EWSMThreeLoopEW2QCD Class Reference

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

#include <EWSMThreeLoopEW2QCD.h>

Collaboration diagram for EWSMThreeLoopEW2QCD:
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Detailed Description

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

Author
HEPfit Collaboration

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

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

where only \(\Delta\rho\) is non-zero in the current class. See also the description of EWSM class for their definitions.

Definition at line 34 of file EWSMThreeLoopEW2QCD.h.

Public Member Functions

double DeltaAlpha_l (const double s) const
 Leptonic contribution of \(O(\alpha^2\alpha_s)\) to the electromagnetic coupling \(\alpha\), denoted as \(\Delta\alpha_{\mathrm{lept}}^{\alpha^2\alpha_s}(s)\). More...
 
double DeltaAlpha_t (const double s) const
 Top-quark contribution of \(O(\alpha^2\alpha_s)\) to the electromagnetic coupling \(\alpha\), denoted as \(\Delta\alpha_{\mathrm{top}}^{\alpha^2\alpha_s}(s)\). More...
 
gslpp::complex deltaKappa_rem_f (const Particle f, const double Mw_i) const
 Remainder contribution of \(O(\alpha^2\alpha_s)\) to the effective couplings \(\kappa_Z^f\), denoted as \(\delta\kappa_{\mathrm{rem}}^{f,\, \alpha^2\alpha_s}\). More...
 
double DeltaR_rem (const double Mw_i) const
 Remainder contribution of \(O(\alpha^2\alpha_s)\) to \(\Delta r\), denoted as \(\Delta r_{\mathrm{rem}}^{\alpha^2\alpha_s}\). More...
 
double DeltaRho (const double Mw_i) const
 Leading three-loop contribution of \(O(\alpha^2\alpha_s)\) to \(\Delta\rho\), denoted as \(\Delta\rho^{\alpha^2\alpha_s}\). More...
 
gslpp::complex deltaRho_rem_f (const Particle f, const double Mw_i) const
 Remainder contribution of \(O(\alpha^2\alpha_s)\) to the effective couplings \(\rho_Z^f\), denoted as \(\delta\rho_{\mathrm{rem}}^{f,\, \alpha^2\alpha_s}\). More...
 
 EWSMThreeLoopEW2QCD (const EWSMcache &cache_i)
 Constructor. More...
 

Private Attributes

const EWSMcachecache
 A reference to an object of type EWSMcache. More...
 

Constructor & Destructor Documentation

EWSMThreeLoopEW2QCD::EWSMThreeLoopEW2QCD ( const EWSMcache cache_i)

Constructor.

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

Definition at line 11 of file EWSMThreeLoopEW2QCD.cpp.

12 : cache(cache_i)
13 {
14 }
const EWSMcache & cache
A reference to an object of type EWSMcache.

Member Function Documentation

double EWSMThreeLoopEW2QCD::DeltaAlpha_l ( const double  s) const

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

This contribution vanishes at \(O(\alpha^2\alpha_s)\).

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

Definition at line 19 of file EWSMThreeLoopEW2QCD.cpp.

20 {
21  return (0.0);
22 }
double EWSMThreeLoopEW2QCD::DeltaAlpha_t ( const double  s) const

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

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

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

Definition at line 24 of file EWSMThreeLoopEW2QCD.cpp.

25 {
26  return (0.0);
27 }
gslpp::complex EWSMThreeLoopEW2QCD::deltaKappa_rem_f ( const Particle  f,
const double  Mw_i 
) const

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

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

Parameters
[in]fa lepton or quark
[in]Mw_ithe \(W\)-boson mass
Returns
\(\delta\kappa_{\mathrm{rem}}^{f,\, \alpha^2\alpha_s}=0\)

Definition at line 74 of file EWSMThreeLoopEW2QCD.cpp.

75 {
76  if (f.is("TOP")) return ( gslpp::complex(0.0, 0.0, false));
77  return ( gslpp::complex(0.0, 0.0, false));
78 }
bool is(std::string name_i) const
Definition: Particle.cpp:23
A class for defining operations on and functions of complex numbers.
Definition: gslpp_complex.h:35
double EWSMThreeLoopEW2QCD::DeltaR_rem ( const double  Mw_i) const

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

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

Parameters
[in]Mw_ithe \(W\)-boson mass
Returns
\(\Delta r_{\mathrm{rem}}^{\alpha^2\alpha_s}=0\)

Definition at line 63 of file EWSMThreeLoopEW2QCD.cpp.

64 {
65  return (0.0);
66 }
double EWSMThreeLoopEW2QCD::DeltaRho ( const double  Mw_i) const

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

This function represents the leading three-loop mixed EW-QCD contribution of \(O(\alpha^2\alpha_s m_t^4/M_Z^4)\) to \(\Delta\rho\). Expressions are available for \(m_h=0\) in [117] and for \(m_h\approx m_t\) and \(m_h\gg m_t\) in [74].

