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EWSUSY Class Reference

A class for SUSY contributions to the EW precision observables. More...

#include <EWSUSY.h>

Detailed Description

A class for SUSY contributions to the EW precision observables.

Author
HEPfit Collaboration
Copyright
GNU General Public License

This class is used for the calculations of SUSY contributions to the EW precision observables, where Rosiek's notation is adopted internally. The conversions from Rosiek's notation to SLHA one are implemented in EWSUSY::SetRosiekParameters(), which is called from SUSY::PostUpdate().

References
Chankowski, Dabelstein, Hollik, Mosle, Pokorski and Rosiek, NPB 417 (1994) 101;
Chankowski, Pokorski and Rosiek, NPB 423 (1994) 437;
Rosiek, hep-ph/9511250, where an updated version is available at author's webpage.

Definition at line 36 of file EWSUSY.h.

Public Member Functions

gslpp::complex delta_v (const double mu, const QCD::lepton M, const QCD::lepton J, const double Mw_i) const
 
double DeltaAlphaL5q_SM_EW1 () const
 The SM one-loop leptonic and five-flavour-hadronic corrections to \(\alpha\) at Z-mass scale. More...
 
double DeltaR_boxLL_SUSY (const double Mw_i) const
 The LL SUSY box corrections to \(\Delta r\) in the 't Hooft-Feynman gauge. More...
 
double DeltaR_boxLR_SUSY (const double Mw_i) const
 The LR SUSY box corrections to \(\Delta r\) in the 't Hooft-Feynman gauge. More...
 
double DeltaR_neutrino_SUSY (const double Mw_i) const
 The renormalized SUSY neutrino wave-function contribution to \(\Delta r\) in the 't Hooft-Feynman gauge. More...
 
double DeltaR_rem_SM (const double Mw_i) const
 The SM one-loop renormalized vertex and box corrections to \(\Delta r\) in the 't Hooft-Feynman gauge. More...
 
double DeltaR_SUSY_EW1 (const double Mw_i) const
 The one-loop SUSY contribution to \(\Delta r\). More...
 
double DeltaR_TOTAL_EW1 (const double Mw_i) const
 The total one-loop contribution to \(\Delta r\) in the MSSM. More...
 
double DeltaR_vertex_SUSY (const double Mw_i) const
 The renormalized SUSY vertex corrections to \(\Delta r\) in the 't Hooft-Feynman gauge. More...
 
gslpp::complex dFA (const double mu, const double p2, const double mi, const double mj, const gslpp::complex cV_aij, const gslpp::complex cV_bji, const gslpp::complex cA_aij, const gslpp::complex cA_bji) const
 The derivative of \(F_A^{ab}(p^2,m_i,m_j,c_V^{aij},c_V^{bji},c_A^{aij},c_A^{bji})\) with respect to \(p^2\). More...
 
 EWSUSY (const SUSY &SUSY_in)
 Constructor. More...
 
gslpp::complex FA (const double mu, const double p2, const double mi, const double mj, const gslpp::complex cV_aij, const gslpp::complex cV_bji, const gslpp::complex cA_aij, const gslpp::complex cA_bji) const
 Fermionic contribuiton to the transverse part of a gauge-boson self-energy, \(F_A^{ab}(p^2,m_i,m_j,c_V^{aij},c_V^{bji},c_A^{aij},c_A^{bji})\). More...
 
gslpp::complex PiT_AZ (const double mu, const double p2, const double Mw_i) const
 The transverse part of the self-energy, \(\Pi_{\gamma Z}^T(p^2)\), for the mixing between photon and Z boson in the 't Hooft-Feynman gauge. More...
 
gslpp::complex PiT_W (const double mu, const double p2, const double Mw_i) const
 The transverse part of the W-boson self-energy, \(\Pi_W^T(p^2)\), in the 't Hooft-Feynman gauge. More...
 
gslpp::complex PiT_Z (const double mu, const double p2, const double Mw_i) const
 The transverse part of the Z-boson self-energy, \(\Pi_Z^T(p^2)\), in the 't Hooft-Feynman gauge. More...
 
double PiThat_W_0 (const double Mw_i) const
 The renormalized transverse W-boson self-energy at zero momentum transefer in the 't Hooft-Feynman gauge. More...
 
gslpp::complex PiTp_A (const double mu, const double p2, const double Mw_i) const
 The derivative of the transverse part of the photon self-energy with respect to \(p^2\), \(\Pi_{\gamma}^{T\prime}(p^2)\), in the 't Hooft-Feynman gauge. More...
 
void SetRosiekParameters ()
 Sets parameters in Rosiek's notation. More...
 
gslpp::complex Sigma_nu_0 (const double mu, const QCD::lepton I, const QCD::lepton J, const double Mw_i) const
 The SUSY neutrino self-energy at zero momentum transfer in the 't Hooft-Feynman gauge. More...
 
gslpp::complex v (const double mu, const QCD::lepton M, const QCD::lepton J, const double Mw_i) const
 

Constructor & Destructor Documentation

◆ EWSUSY()

EWSUSY::EWSUSY ( const SUSY &  SUSY_in)

Constructor.

Parameters
[in]SUSY_inA reference to a SUSY object.

Definition at line 29 of file EWSUSY.cpp.

30 : PV(true), mySUSY(SUSY_in),
31  Yu(3,3,0.0), Yd(3,3,0.0), Yl(3,3,0.0),
32  Au(3,3,0.0), Ad(3,3,0.0), Al(3,3,0.0),
33  Zm(2,2,0.), Zp(2,2,0.), ZN(4,4,0.),
34  ZU(6,6,0.), ZD(6,6,0.), ZL(6,6,0.), Zne(6,6,0.),
35  ZR(2,2,0.), ZH(2,2,0.)
36 {
37 }

Member Function Documentation

◆ delta_v()

gslpp::complex EWSUSY::delta_v ( const double  mu,
const QCD::lepton  M,
const QCD::lepton  J,
const double  Mw_i 
) const
Parameters
[in]muThe renormalization scale \(\mu\).
[in]MA charged lepton.
[in]JA neutrino.
[in]Mw_iThe W-boson mass \(M_W\).
Returns
\(\delta v(M,J)\).
References
Eq. (A.21) in [Chankowski, Dabelstein, Hollik, Mosle, Pokorski and Rosiek, NPB 417 (1994) 101].

Definition at line 1029 of file EWSUSY.cpp.

1031 {
1032  int intM, intJ;
1033  switch (M) {
1034  case StandardModel::ELECTRON:
1035  case StandardModel::MU:
1036  case StandardModel::TAU:
1037  intM = ((int)M - StandardModel::ELECTRON)/2;
1038  break;
1039  default:
1040  throw std::runtime_error("EWSUSY::delta_v(): Wrong argument!");
1041  }
1042  switch (J) {
1043  case StandardModel::NEUTRINO_1:
1044  case StandardModel::NEUTRINO_2:
1045  case StandardModel::NEUTRINO_3:
1046  intJ = ((int)J - StandardModel::NEUTRINO_1)/2;
1047  break;
1048  default:
1049  throw std::runtime_error("EWSUSY::delta_v(): Wrong argument!");
1050  }
1051 
1052  gslpp::complex delv = gslpp::complex(0.0, 0.0, false);
1053  double muIR = mu; /* fictional scale, since B0p(0,m1^2,m2^2) is IR finite */
1054  gslpp::complex b0p, b0;
1055 
1056  /* charged-slepton - neutralino loops */
1057  for (int k=0; k<6; ++k)
1058  for (int j=0; j<4; ++j) {
1059  b0p = PV.B0p(muIR*muIR, 0.0, Mse2[k], mN[j]*mN[j]);
1060  b0 = PV.B0(mu*mu, 0.0, Mse2[k], mN[j]*mN[j]);
1061  delv += 0.5*L_eLN(intM, k, j, Mw_i)*L_eLN(intJ, k, j, Mw_i).conjugate()
1062  *( (Mse2[k] - mN[j]*mN[j])*b0p - b0 );
1063  }
1064 
1065  /* sneutrino - chargino loops */
1066  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
1067  for (int i=0; i<2; ++i) {
1068  b0p = PV.B0p(muIR*muIR, 0.0, Msn2[K], mC[i]*mC[i]);
1069  b0 = PV.B0(mu*mu, 0.0, Msn2[K], mC[i]*mC[i]);
1070  delv += 0.5*L_esnC(intM, K, i, Mw_i)*L_esnC(intJ, K, i, Mw_i).conjugate()
1071  *( (Msn2[K] - mC[i]*mC[i])*b0p - b0 );
1072  }
1073 
1074  return ( delv/16.0/M_PI/M_PI );
1075 }

◆ DeltaAlphaL5q_SM_EW1()

double EWSUSY::DeltaAlphaL5q_SM_EW1 ( ) const

The SM one-loop leptonic and five-flavour-hadronic corrections to \(\alpha\) at Z-mass scale.

