMuw()) * b)
458 + Alsm / 4. / M_PI * J[2]);
459 return (eta * S0tt);
460}
QCD::getMut
const double getMut() const
A get method to access the threshold between six- and five-flavour theory in GeV.
Definition: QCD.h:573
StandardModel::getMuw
const double getMuw() const
A get method to retrieve the matching scale around the weak scale.
Definition: StandardModel.h:951
StandardModel::getMatching
virtual StandardModelMatching & getMatching() const
A get method to access the member reference of type StandardModelMatching.
Definition: StandardModel.h:965

◆ etacc()

double EvolDF2::etacc ( double  mu) const

Buras et al, hep-ph/9512380.

Parameters
mu
Returns
the NLO corrective factor for the charm-charm contribution to the kaon oscillations

Definition at line 229 of file EvolDF2.cpp.

230{
231 double N = model.getNc();
232 double N2 = N * N;
233 double gamma0[2] = {0.}, gamma1[2][4] = {
234 {0.}
235 }, d[2][4] = {
236 {0.}
237 },
238 J[2][4] = {
239 {0.}
240 }, dd[2][2][4] = {
241 {
242 {0.}
243 }
244 }, JJ[2][2][4] = {
245 {
246 {0.}
247 }
248 },
249 B[2] = {0.}; // 0 = + ; 1 = - ;
250 double tau[2][2] = {
251 {0.}
252 }, K[2][2] = {
253 {0.}
254 }, beta[2][2] = {
255 {0.}
256 };
257
258 gamma0[0] = 6. * (N - 1.) / N;
259 gamma0[1] = -6. * (N + 1.) / N;
260
261 gamma1[0][0] = ((N - 1.) / (2. * N)) * (-21. + 57. / N - 19. / 3. * N + 4. / 3. * 3.);
262 gamma1[1][0] = ((N + 1.) / (2. * N)) * (-21. - 57. / N + 19. / 3. * N - 4. / 3. * 3.);
263 gamma1[0][1] = ((N - 1.) / (2. * N)) * (-21. + 57. / N - 19. / 3. * N + 4. / 3. * 4.);
264 gamma1[1][1] = ((N + 1.) / (2. * N)) * (-21. - 57. / N + 19. / 3. * N - 4. / 3. * 4.);
265 gamma1[0][2] = ((N - 1.) / (2. * N)) * (-21. + 57. / N - 19. / 3. * N + 4. / 3. * 5.);
266 gamma1[1][2] = ((N + 1.) / (2. * N)) * (-21. - 57. / N + 19. / 3. * N - 4. / 3. * 5.);
267 gamma1[0][3] = ((N - 1.) / (2. * N)) * (-21. + 57. / N - 19. / 3. * N + 4. / 3. * 6.);
268 gamma1[1][3] = ((N + 1.) / (2. * N)) * (-21. - 57. / N + 19. / 3. * N - 4. / 3. * 6.);
269
270 for (int i = 0; i < 2; i++) { // 0 = + ; 1 = - ;
271 for (int j = 0; j < 4; j++) { // j = nf - 3;
272 d[i][j] = gamma0[i] / 2. / model.Beta0(j + 3);
273 J[i][j] = d[i][j] / model.Beta0(j + 3) * model.Beta1(j + 3) -
274 gamma1[i][j] / 2. / model.Beta0(j + 3);
275 }
276
277 }
278
279 for (int i = 0; i < 2; i++) { // 0 = + ; 1 = - ;
280 for (int j = 0; j < 2; j++) { // 0 = + ; 1 = - ;
281 for (int k = 0; k < 4; k++) { // k = nf - 3;
282 dd[i][j][k] = d[i][k] + d[j][k];
283 JJ[i][j][k] = J[i][k] + J[j][k];
284 }
285 }
286 }
287
288 tau[0][0] = (N + 3.) / 4.;
289 tau[1][0] = -(N - 1.) / 4.;
290 tau[0][1] = tau[1][0];
291 tau[1][1] = (N - 1.) / 4.;
292
293 K[0][0] = 3. * (N - 1.) * tau[0][0];
294 K[1][0] = 3. * (N + 1.) * tau[0][1];
295 K[0][1] = K[1][0];
296 K[1][1] = 3. * (N + 3.) * tau[1][1];
297
298 beta[0][0] = (1. - N) * (M_PI * M_PI * (N2 - 6.) / (12. * N) + 3. * (-N2 + 2. * N + 13.) / (4. * N));
299 beta[1][0] = (1. - N) * (M_PI * M_PI * (-N2 + 2. * N - 2.) / (12. * N) + (3. * N2 + 13.) / (4. * N));
300 beta[0][1] = beta[1][0];
301 beta[1][1] = (1. - N) * (M_PI * M_PI * (N2 - 4. * N + 2) / (12. * N) - (3. * N2 + 10. * N + 13.) / (4. * N));
302
303 B[0] = 11. * (N - 1.) / (2. * N);
304 B[1] = -11. * (N + 1.) / (2. * N);
305
306 double eta = 0.;
307 double as_mb__as_muc = model.Als(model.getMub(), FULLNLO) / model.Als(model.getMuc(), FULLNLO);
308 double as_muw__as_mb = model.Als(model.getMuw(), FULLNLO) / model.Als(model.getMub(), FULLNLO);
309 double as_muc__4pi = model.Als(model.getMuc(), FULLNLO) / 4. / M_PI;
310 double log_muc__mc = log(model.getMuc() / model.getQuarks(QCD::CHARM).getMass());
311 double as_mb__4pi = model.Als(model.getMub(), FULLNLO) / 4. / M_PI;
312 double as_muw__4pi = model.Als(model.getMuw(), FULLNLO) / 4. / M_PI;
313
314
315 for (int i = 0; i < 2; i++) {
316 for (int j = 0; j < 2; j++) {
317 eta += pow(as_mb__as_muc, dd[i][j][1]) *
318 pow(as_muw__as_mb, dd[i][j][2]) *
319 (tau[i][j] + as_muc__4pi * (2. * K[i][j] *
320 log_muc__mc + tau[i][j] * (JJ[i][j][1] - J[0][0]) + beta[i][j]) +
321 tau[i][j]*(as_mb__4pi * (JJ[i][j][2] - JJ[i][j][1]) +
322 as_muw__4pi * (B[i] + B[j] - JJ[i][j][2])));
323 }
324 }
325
326 eta *= pow(model.Als(model.getMuc()), d[0][0]);
327 eta *= pow(model.Als(mu, FULLNLO), -2. / 9.);
328
329 return (eta * (1. + model.Als(mu, FULLNLO) / 4. / M_PI * J[0][0]));
330}
Particle::getMass
const double & getMass() const
A get method to access the particle mass.
Definition: Particle.h:61
QCD::getMuc
const double getMuc() const
A get method to access the threshold between four- and three-flavour theory in GeV.
Definition: QCD.h:591
QCD::CHARM
@ CHARM
Definition: QCD.h:326
QCD::getQuarks
const Particle & getQuarks(const QCD::quark q) const
A get method to access a quark as an object of the type Particle.
Definition: QCD.h:536
QCD::getMub
const double getMub() const
A get method to access the threshold between five- and four-flavour theory in GeV.
Definition: QCD.h:582