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

Definition at line 29 of file EWSMThreeLoopEW2QCD.cpp.

30 {
31  double Mw = Mw_i;
32  double mh = cache.getSM().getMHl();
33  double Mt = cache.getSM().getMtpole();
34  double DeltaRho;
35  if (mh == 0.0) {
36  DeltaRho = 4.0 * (185.0 / 3.0 + 729.0 / 4.0 * cache.getS2()
37  - 48.0 * cache.getZeta2() * cache.getLog2()
38  - 151.0 / 6.0 * cache.getZeta2() + 29.0 * cache.getZeta3()
39  - 24.0 * cache.getZeta4() + 12.0 * cache.getB4());
40  } else if (mh > 0.0 && mh <= 2.5 * Mt) {
41  double delta = mh / Mt - 1.0;
42  DeltaRho = 157.295 + 112.00 * delta - 24.73 * delta * delta
43  + 7.39 * pow(delta, 3.0) - 3.52 * pow(delta, 4.0)
44  + 2.06 * pow(delta, 5.0);
45  } else if (mh > 2.5 * Mt) {
46  double Y = 4.0 * pow(Mt / mh, 2.0);
47  double logY = 2.0 * (cache.getLog2() + cache.logMTOPtoMH());
48  double logY2 = logY*logY;
49  double logY3 = logY2*logY;
50  DeltaRho = 79.73 - 47.77 * logY + 42.07 * logY2 + 9.00 * logY3
51  + Y * (225.16 - 179.74 * logY + 70.22 * logY2 - 19.22 * logY3)
52  + Y * Y * (-76.07 + 25.33 * logY - 9.17 * logY2 - 5.57 * logY3)
53  + Y * Y * Y * (-10.10 - 24.69 * logY - 0.30 * logY2 - 5.46 * logY3)
54  + Y * Y * Y * Y * (-4.52 - 32.85 * logY + 0.72 * logY2 - 5.25 * logY3)
55  + Y * Y * Y * Y * Y * (-2.55 - 36.61 * logY + 1.06 * logY2 - 5.14 * logY3);
56  } else {
57  throw std::runtime_error("Higgs mass is out of range in EWSMThreeLoopEW2QCD::DeltaRho()");
58  }
59  DeltaRho *= pow(cache.Xt_alpha(Mw), 2.0) * cache.alsMt() / M_PI;
60  return DeltaRho;
61 }
double getLog2() const
A get method to access the constant .
Definition: EWSMcache.h:223
double getB4() const
A get method to access the constant .
Definition: EWSMcache.h:214
double getZeta3() const
A get method to access the value of the zeta function .
Definition: EWSMcache.h:146
double Xt_alpha(const double Mw_i) const
The quantity with the coupling .
Definition: EWSMcache.h:355
complex pow(const complex &z1, const complex &z2)
double alsMt() const
The strong coupling at NNLO.
Definition: EWSMcache.h:378
const EWSMcache & cache
A reference to an object of type EWSMcache.
double getZeta2() const
A get method to access the value of the zeta function .
Definition: EWSMcache.h:137
double getZeta4() const
A get method to access the value of the zeta function .
Definition: EWSMcache.h:155
double getMtpole() const
A get method to access the pole mass of the top quark.
Definition: QCD.h:923
An observable class for the -boson mass.
Definition: Mw.h:22
double logMTOPtoMH() const
A cache method.
Definition: EWSMcache.cpp:126
double DeltaRho(const double Mw_i) const
Leading three-loop contribution of to , denoted as .
double getS2() const
A get method to access the constant .
Definition: EWSMcache.h:180
double getMHl() const
A get method to retrieve the Higgs mass .
const StandardModel & getSM() const
Definition: EWSMcache.h:56
gslpp::complex EWSMThreeLoopEW2QCD::deltaRho_rem_f ( const Particle  f,
const double  Mw_i 
) const

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

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

Parameters
[in]fa lepton or quark
[in]Mw_ithe \(W\)-boson mass
Returns
\(\delta\rho_{\mathrm{rem}}^{f,\, \alpha^2\alpha_s}=0\)

Definition at line 68 of file EWSMThreeLoopEW2QCD.cpp.

69 {
70  if (f.is("TOP")) return ( gslpp::complex(0.0, 0.0, false));
71  return ( gslpp::complex(0.0, 0.0, false));
72 }
bool is(std::string name_i) const
Definition: Particle.cpp:23
A class for defining operations on and functions of complex numbers.
Definition: gslpp_complex.h:35

Member Data Documentation

const EWSMcache& EWSMThreeLoopEW2QCD::cache
private

A reference to an object of type EWSMcache.

Definition at line 113 of file EWSMThreeLoopEW2QCD.h.


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