Returns
\(\Delta\alpha^{\ell + 5q}(M_Z^2)\) at one-loop level.

Definition at line 1178 of file EWSUSY.cpp.

1179 {
1180  /* Renormalization scale (varied for checking the cancellation of UV divergences */
1181  double mu = mySUSY.getMz() * RenormalizationScaleFactor;
1182 
1183  double Mz2 = mySUSY.getMz()*mySUSY.getMz();
1184  double e = sqrt(4.0*M_PI*mySUSY.getAle());
1185  double Nc = mySUSY.getNc();
1186 
1187  double DelA_l = 0.0, DelA_d = 0.0, DelA_u = 0.0;
1188 
1189  /* SM fermion loops */
1190  gslpp::complex cV_Aee = - e;
1191  gslpp::complex cA_Aee = 0.0;
1192  gslpp::complex cV_Add = - e/3.0;
1193  gslpp::complex cA_Add = 0.0;
1194  gslpp::complex cV_Auu = 2.0/3.0*e;
1195  gslpp::complex cA_Auu = 0.0;
1196  for (int I=0; I<3; ++I) {
1197  /* charged leptons */
1198  DelA_l += FA(mu, Mz2, m_l[I], m_l[I], cV_Aee, cV_Aee, cA_Aee, cA_Aee).real()/Mz2;
1199  DelA_l -= dFA(mu, 0.0, m_l[I], m_l[I], cV_Aee, cV_Aee, cA_Aee, cA_Aee).real();
1200 
1201  /* down-type quarks */
1202  DelA_d += Nc*FA(mu, Mz2, m_d[I], m_d[I], cV_Add, cV_Add, cA_Add, cA_Add).real()/Mz2;
1203  DelA_d -= Nc*dFA(mu, 0.0, m_d[I], m_d[I], cV_Add, cV_Add, cA_Add, cA_Add).real();
1204 
1205  /* up-type quarks, not including top quark */
1206  if (I!=3) {
1207  DelA_u += Nc*FA(mu, Mz2, m_u[I], m_u[I], cV_Auu, cV_Auu, cA_Auu, cA_Auu).real()/Mz2;
1208  DelA_u -= Nc*dFA(mu, 0.0, m_u[I], m_u[I], cV_Auu, cV_Auu, cA_Auu, cA_Auu).real();
1209  }
1210  }
1211 
1212  /* Debug */
1213  //std::cout << "EWSUSY(l) " << DelA_l/16.0/M_PI/M_PI << std::endl;
1214  //std::cout << "EWSM(l) " << getMyOneLoopEW()->DeltaAlpha_l(Mz2) << std::endl;
1215  //std::cout << "EWSUSY(q) " << (DelA_d + DelA_u)/16.0/M_PI/M_PI << std::endl;
1216  //std::cout << "EWSM(had) " << getMyOneLoopEW()->DeltaAlpha_5q(Mz2) << std::endl;
1217 
1218  return ( (DelA_l + DelA_d + DelA_u)/16.0/M_PI/M_PI );
1219 }

◆ DeltaR_boxLL_SUSY()

double EWSUSY::DeltaR_boxLL_SUSY ( const double  Mw_i) const

The LL SUSY box corrections to \(\Delta r\) in the 't Hooft-Feynman gauge.

Parameters
[in]Mw_iThe W-boson mass \(M_W\).
Returns
The LL SUSY box corrections to \(\Delta r\) in the 't Hooft-Feynman gauge.
References
Eqs. (A.5), (A.6), (A.7) and (A.19) in [Chankowski, Dabelstein, Hollik, Mosle, Pokorski and Rosiek, NPB 417 (1994) 101].

Definition at line 774 of file EWSUSY.cpp.

775 {
776  int M = 1; // MU
777  int N = 0; // ELECTRON
778  int J = 1; // NEUTRINO_2
779  int I = 0; // NEUTRINO_1
780 
781  gslpp::complex a11 = gslpp::complex(0.0, 0.0, false);
782  gslpp::complex a12 = gslpp::complex(0.0, 0.0, false);
783 
784  /* charged-lepton - sneutrino - chargino - neutralino loop */
785  for (int k=0; k<6; ++k)
786  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
787  for (int i=0; i<2; ++i)
788  for (int j=0; j<4; ++j) {
789  gslpp::complex FF = F(sqrt(Mse2[k]), sqrt(Msn2[K]), mC[i], mN[j]);
790  a11 += 0.5
791  *L_esnC(M, K, i, Mw_i)
792  *L_nLC(I, k, i, Mw_i)
793  *L_nsnN(J, K, j, Mw_i).conjugate()
794  *L_eLN(N, k, j, Mw_i).conjugate()
795  *mC[i]*mN[j]*FF;
796  a11 += 0.5
797  *L_eLN(M, k, j, Mw_i)
798  *L_nsnN(I, K, j, Mw_i)
799  *L_nLC(J, k, i, Mw_i).conjugate()
800  *L_esnC(N, K, i, Mw_i).conjugate()
801  *mC[i]*mN[j]*FF;
802  }
803 
804  /* charged-lepton - charged-lepton - chargino - neutralino loop */
805  for (int k=0; k<6; ++k)
806  for (int l=0; l<6; ++l)
807  for (int i=0; i<2; ++i)
808  for (int j=0; j<4; ++j) {
809  a11 += L_eLN(M, k, j, Mw_i)
810  *L_nLC(J, k, i, Mw_i).conjugate()
811  *L_nLC(I, l, i, Mw_i)
812  *L_eLN(N, l, j, Mw_i).conjugate()
813  *H(sqrt(Mse2[k]), sqrt(Mse2[l]), mC[i], mN[j]);
814  }
815 
816  /* sneutrino - sneutrino - chargino - neutralino loop */
817  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
818  for (int L=0; L<3; ++L) /* L=0-2 for left-handed sneutrinos */
819  for (int i=0; i<2; ++i)
820  for (int j=0; j<4; ++j) {
821  a11 += L_esnC(M, K, i, Mw_i)
822  *L_nsnN(J, K, j, Mw_i).conjugate()
823  *L_nsnN(I, L, j, Mw_i)
824  *L_esnC(N, L, i, Mw_i).conjugate()
825  *H(sqrt(Msn2[K]), sqrt(Msn2[L]), mC[i], mN[j]);
826  }
827 
828  /* charged-lepton - sneutrino - chargino - chargino loop */
829  for (int k=0; k<6; ++k)
830  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
831  for (int i=0; i<2; ++i)
832  for (int j=0; j<2; ++j) {
833  a12 += 0.5
834  *L_esnC(M, K, i, Mw_i)
835  *L_nLC(I, k, i, Mw_i)
836  *L_nLC(J, k, j, Mw_i).conjugate()
837  *L_esnC(N, K, j, Mw_i).conjugate()
838  *mC[i]*mC[j]*F(sqrt(Mse2[k]), sqrt(Msn2[K]), mC[i], mC[j]);
839  }
840 
841  /* charged-lepton - sneutrino - neutralino - neutralino loop */
842  for (int k=0; k<6; ++k)
843  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
844  for (int i=0; i<4; ++i)
845  for (int j=0; j<4; ++j) {
846  a12 += 0.5
847  *L_eLN(M, k, i, Mw_i)
848  *L_nsnN(I, K, i, Mw_i)
849  *L_nsnN(J, K, j, Mw_i).conjugate()
850  *L_eLN(N, k, j, Mw_i).conjugate()
851  *mN[i]*mN[j]*F(sqrt(Mse2[k]), sqrt(Msn2[K]), mN[i], mN[j]);
852  a12 += L_eLN(M, k, i, Mw_i)
853  *L_nsnN(J, K, i, Mw_i).conjugate()
854  *L_nsnN(I, K, j, Mw_i)
855  *L_eLN(N, k, j, Mw_i).conjugate()
856  *H(sqrt(Mse2[k]), sqrt(Msn2[K]), mN[i], mN[j]);
857  }
858 
859  gslpp::complex a1 = (a11 + a12)/16.0/M_PI/M_PI;
860 
861  double sW2 = 1.0 - Mw_i*Mw_i/mySUSY.getMz()/mySUSY.getMz();
862  return ( - sW2*Mw_i*Mw_i/2.0/M_PI/mySUSY.getAle()*a1.real() );
863 }

◆ DeltaR_boxLR_SUSY()

double EWSUSY::DeltaR_boxLR_SUSY ( const double  Mw_i) const

The LR SUSY box corrections to \(\Delta r\) in the 't Hooft-Feynman gauge.