◆ etact()

double EvolDF2::etact ( double  mu) const

Buras et al, hep-ph/9512380.

Parameters
mu
Returns
the NLO corrective factor for the charm-top contribution to the kaon oscillations

Definition at line 332 of file EvolDF2.cpp.

333{
334
335 //temporary fix waiting for NNLO
336
337 double K = model.Als4(model.getMuw()) / model.Als4(model.getMuc());
338#if SUSYFIT_DEBUG & 2
339 std::cout << "K = " << K << std::endl;
340#endif
341 double Kpp = pow(K, 12. / 25.);
342 double Kpm = pow(K, -6. / 25.);
343 double Kmm = pow(K, -24. / 25.);
344 double K7 = pow(K, 1. / 5.);
345 double xc = model.Mrun4(model.getMuc(), model.getQuarks(QCD::CHARM).getMass_scale(), model.getQuarks(QCD::CHARM).getMass()) / model.Mw();
346 xc *= xc;
347 double xt = model.Mrun4(model.getMuw(), model.getQuarks(QCD::TOP).getMass_scale(), model.getQuarks(QCD::TOP).getMass()) / model.Mw();
348 xt *= xt;
349
350 double J3 = 6. * (3. - 1.) / 3. / 2. / model.Beta0(3) / model.Beta0(3) * model.Beta1(3) -
351 ((3. - 1.) / (2. * 3.)) * (-21. + 57. / 3. - 19. + 4.) / 2. / model.Beta0(3);
352
353
354 double eta = 0.;
355 double AlsC = model.Als4(model.getMuc());
356
357 eta = (M_PI / AlsC * (-18. / 7. * Kpp - 12. / 11. * Kpm + 6. / 29. * Kmm + 7716. / 2233. * K7) *
358 (1. - AlsC / (4. * M_PI) * 307. / 162.) + (log(model.getMuc() /
359 model.getQuarks(QCD::CHARM).getMass()) - 0.25) * (3. * Kpp - 2. * Kpm + Kmm) +
360 262497. / 35000. * Kpp - 123. / 625. * Kpm + 1108657. / 1305000. * Kmm - 277133. / 50750. * K7 +
361 K * (-21093. / 8750. * Kpp + 13331. / 13750. * Kpm - 10181. / 18125. * Kmm - 1731104. / 2512125. * K7) +
362 (log(xt) - (3. * xt) / (4. - 4. * xt) - log(xt) * (3. * xt * xt) / (4. * (1. - xt) * (1. - xt)) + 0.5) * K * K7) * xc / (model.getMatching().S0(xc, xt)) * pow(AlsC, 2. / 9.);
363
364 return (eta * (1. + model.Als(mu, FULLNLO) / 4. / M_PI * J3) * pow(model.Als(mu, FULLNLO), -2. / 9.));
365}
Particle::getMass_scale
double getMass_scale() const
A get method to access the scale at which the particle mass is defined.
Definition: Particle.h:133
QCD::Als4
const double Als4(const double mu) const
The value of at any scale with the number of flavours .
Definition: QCD.cpp:657
QCD::Mrun4
const double Mrun4(const double mu_f, const double mu_i, const double m) const
The running of a mass with the number of flavours .
Definition: QCD.cpp:1531
QCD::TOP
@ TOP
Definition: QCD.h:328
StandardModel::Mw
virtual const double Mw() const
The SM prediction for the -boson mass in the on-shell scheme, .
Definition: StandardModel/src/StandardModel.cpp:1019

◆ etatt()

double EvolDF2::etatt ( double  mu) const

Buras et al, hep-ph/9512380.