Parameters
[in]Mw_iThe W-boson mass \(M_W\).
Returns
The LR SUSY box corrections to \(\Delta r\) in the 't Hooft-Feynman gauge.
References
Eqs. (A.8), (A.9) and (A.10) in [Chankowski, Dabelstein, Hollik, Mosle, Pokorski and Rosiek, NPB 417 (1994) 101].

Definition at line 865 of file EWSUSY.cpp.

866 {
867  int M = 1; // MU
868  int N = 0; // ELECTRON
869  int J = 1; // NEUTRINO_2
870  int I = 0; // NEUTRINO_1
871 
872  gslpp::complex a21 = gslpp::complex(0.0, 0.0, false);
873  gslpp::complex a22 = gslpp::complex(0.0, 0.0, false);
874 
875  /* charged-lepton - sneutrino - chargino - neutralino loop */
876  for (int k=0; k<6; ++k)
877  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
878  for (int i=0; i<2; ++i)
879  for (int j=0; j<4; ++j) {
880  gslpp::complex HH = H(sqrt(Mse2[k]), sqrt(Msn2[K]), mC[i], mN[j]);
881  a21 += - 2.0
882  *R_esnC(M, K, i)
883  *L_nLC(I, k, i, Mw_i)
884  *L_nsnN(J, K, j, Mw_i).conjugate()
885  *R_eLN(N, k, j, Mw_i).conjugate()
886  *HH;
887  a21 += - 2.0
888  *R_eLN(M, k, j, Mw_i)
889  *L_nsnN(I, K, j, Mw_i)
890  *L_nLC(J, k, i, Mw_i).conjugate()
891  *R_esnC(N, K, i).conjugate()
892  *HH;
893  }
894 
895  /* charged-lepton - charged-lepton - chargino - neutralino loop */
896  for (int k=0; k<6; ++k)
897  for (int l=0; l<6; ++l)
898  for (int i=0; i<2; ++i)
899  for (int j=0; j<4; ++j) {
900  a21 += - 2.0
901  *R_eLN(M, k, j, Mw_i)
902  *L_nLC(J, k, i, Mw_i).conjugate()
903  *L_nLC(I, l, i, Mw_i)
904  *R_eLN(N, l, j, Mw_i).conjugate()
905  *H(sqrt(Mse2[k]), sqrt(Mse2[l]), mC[i], mN[j]);
906  }
907 
908  /* sneutrino - sneutrino - chargino - neutralino loop */
909  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
910  for (int L=0; L<3; ++L) /* L=0-2 for left-handed sneutrinos */
911  for (int i=0; i<2; ++i)
912  for (int j=0; j<4; ++j) {
913  a21 += - 2.0
914  *R_esnC(M, K, i)
915  *L_nsnN(J, K, j, Mw_i).conjugate()
916  *L_nsnN(I, L, j, Mw_i)
917  *R_esnC(N, L, i).conjugate()
918  *H(sqrt(Msn2[K]), sqrt(Msn2[L]), mC[i], mN[j]);
919  }
920 
921  /* charged-lepton - sneutrino - neutralino - neutralino loop */
922  for (int k=0; k<6; ++k)
923  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
924  for (int i=0; i<4; ++i)
925  for (int j=0; j<4; ++j) {
926  a22 += R_eLN(M, k, i, Mw_i)
927  *L_nsnN(J, K, i, Mw_i).conjugate()
928  *L_nsnN(I, K, j, Mw_i)
929  *R_eLN(N, k, j, Mw_i).conjugate()
930  *mN[i]*mN[j]*F(sqrt(Mse2[k]), sqrt(Msn2[K]), mN[i], mN[j]);
931  a22 += 2.0
932  *R_eLN(M, k, i, Mw_i)
933  *L_nsnN(I, K, i, Mw_i)
934  *L_nsnN(J, K, j, Mw_i).conjugate()
935  *R_eLN(N, k, j, Mw_i).conjugate()
936  *H(sqrt(Mse2[k]), sqrt(Msn2[K]), mN[i], mN[j]);
937  }
938 
939  /* charged-lepton - sneutrino - chargino - chargino loop */
940  for (int k=0; k<6; ++k)
941  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
942  for (int i=0; i<2; ++i)
943  for (int j=0; j<2; ++j) {
944  a22 += 2.0
945  *R_esnC(M, K, i)
946  *L_nLC(I, k, i, Mw_i)
947  *L_nLC(J, k, j, Mw_i).conjugate()
948  *R_esnC(N, K, j).conjugate()
949  *H(sqrt(Mse2[k]), sqrt(Msn2[K]), mC[i], mC[j]);
950  }
951 
952  gslpp::complex a2 = (a21 + a22)/16.0/M_PI/M_PI;
953 
954  double sW2 = 1.0 - Mw_i*Mw_i/mySUSY.getMz()/mySUSY.getMz();
955  return ( sW2*Mw_i*Mw_i/4.0/M_PI/mySUSY.getAle()*a2.real() );
956 }

◆ DeltaR_neutrino_SUSY()

double EWSUSY::DeltaR_neutrino_SUSY ( const double  Mw_i) const

The renormalized SUSY neutrino wave-function contribution to \(\Delta r\) in the 't Hooft-Feynman gauge.

Parameters
[in]Mw_iThe W-boson mass \(M_W\).
Returns
The renormalized SUSY neutrino wave-function contribution to \(\Delta r\) in the 't Hooft-Feynman gauge.
References
Eqs. (A.21), (A.24) and (A.25) in [Chankowski, Dabelstein, Hollik, Mosle, Pokorski and Rosiek, NPB 417 (1994) 101].

Definition at line 1136 of file EWSUSY.cpp.

1137 {
1138  /* Renormalization scale (varied for checking the cancellation of UV divergences */
1139  double mu = Mw_i * RenormalizationScaleFactor;
1140 
1141  return ( ( Sigma_nu_0(mu, mySUSY.NEUTRINO_1, mySUSY.NEUTRINO_1, Mw_i).real()
1142  - delta_v(mu, mySUSY.ELECTRON, mySUSY.NEUTRINO_1, Mw_i).real()
1143  + Sigma_nu_0(mu, mySUSY.NEUTRINO_2, mySUSY.NEUTRINO_2, Mw_i).real()
1144  - delta_v(mu, mySUSY.MU, mySUSY.NEUTRINO_2, Mw_i).real() )/2.0 );
1145 }

◆ DeltaR_rem_SM()

double EWSUSY::DeltaR_rem_SM ( const double  Mw_i) const

The SM one-loop renormalized vertex and box corrections to \(\Delta r\) in the 't Hooft-Feynman gauge.

Parameters
[in]Mw_iThe W-boson mass \(M_W\).
Returns
The SM one-loop renormalized vertex and box corrections to \(\Delta r\) in the 't Hooft-Feynman gauge.
References
Eq. (4) in [Chankowski, Dabelstein, Hollik, Mosle, Pokorski and Rosiek, NPB 417 (1994) 101].

Definition at line 764 of file EWSUSY.cpp.

765 {
766  double cW2 = Mw_i*Mw_i/mySUSY.getMz()/mySUSY.getMz();
767  double sW2 = 1.0 - cW2;
768 
769  /* renormalized vertex corrections + box */
770  return ( mySUSY.getAle()/4.0/M_PI/sW2
771  *(6.0 + (7.0 - 4.0*sW2)/2.0/sW2*log(cW2)) );
772 }

◆ DeltaR_SUSY_EW1()

double EWSUSY::DeltaR_SUSY_EW1 ( const double  Mw_i) const

The one-loop SUSY contribution to \(\Delta r\).

Returns
\(\Delta r_{\rm SUSY}^{\alpha}\).

Definition at line 1221 of file EWSUSY.cpp.

1222 {
1223  double cW2 = Mw_i*Mw_i/mySUSY.getMz()/mySUSY.getMz();
1224  double sW2 = 1.0 - cW2;
1225 
1226  /* SM one-loop contributions */
1227  double DeltaAlphaL5q_EW1 = DeltaAlphaL5q_SM_EW1();
1228  double DeltaRho_EW1 = mySUSY.getMyOneLoopEW()->DeltaRho(Mw_i);
1229  double DeltaR_rem_EW1 = mySUSY.getMyOneLoopEW()->DeltaR_rem(Mw_i);
1230  double DeltaR_SM_EW1 = DeltaAlphaL5q_EW1 - cW2/sW2*DeltaRho_EW1 + DeltaR_rem_EW1;
1231 
1232  /* Debug */
1233  //std::cout << std::endl;
1234  //std::cout << "DeltaAlphaL5q_EW1 = " << DeltaAlphaL5q_EW1 << std::endl;
1235  //std::cout << "-cW2/sW2*DeltaRho_EW1 = " << - cW2/sW2*DeltaRho_EW1 << std::endl;
1236  //std::cout << "DeltaR_rem_EW1 = " << DeltaR_rem_EW1 << std::endl;
1237  //std::cout << "DeltaR_SM_EW1 = " << DeltaR_SM_EW1 << std::endl;
1238 
1239  return ( DeltaR_TOTAL_EW1(Mw_i) - DeltaR_SM_EW1 );
1240 }

◆ DeltaR_TOTAL_EW1()

double EWSUSY::DeltaR_TOTAL_EW1 ( const double  Mw_i) const

The total one-loop contribution to \(\Delta r\) in the MSSM.

Returns
\(\Delta r_{\rm MSSM}^{\alpha} = \Delta r_{\rm SM}^{\alpha} + \Delta r_{\rm SUSY}^{\alpha}\).

Definition at line 1147 of file EWSUSY.cpp.

1148 {
1149  double DeltaR = 0.0;
1150 
1151  /* SM+SUSY renormalized W self energy */
1152  DeltaR += - PiThat_W_0(Mw_i)/Mw_i/Mw_i;
1153 
1154  /* SM renormalized vertex + box */
1155  DeltaR += DeltaR_rem_SM(Mw_i);
1156 
1157  /* SUSY box corrections */
1158  DeltaR += DeltaR_boxLL_SUSY(Mw_i);
1159  DeltaR += DeltaR_boxLR_SUSY(Mw_i);
1160 
1161  /* SUSY renormalized vertex corrections */
1162  DeltaR += DeltaR_vertex_SUSY(Mw_i);
1163 
1164  /* SUSY renormalized neutrino wave function */
1165  DeltaR += DeltaR_neutrino_SUSY(Mw_i);
1166 
1167  /* Debug */
1168  //std::cout << "MSSM WSE = " << - PiThat_W_0(Mw_i)/Mw_i/Mw_i << std::endl;
1169  //std::cout << "SM VC+Box = " << DeltaR_rem_SM(Mw_i) << std::endl;
1170  //std::cout << "SUSY BoxLL = " << DeltaR_boxLL_SUSY(Mw_i) << std::endl;
1171  //std::cout << "SUSY BoxLR = " << DeltaR_boxLR_SUSY(Mw_i) << std::endl;
1172  //std::cout << "SUSY VC = " << DeltaR_vertex_SUSY(Mw_i) << std::endl;
1173  //std::cout << "SUSY nuSE = " << DeltaR_neutrino_SUSY(Mw_i) << std::endl;
1174 
1175  return DeltaR;
1176 }

◆ DeltaR_vertex_SUSY()

double EWSUSY::DeltaR_vertex_SUSY ( const double  Mw_i) const

The renormalized SUSY vertex corrections to \(\Delta r\) in the 't Hooft-Feynman gauge.

Parameters
[in]Mw_iThe W-boson mass \(M_W\).
Returns
The renormalized SUSY vertex corrections to \(\Delta r\) in the 't Hooft-Feynman gauge.
References
Eqs. (A.19), (A.21) and (A.23) in [Chankowski, Dabelstein, Hollik, Mosle, Pokorski and Rosiek, NPB 417 (1994) 101].

Definition at line 1077 of file EWSUSY.cpp.

1078 {
1079  /* Renormalization scale (varied for checking the cancellation of UV divergences */
1080  double mu = Mw_i * RenormalizationScaleFactor;
1081 
1082  return ( v(mu, mySUSY.ELECTRON, mySUSY.NEUTRINO_1, Mw_i).real()
1083  + delta_v(mu, mySUSY.ELECTRON, mySUSY.NEUTRINO_1, Mw_i).real()
1084  + v(mu, mySUSY.MU, mySUSY.NEUTRINO_2, Mw_i).real()
1085  + delta_v(mu, mySUSY.MU, mySUSY.NEUTRINO_2, Mw_i).real() );
1086 }

◆ dFA()

gslpp::complex EWSUSY::dFA ( const double  mu,
const double  p2,
const double  mi,
const double  mj,
const gslpp::complex  cV_aij,
const gslpp::complex  cV_bji,
const gslpp::complex  cA_aij,
const gslpp::complex  cA_bji 
) const

The derivative of \(F_A^{ab}(p^2,m_i,m_j,c_V^{aij},c_V^{bji},c_A^{aij},c_A^{bji})\) with respect to \(p^2\).

Parameters
[in]muThe renormalization scale \(\mu\).
[in]p2The momentum squared \(p^2\).
[in]miThe mass of a fermion \((i)\) running in the loop.
[in]mjThe mass of a fermion \((j)\) running in the loop.
[in]cV_aijThe vector coupling \(c_V^{aij}\) for a vertex with an incoming vector meson \((a)\), an incoming fermion \((i)\) and an outgoing fermion \((j)\).
[in]cV_bjiThe vector coupling \(c_V^{bji}\) for a vertex with an incoming vector meson \((b)\), an incoming fermion \((j)\) and an outgoing fermion \((i)\).
[in]cA_aijThe axial-vector coupling \(c_A^{aij}\) for a vertex with an incoming vector meson \((a)\), an incoming fermion \((i)\) and an outgoing fermion \((j)\).
[in]cA_bjiThe axial-vector coupling \(c_A^{bji}\) for a vertex with an incoming vector meson \((b)\), an incoming fermion \((j)\) and an outgoing fermion \((i)\).
Returns
The derivative of \(F_A^{ab}(p^2,m_i,m_j,c_V^{aij},c_V^{bji},c_A^{aij},c_A^{bji})\) with respect to \(p^2\) renormalized at the scale \(\mu\).
References
Eq. (A.7) in [Chankowski, Pokorski and Rosiek, NPB 423 (1994) 437].

Definition at line 115 of file EWSUSY.cpp.