Parameters
mu
Returns
the NLO corrective factor for the top-top contribution to the kaon oscillations

Definition at line 367 of file EvolDF2.cpp.

368{
369 double N = model.getNc();
370 double x = model.getMatching().x_t(model.getMut());
371 double x2 = x * x;
372 double x3 = x2 * x;
373 double x4 = x3 * x;
374 double xm2 = (1 - x) * (1 - x);
375 double xm3 = xm2 * (1 - x);
376 //double xm4 = xm3 * (1 - x);
377 double logx = log(x);
378 //double Li2 = gsl_sf_dilog(1-x);
379
380 double S0tt = (4. * x - 11. * x2 + x3) / 4. / xm2 -
381 3. * x3 / (2. * xm3) * logx;
382
383 double Bt = 5. * (N - 1.) / 2. / N + 3. * (N * N - 1.) / 2. / N;
384
385 double gamma0 = 6. * (N - 1.) / N;
386
387 double gamma1[4] = {0.}, J[4] = {0.};
388
389 for (int i = 0; i < 4; ++i) {
390 gamma1[i] = (N - 1.) / (2. * N) * (-21. + 57. / N - 19. / 3. * N + 4. / 3. * (i + 3.));
391 J[i] = gamma0 * model.Beta1(3 + i) / 2. / model.Beta0(3 + i) / model.Beta0(3 + i)
392 - gamma1[i] / 2. / model.Beta0(3 + i);
393 }
394
395 double b = (4. - 22. * x + 15. * x2 + 2. * x3 + x4 - 18. * x2 * logx)
396 / ((-1. + x) * (-4. + 15. * x - 12. * x2 + x3 + 6. * x2 * logx));
397
398 double AlsT = model.Als(model.getMut());
399 double AlsB = model.Als(model.getMub());
400 double AlsC = model.Als(model.getMuc());
401 double eta = pow(AlsC, 6. / 27.) *
402 pow(AlsB / AlsC, 6. / 25.) *
403 pow(AlsT / AlsB, 6. / 23.) *
404 (1. + AlsC / 4. / M_PI * (J[1] - J[0]) +
405 AlsB / 4. / M_PI * (J[2] - J[1])
406 + AlsT / 4. / M_PI * (model.getMatching().S1(x) / S0tt
407 + Bt - J[2] + gamma0 * log(model.getMut() / model.getMuw())
408 + 6 * (N * N - 1) / N * log(model.getMut() / model.getMuw()) * b));
409 /* double J3 = 6. * (N - 1.) / N * (model.Beta1(3) / 2. / model.Beta0(3) / model.Beta0(3)) -
410 (N - 1.) / (2. * N) * (-21. + 57. / N - 19./3. * N + 4.) / 2. / model.Beta0(3);*/
411#if SUSYFIT_DEBUG & 2
412 std::cout << "AlsT = " << AlsT << " AlsC = " << AlsC << " AlsB = " << AlsB << " mub = " << model.getMub() << std::endl;
413 std::cout << "etatt = " << eta*(1. + model.Als(m, FULLNLO) / 4. / M_PI * J[0]) * pow(model.Als(m, FULLNLO), -2. / 9.)
414 << " mut = " << model.getMut() << " Muw = " << model.getMuw() << std::endl;
415#endif
416 return (eta * (1. + model.Als(m, FULLNLO) / 4. / M_PI * J[0]) * pow(model.Als(m, FULLNLO), -2. / 9.));
417}

Member Data Documentation

◆ a

double EvolDF2::a[5]
private

Definition at line 93 of file EvolDF2.h.

◆ alsMZ_cache

double EvolDF2::alsMZ_cache = 0.
private

Definition at line 99 of file EvolDF2.h.

◆ b

double EvolDF2::b[5][5][5]
private

Definition at line 94 of file EvolDF2.h.

◆ c

double EvolDF2::c[3][5][5][5]
private

Definition at line 95 of file EvolDF2.h.

◆ d

double EvolDF2::d[3][5][5][5]
private

Definition at line 96 of file EvolDF2.h.

◆ dim

unsigned int EvolDF2::dim
private

Definition at line 98 of file EvolDF2.h.

◆ model

const StandardModel& EvolDF2::model
private

Definition at line 97 of file EvolDF2.h.

◆ Mz_cache

double EvolDF2::Mz_cache = 0.
private

Definition at line 100 of file EvolDF2.h.

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