119 {
120  double mu2 = mu*mu, mi2 = mi*mi, mj2 = mj*mj;
121 
122  /* PV functions */
123  gslpp::complex B0 = PV.B0(mu2, p2, mi2, mj2);
124  gslpp::complex B0p = PV.B0p(mu2, p2, mi2, mj2);
125  gslpp::complex B00p = PV.B00p(mu2, p2, mi2, mj2);
126 
127  if (mi == mj && cA_aij == 0.0 && cA_bji == 0.0)
128  return ( -2.0*cV_aij*cV_bji*(4.0*B00p + p2*B0p + B0) );
129  else
130  return ( -2.0*(cV_aij*cV_bji + cA_aij*cA_bji)
131  *(4.0*B00p + (p2 - mi*mi - mj*mj)*B0p + B0)
132  -4.0*(cV_aij*cV_bji - cA_aij*cA_bji)*mi*mj*B0p );
133 }

◆ FA()

gslpp::complex EWSUSY::FA ( const double  mu,
const double  p2,
const double  mi,
const double  mj,
const gslpp::complex  cV_aij,
const gslpp::complex  cV_bji,
const gslpp::complex  cA_aij,
const gslpp::complex  cA_bji 
) const

Fermionic contribuiton to the transverse part of a gauge-boson self-energy, \(F_A^{ab}(p^2,m_i,m_j,c_V^{aij},c_V^{bji},c_A^{aij},c_A^{bji})\).

Parameters
[in]muThe renormalization scale \(\mu\).
[in]p2The momentum squared \(p^2\).
[in]miThe mass of a fermion \((i)\) running in the loop.
[in]mjThe mass of a fermion \((j)\) running in the loop.
[in]cV_aijThe vector coupling \(c_V^{aij}\) for a vertex with an incoming vector meson \((a)\), an incoming fermion \((i)\) and an outgoing fermion \((j)\).
[in]cV_bjiThe vector coupling \(c_V^{bji}\) for a vertex with an incoming vector meson \((b)\), an incoming fermion \((j)\) and an outgoing fermion \((i)\).
[in]cA_aijThe axial-vector coupling \(c_A^{aij}\) for a vertex with an incoming vector meson \((a)\), an incoming fermion \((i)\) and an outgoing fermion \((j)\).
[in]cA_bjiThe axial-vector coupling \(c_A^{bji}\) for a vertex with an incoming vector meson \((b)\), an incoming fermion \((j)\) and an outgoing fermion \((i)\).
Returns
\(F_A^{ab}(p^2,m_i,m_j,c_V^{aij},c_V^{bji},c_A^{aij},c_A^{bji})\) renormalized at the scale \(\mu\).
References
Eq. (A.7) in [Chankowski, Pokorski and Rosiek, NPB 423 (1994) 437].

Definition at line 97 of file EWSUSY.cpp.

101 {
102  double mu2 = mu*mu, mi2 = mi*mi, mj2 = mj*mj;
103 
104  /* PV functions */
105  double A0i = PV.A0(mu2, mi2);
106  double A0j = PV.A0(mu2, mj2);
107  gslpp::complex B0 = PV.B0(mu2, p2, mi2, mj2);
108  gslpp::complex B00 = PV.B00(mu2, p2, mi2, mj2);
109 
110  return ( -2.0*(cV_aij*cV_bji + cA_aij*cA_bji)
111  *(4.0*B00 + A0i + A0j + (p2 - mi*mi - mj*mj)*B0)
112  -4.0*(cV_aij*cV_bji - cA_aij*cA_bji)*mi*mj*B0 );
113 }

◆ PiT_AZ()

gslpp::complex EWSUSY::PiT_AZ ( const double  mu,
const double  p2,
const double  Mw_i 
) const

The transverse part of the self-energy, \(\Pi_{\gamma Z}^T(p^2)\), for the mixing between photon and Z boson in the 't Hooft-Feynman gauge.

Parameters
[in]muThe renormalization scale \(\mu\).
[in]p2The momentum squared \(p^2\).
[in]Mw_iThe W-boson mass \(M_W\).
Returns
\(\Pi_{\gamma Z}^T(p^2)\) renormalized at the scale \(\mu\) in the 't Hooft-Feynman gauge.
References
Eq. (A.18) in [Chankowski, Pokorski and Rosiek, NPB 423 (1994) 437].

Definition at line 499 of file EWSUSY.cpp.

500 {
501  double mu2 = mu*mu;
502  double e2 = 4.0*M_PI*mySUSY.getAle();
503  double e = sqrt(e2);
504  double Mz = mySUSY.getMz();
505  double Nc = mySUSY.getNc();
506 
507  /* variables depending on Mw_i */
508  double Mw2 = Mw_i*Mw_i;
509  double mHp2[2] = {mySUSY.getMHp()*mySUSY.getMHp(), Mw2}; /* H^+_i = (H^+, G^+) */
510  double cW = Mw_i/Mz;
511  double cW2 = cW*cW;
512  double sW2 = 1.0 - cW2;
513  double sW = sqrt(sW2);
514  double g2 = e/sW;
515  double e_4sc = e/4.0/sW/cW;
516  double e_2sc = 2.0*e_4sc;
517  double e2_sc = e2/sW/cW;
518 
519  gslpp::complex PiT_f = gslpp::complex(0.0, 0.0, false);
520  gslpp::complex PiT_sf = gslpp::complex(0.0, 0.0, false);
521  gslpp::complex PiT_ch = gslpp::complex(0.0, 0.0, false);
522  gslpp::complex PiT_WZH = gslpp::complex(0.0, 0.0, false);
523  double a0;
524  gslpp::complex b0, b00;
525 
526  /* SM fermion loops */
527  gslpp::complex cV_Aee = - e;
528  gslpp::complex cA_Aee = 0.0;
529  gslpp::complex cV_Add = - e/3.0;
530  gslpp::complex cA_Add = 0.0;
531  gslpp::complex cV_Auu = 2.0/3.0*e;
532  gslpp::complex cA_Auu = 0.0;
533  gslpp::complex cV_Zee = - e_4sc*(1.0 - 4.0*sW2);
534  gslpp::complex cA_Zee = - e_4sc;
535  gslpp::complex cV_Zdd = - e_4sc*(1.0 - 4.0/3.0*sW2);
536  gslpp::complex cA_Zdd = - e_4sc;
537  gslpp::complex cV_Zuu = e_4sc*(1.0 - 8.0/3.0*sW2);
538  gslpp::complex cA_Zuu = e_4sc;
539  for (int I=0; I<3; ++I) {
540  /* charged leptons */
541  PiT_f += FA(mu, p2, m_l[I], m_l[I], cV_Aee, cV_Zee, cA_Aee, cA_Zee);
542 
543  /* down-type quarks */
544  PiT_f += Nc*FA(mu, p2, m_d[I], m_d[I], cV_Add, cV_Zdd, cA_Add, cA_Zdd);
545 
546  /* up-type quarks */
547  PiT_f += Nc*FA(mu, p2, m_u[I], m_u[I], cV_Auu, cV_Zuu, cA_Auu, cA_Zuu);
548  }
549 
550  /* charged-slepton loops */
551  gslpp::complex VZLL_nn, VAZLL_nn;
552  for (int n=0; n<6; ++n) {
553  VZLL_nn = gslpp::complex(0.0, 0.0, false);
554  for (int I=0; I<3; ++I) /* sum over left-handed sleptons */
555  VZLL_nn += - e_2sc*ZL(I,n)*ZL(I,n).conjugate();
556  VZLL_nn += - e_2sc*(- 2.0*sW2);
557  b00 = PV.B00(mu2, p2, Mse2[n], Mse2[n]);
558  /* typo in the paper: e^2 --> e */
559  PiT_sf += - 4.0*e*VZLL_nn*b00;
560 
561  VAZLL_nn = gslpp::complex(0.0, 0.0, false);
562  for (int I=0; I<3; ++I) /* sum over left-handed sleptons */
563  VAZLL_nn += e2_sc*ZL(I,n)*ZL(I,n).conjugate();
564  VAZLL_nn += e2_sc*(- 2.0*sW2);
565  a0 = PV.A0(mu2, Mse2[n]);
566  PiT_sf += VAZLL_nn*a0;
567  }
568 
569  /* down-type squark loops */
570  gslpp::complex VZDD_nn, VAZDD_nn;
571  for (int n=0; n<6; ++n) {
572  VZDD_nn = gslpp::complex(0.0, 0.0, false);
573  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
574  VZDD_nn += - e_2sc*ZD(I,n)*ZD(I,n).conjugate();
575  VZDD_nn += - e_2sc*(- 2.0/3.0*sW2);
576  b00 = PV.B00(mu2, p2, Msd2[n], Msd2[n]);
577  /* typo in the paper: e^2 --> e */
578  PiT_sf += - 4.0*e*Nc/3.0*VZDD_nn*b00;
579 
580  VAZDD_nn = gslpp::complex(0.0, 0.0, false);
581  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
582  VAZDD_nn += e2_sc/3.0*ZD(I,n)*ZD(I,n).conjugate();
583  VAZDD_nn += e2_sc/3.0*(- 2.0/3.0*sW2);
584  a0 = PV.A0(mu2, Msd2[n]);
585  PiT_sf += Nc*VAZDD_nn*a0;
586  }
587 
588  /* up-type squark loops */
589  gslpp::complex VZUU_nn, VAZUU_nn;
590  for (int n=0; n<6; ++n) {
591  VZUU_nn = gslpp::complex(0.0, 0.0, false);
592  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
593  VZUU_nn += e_2sc*ZU(I,n).conjugate()*ZU(I,n);
594  VZUU_nn += e_2sc*(- 4.0/3.0*sW2);
595  b00 = PV.B00(mu2, p2, Msu2[n], Msu2[n]);
596  /* typo in the paper: e^2 --> e */
597  PiT_sf += 4.0*e*Nc*2.0/3.0*VZUU_nn*b00;
598 
599  VAZUU_nn = gslpp::complex(0.0, 0.0, false);
600  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
601  VAZUU_nn += 2.0*e2_sc/3.0*ZU(I,n).conjugate()*ZU(I,n);
602  VAZUU_nn += 2.0*e2_sc/3.0*(- 4.0/3.0*sW2);
603  a0 = PV.A0(mu2, Msu2[n]);
604  PiT_sf += Nc*VAZUU_nn*a0;
605  }
606 
607  /* chargino loops */
608  gslpp::complex cV_Aii = e;
609  gslpp::complex cA_Aii = 0.0;
610  gslpp::complex cV_Zii, cA_Zii;
611  for (int i=0; i<2; ++i) {
612  cV_Zii = e_4sc*( Zp(0,i).conjugate()*Zp(0,i)
613  + Zm(0,i)*Zm(0,i).conjugate() + 2.0*(cW2 - sW2) );
614  cA_Zii = e_4sc*( Zp(0,i).conjugate()*Zp(0,i)
615  - Zm(0,i)*Zm(0,i).conjugate() );
616  PiT_ch += FA(mu, p2, mC[i], mC[i], cV_Aii, cV_Zii, cA_Aii, cA_Zii);
617  }
618 
619  /* W-boson - charged-Goldstone-boson loops */
620  b0 = PV.B0(mu2, p2, Mw2, Mw2);
621  PiT_WZH += 2.0*e2*cW*sW*Mz*Mz*b0;
622 
623  /* W-boson loops */
624  a0 = PV.A0(mu2, Mw2);
625  //b0 = PV.B0(mu2, p2, Mw2, Mw2); /* same as the above */
626  b00 = PV.B00(mu2, p2, Mw2, Mw2);
627  PiT_WZH += 2.0*e*g2*cW*(2.0*a0 + (2.0*p2 + Mw2)*b0 + 4.0*b00);
628 
629  /* charged-Higgs loops */
630  double cot_2thW = (cW2 - sW2)/(2.0*sW*cW);
631  for (int i=0; i<2; ++i) {
632  a0 = PV.A0(mu2, mHp2[i]);
633  b00 = PV.B00(mu2, p2, mHp2[i], mHp2[i]);
634  PiT_WZH += 2.0*e2*cot_2thW*(2.0*b00 + a0);
635  }
636 
637  /* Sum of all contributions */
638  gslpp::complex PiT = PiT_f + PiT_sf + PiT_ch + PiT_WZH;
639 
640  return ( PiT/16.0/M_PI/M_PI );
641 }

◆ PiT_W()

gslpp::complex EWSUSY::PiT_W ( const double  mu,
const double  p2,
const double  Mw_i 
) const

The transverse part of the W-boson self-energy, \(\Pi_W^T(p^2)\), in the 't Hooft-Feynman gauge.

Parameters
[in]muThe renormalization scale \(\mu\).
[in]p2The momentum squared \(p^2\).
[in]Mw_iThe W-boson mass \(M_W\).
Returns
\(\Pi_W^T(p^2)\) renormalized at the scale \(\mu\) in the 't Hooft-Feynman gauge.
References
Eq. (A.20) in [Chankowski, Pokorski and Rosiek, NPB 423 (1994) 437].

Definition at line 333 of file EWSUSY.cpp.

334 {
335  double mu2 = mu*mu;
336  double e2 = 4.0*M_PI*mySUSY.getAle();
337  double e = sqrt(e2);
338  double Mz = mySUSY.getMz();
339  double Nc = mySUSY.getNc();
340 
341  /* variables depending on Mw_i */
342  double Mw2 = Mw_i*Mw_i;
343  double mHp2[2] = {mySUSY.getMHp()*mySUSY.getMHp(), Mw2}; /* H^+_i = (H^+, G^+) */
344  double cW = Mw_i/Mz;
345  double cW2 = cW*cW;
346  double sW2 = 1.0 - cW2;
347  double sW = sqrt(sW2);
348  double g2sq = e2/sW2; /* g2 squared */
349  double e_2s = e/2.0/sW;
350  double e_sq2s = e/sqrt(2.0)/sW;
351  double e_2sq2s = e_sq2s/2.0;
352  double e2_2s2 = e2/2.0/sW2;
353 
354  gslpp::complex PiT_f = gslpp::complex(0.0, 0.0, false);
355  gslpp::complex PiT_sf = gslpp::complex(0.0, 0.0, false);
356  gslpp::complex PiT_ch = gslpp::complex(0.0, 0.0, false);
357  gslpp::complex PiT_WZH = gslpp::complex(0.0, 0.0, false);
358  double a0;
359  gslpp::complex b0, b00;
360 
361  /* SM fermion loops */
362  gslpp::complex cV_Wen = e_2sq2s;
363  gslpp::complex cA_Wen = e_2sq2s;
364  gslpp::complex cV_Wne = cV_Wen.conjugate();
365  gslpp::complex cA_Wne = cA_Wen.conjugate();
366  gslpp::complex cV_Wdu = e_2sq2s; /* no CKM */
367  gslpp::complex cA_Wdu = e_2sq2s; /* no CKM */
368  gslpp::complex cV_Wud = cV_Wdu.conjugate();
369  gslpp::complex cA_Wud = cA_Wdu.conjugate();
370  for (int I=0; I<3; ++I) {
371  /* leptons */
372  PiT_f += FA(mu, p2, m_l[I], 0.0, cV_Wen, cV_Wne, cA_Wen, cA_Wne);
373 
374  /* quarks (no CKM) */
375  PiT_f += Nc*FA(mu, p2, m_d[I], m_u[I], cV_Wdu, cV_Wud, cA_Wdu, cA_Wud);
376  }
377 
378  /* slepton loops */
379  gslpp::complex VWsnL_In, VWWsnsn_II, VWWLL_nn;
380  for (int I=0; I<3; ++I) { /* I=0-2 for left-handed sneutrinos */
381  for (int n=0; n<6; ++n) {
382  VWsnL_In = gslpp::complex(0.0, 0.0, false);
383  for (int J=0; J<3; ++J) /* sum over left-handed sleptons */
384  VWsnL_In += e_sq2s*Zne(J,I)*ZL(J,n);
385  b00 = PV.B00(mu2, p2, Msn2[I], Mse2[n]);
386  PiT_sf += 4.0*VWsnL_In.abs2()*b00;
387  }
388  VWWsnsn_II = e2_2s2;
389  a0 = PV.A0(mu2, Msn2[I]);
390  PiT_sf += VWWsnsn_II*a0;
391  }
392  for (int n=0; n<6; ++n) {
393  VWWLL_nn = gslpp::complex(0.0, 0.0, false);
394  for (int I=0; I<3; ++I) /* sum over left-handed sleptons */
395  VWWLL_nn += e2_2s2*ZL(I,n)*ZL(I,n).conjugate();
396  a0 = PV.A0(mu2, Mse2[n]);
397  PiT_sf += VWWLL_nn*a0;
398  }
399 
400  /* squark loops (no CKM) */
401  gslpp::complex VWDU_nm, VWWDD_nn, VWWUU_nn;
402  for (int n=0; n<6; ++n) {
403  for (int m=0; m<6; ++m) {
404  VWDU_nm = gslpp::complex(0.0, 0.0, false);
405  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
406  VWDU_nm += e_sq2s*ZD(I,n).conjugate()*ZU(I,m).conjugate();
407  b00 = PV.B00(mu2, p2, Msd2[n], Msu2[m]);
408  PiT_sf += 4.0*Nc*VWDU_nm.abs2()*b00;
409  }
410  VWWDD_nn = gslpp::complex(0.0, 0.0, false);
411  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
412  VWWDD_nn += e2_2s2*ZD(I,n)*ZD(I,n).conjugate();
413  a0 = PV.A0(mu2, Msd2[n]);
414  PiT_sf += Nc*VWWDD_nn*a0;
415  VWWUU_nn = gslpp::complex(0.0, 0.0, false);
416  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
417  VWWUU_nn += e2_2s2*ZU(I,n).conjugate()*ZU(I,n);
418  a0 = PV.A0(mu2, Msu2[n]);
419  PiT_sf += Nc*VWWUU_nn*a0;
420  }
421 
422  /* chargino - neutralino loops */
423  gslpp::complex cV_Wij, cV_Wji, cA_Wij, cA_Wji;
424  for (int i=0; i<2; ++i)
425  for (int j=0; j<4; ++j) {
426  /* W^+ + neutralino(j) -> chi^+(i) */
427  /* W^+ + chi^-(i) -> neutralino(j) */
428  cV_Wji = - e_2s*( ZN(1,j)*Zp(0,i).conjugate()
429  - ZN(3,j)*Zp(1,i).conjugate()/sqrt(2.0)
430  + ZN(1,j).conjugate()*Zm(0,i)
431  + ZN(2,j).conjugate()*Zm(1,i)/sqrt(2.0) );
432  cV_Wij = cV_Wji.conjugate();
433  cA_Wji = - e_2s*( ZN(1,j)*Zp(0,i).conjugate()
434  - ZN(3,j)*Zp(1,i).conjugate()/sqrt(2.0)
435  - ZN(1,j).conjugate()*Zm(0,i)
436  - ZN(2,j).conjugate()*Zm(1,i)/sqrt(2.0) );
437  cA_Wij = cA_Wji.conjugate();
438  PiT_ch += FA(mu, p2, mC[i], mN[j], cV_Wij, cV_Wji, cA_Wij, cA_Wji);
439  }
440 
441  /* Higgs loops */
442  double AM_ij;
443  for (int i=0; i<2; ++i) {
444  for (int j=0; j<2; ++j) {
445  AM_ij = ZR(0,i)*ZH(0,j) - ZR(1,i)*ZH(1,j);
446  b00 = PV.B00(mu2, p2, mH02[i], mHp2[j]);
447  PiT_WZH += g2sq*AM_ij*AM_ij*b00;
448  }
449  b00 = PV.B00(mu2, p2, mH02[i+2], mHp2[i]);
450  PiT_WZH += g2sq*b00;
451  }
452  for (int i=0; i<4; ++i) {
453  a0 = PV.A0(mu2, mH02[i]);
454  PiT_WZH += g2sq/4.0*a0;
455  }
456  for (int i=0; i<2; ++i) {
457  a0 = PV.A0(mu2, mHp2[i]);
458  PiT_WZH += g2sq/2.0*a0;
459  }
460 
461  /* photon - charged-Goldstone-boson loops */
462  b0 = PV.B0(mu2, p2, Mw2, 0.0);
463  PiT_WZH += - e2*Mw2*b0;
464 
465  /* W-boson - Higgs loops */
466  double CR_i;
467  for (int i=0; i<2; ++i) {
468  CR_i = mySUSY.v1()*ZR(0,i) + mySUSY.v2()*ZR(1,i);
469  b0 = PV.B0(mu2, p2, Mw2, mH02[i]);
470  /* Mw^2/v^2 is substituted for g2^2/4 compared to the expression in the
471  * paper, in order to ensure the cancellation of the UV divergences in
472  * the case where Mw is not the tree-level value. */
473  PiT_WZH += - g2sq*Mw2/mySUSY.v()/mySUSY.v()*CR_i*CR_i*b0;
474  }
475 
476  /* Z-boson - charged-Goldstone-boson loops */
477  b0 = PV.B0(mu2, p2, Mw2, Mz*Mz);
478  PiT_WZH += - e2*sW2*Mz*Mz*b0;
479 
480  /* gauge-boson loops */
481  a0 = PV.A0(mu2, Mw2);
482  b0 = PV.B0(mu2, p2, Mw2, Mz*Mz);
483  b00 = PV.B00(mu2, p2, Mz*Mz, Mw2);
484  PiT_WZH += g2sq*cW2*(2.0*PV.A0(mu2, Mz*Mz) - a0
485  + (4.0*p2 + Mz*Mz + Mw2)*b0 + 8.0*b00);
486  //
487  PiT_WZH += 3.0*g2sq*a0;
488  //
489  b0 = PV.B0(mu2, p2, Mw2, 0.0);
490  b00 = PV.B00(mu2, p2, Mw2, 0.0);
491  PiT_WZH += e2*((4.0*p2 + Mw2)*b0 - a0 + 8.0*b00);
492 
493  /* Sum of all contributions */
494  gslpp::complex PiT = PiT_f + PiT_sf + PiT_ch + PiT_WZH;
495 
496  return ( PiT/16.0/M_PI/M_PI );
497 }

◆ PiT_Z()

gslpp::complex EWSUSY::PiT_Z ( const double  mu,
const double  p2,
const double  Mw_i 
) const

The transverse part of the Z-boson self-energy, \(\Pi_Z^T(p^2)\), in the 't Hooft-Feynman gauge.

Parameters
[in]muThe renormalization scale \(\mu\).
[in]p2The momentum squared \(p^2\).
[in]Mw_iThe W-boson mass \(M_W\).
Returns
\(\Pi_Z^T(p^2)\) renormalized at the scale \(\mu\) in the 't Hooft-Feynman gauge.
References
Eq. (A.15) in [Chankowski, Pokorski and Rosiek, NPB 423 (1994) 437].

Definition at line 135 of file EWSUSY.cpp.

136 {
137  double mu2 = mu*mu;
138  double e2 = 4.0*M_PI*mySUSY.getAle();
139  double e = sqrt(e2);
140  double Mz = mySUSY.getMz();
141  double Nc = mySUSY.getNc();
142 
143  /* variables depending on Mw_i */
144  double Mw2 = Mw_i*Mw_i;
145  double mHp2[2] = {mySUSY.getMHp()*mySUSY.getMHp(), Mw2}; /* H^+_i = (H^+, G^+) */
146  double cW = Mw_i/Mz;
147  double cW2 = cW*cW;
148  double sW2 = 1.0 - cW2;
149  double sW = sqrt(sW2);
150  double g2sq = e2/sW2; /* g2 squared */
151  double e_4sc = e/4.0/sW/cW;
152  double e_2sc = 2.0*e_4sc;
153 
154  gslpp::complex PiT_f = gslpp::complex(0.0, 0.0, false);
155  gslpp::complex PiT_sf = gslpp::complex(0.0, 0.0, false);
156  gslpp::complex PiT_ch = gslpp::complex(0.0, 0.0, false);
157  gslpp::complex PiT_WZH = gslpp::complex(0.0, 0.0, false);
158  double a0;
159  gslpp::complex b0, b00;
160  gslpp::complex cV_Zij, cV_Zji, cA_Zij, cA_Zji;
161  gslpp::matrix<double> Id6 = gslpp::matrix<double>::Id(6);
162  gslpp::matrix<double> Id2 = gslpp::matrix<double>::Id(2);
163 
164  /* neutrino loops */
165  b0 = PV.B0(mu2, p2, 0.0, 0.0);
166  b00 = PV.B00(mu2, p2, 0.0, 0.0);
167  PiT_f += - 3.0/4.0*g2sq/cW2*(4.0*b00 + p2*b0);
168 
169  /* other SM fermion loops */
170  gslpp::complex cV_Zee = - e_4sc*(1.0 - 4.0*sW2);
171  gslpp::complex cA_Zee = - e_4sc;
172  gslpp::complex cV_Zdd = - e_4sc*(1.0 - 4.0/3.0*sW2);
173  gslpp::complex cA_Zdd = - e_4sc;
174  gslpp::complex cV_Zuu = e_4sc*(1.0 - 8.0/3.0*sW2);
175  gslpp::complex cA_Zuu = e_4sc;
176  for (int I=0; I<3; ++I) {
177  /* charged leptons */
178  PiT_f += FA(mu, p2, m_l[I], m_l[I], cV_Zee, cV_Zee, cA_Zee, cA_Zee);
179 
180  /* down-type quarks */
181  PiT_f += Nc*FA(mu, p2, m_d[I], m_d[I], cV_Zdd, cV_Zdd, cA_Zdd, cA_Zdd);
182 
183  /* up-type quarks */
184  PiT_f += Nc*FA(mu, p2, m_u[I], m_u[I], cV_Zuu, cV_Zuu, cA_Zuu, cA_Zuu);
185  }
186 
187  /* sneutrino loops */
188  gslpp::complex VZsnsn_II = e_2sc;
189  gslpp::complex VZZsnsn_II = e2/2.0/sW2/cW2;
190  for (int I=0; I<3; ++I) { /* I=0-2 for left-handed sneutrinos */
191  b00 = PV.B00(mu2, p2, Msn2[I], Msn2[I]);
192  PiT_sf += 4.0*VZsnsn_II.abs2()*b00;
193  a0 = PV.A0(mu2, Msn2[I]);
194  PiT_sf += VZZsnsn_II*a0;
195  }
196 
197  /* charged-slepton loops */
198  gslpp::complex VZLL_mn, VZZLL_nn;
199  for (int n=0; n<6; ++n) {
200  for (int m=0; m<6; ++m) {
201  VZLL_mn = gslpp::complex(0.0, 0.0, false);
202  for (int I=0; I<3; ++I) /* sum over left-handed sleptons */
203  VZLL_mn += - e_2sc*ZL(I,n)*ZL(I,m).conjugate();
204  VZLL_mn += - e_2sc*(- 2.0*sW2*Id6(m,n));
205  b00 = PV.B00(mu2, p2, Mse2[m], Mse2[n]);
206  PiT_sf += 4.0*VZLL_mn.abs2()*b00;
207  }
208  VZZLL_nn = gslpp::complex(0.0, 0.0, false);
209  VZZLL_nn += 2.0*e2/cW2*sW2;
210  for (int I=0; I<3; ++I) /* sum over left-handed sleptons */
211  VZZLL_nn += 2.0*e2/cW2*(1.0 - 4.0*sW2)/4.0/sW2*ZL(I,n)*ZL(I,n).conjugate();
212  a0 = PV.A0(mu2, Mse2[n]);
213  PiT_sf += VZZLL_nn*a0;
214  }
215 
216  /* down-type squark loops */
217  gslpp::complex VZDD_mn, VZZDD_nn;
218  for (int n=0; n<6; ++n) {
219  for (int m=0; m<6; ++m) {
220  VZDD_mn = gslpp::complex(0.0, 0.0, false);
221  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
222  VZDD_mn += - e_2sc*ZD(I,n)*ZD(I,m).conjugate();
223  VZDD_mn += - e_2sc*(- 2.0/3.0*sW2*Id6(m,n));
224  b00 = PV.B00(mu2, p2, Msd2[m], Msd2[n]);
225  PiT_sf += 4.0*Nc*VZDD_mn.abs2()*b00;
226  }
227  VZZDD_nn = gslpp::complex(0.0, 0.0, false);
228  VZZDD_nn += 2.0*e2/3.0/cW2*sW2/3.0;
229  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
230  VZZDD_nn += 2.0*e2/3.0/cW2*(3.0 - 4.0*sW2)/4.0/sW2*ZD(I,n)*ZD(I,n).conjugate();
231  a0 = PV.A0(mu2, Msd2[n]);
232  PiT_sf += Nc*VZZDD_nn*a0;
233  }
234 
235  /* up-type squark loops */
236  gslpp::complex VZUU_mn, VZZUU_nn;
237  for (int n=0; n<6; ++n) {
238  for (int m=0; m<6; ++m) {
239  VZUU_mn = gslpp::complex(0.0, 0.0, false);
240  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
241  VZUU_mn += e_2sc*ZU(I,m).conjugate()*ZU(I,n);
242  VZUU_mn += e_2sc*(- 4.0/3.0*sW2*Id6(m,n));
243  b00 = PV.B00(mu2, p2, Msu2[m], Msu2[n]);
244  PiT_sf += 4.0*Nc*VZUU_mn.abs2()*b00;
245  }
246  VZZUU_nn = gslpp::complex(0.0, 0.0, false);
247  VZZUU_nn += 2.0*e2/3.0/cW2*4.0*sW2/3.0;
248  for (int I=0; I<3; ++I) /* sum over left-handed squarks */
249  VZZUU_nn += 2.0*e2/3.0/cW2*(3.0 - 8.0*sW2)/4.0/sW2*ZU(I,n).conjugate()*ZU(I,n);
250  a0 = PV.A0(mu2, Msu2[n]);
251  PiT_sf += Nc*VZZUU_nn*a0;
252  }
253 
254  /* chargino loops */
255  for (int i=0; i<2; ++i)
256  for (int j=0; j<2; ++j) {
257  cV_Zij = e_4sc*( Zp(0,j).conjugate()*Zp(0,i)
258  + Zm(0,j)*Zm(0,i).conjugate()
259  + 2.0*(cW2 - sW2)*Id2(j,i) );
260  cV_Zji = cV_Zij.conjugate();
261  cA_Zij = e_4sc*( Zp(0,j).conjugate()*Zp(0,i)
262  - Zm(0,j)*Zm(0,i).conjugate() );
263  cA_Zji = cA_Zij.conjugate();
264  PiT_ch += FA(mu, p2, mC[i], mC[j], cV_Zij, cV_Zji, cA_Zij, cA_Zji);
265  }
266 
267  /* neutralino loops */
268  for (int i=0; i<4; ++i)
269  for (int j=0; j<4; ++j) {
270  cV_Zij = - e_4sc*( ZN(3,j).conjugate()*ZN(3,i)
271  - ZN(2,j).conjugate()*ZN(2,i)
272  - ZN(3,j)*ZN(3,i).conjugate()
273  + ZN(2,j)*ZN(2,i).conjugate() );
274  cV_Zji = cV_Zij.conjugate();
275  cA_Zij = - e_4sc*( ZN(3,j).conjugate()*ZN(3,i)
276  - ZN(2,j).conjugate()*ZN(2,i)
277  + ZN(3,j)*ZN(3,i).conjugate()
278  - ZN(2,j)*ZN(2,i).conjugate() );
279  cA_Zji = cA_Zij.conjugate();
280  PiT_ch += 0.5*FA(mu, p2, mN[i], mN[j], cV_Zij, cV_Zji, cA_Zij, cA_Zji);
281  }
282 
283  /* charged-Higgs loops */
284  double cot_2thW = (cW2 - sW2)/(2.0*sW*cW);
285  for (int i=0; i<2; ++i) {
286  b00 = PV.B00(mu2, p2, mHp2[i], mHp2[i]);
287  a0 = PV.A0(mu2, mHp2[i]);
288  PiT_WZH += 2.0*e2*cot_2thW*cot_2thW*(2.0*b00 + a0);
289  }
290 
291  /* neutral-Higgs loops */
292  double AM_ij;
293  for (int i=0; i<2; ++i)
294  for (int j=0; j<2; ++j) {
295  AM_ij = ZR(0,i)*ZH(0,j) - ZR(1,i)*ZH(1,j);
296  b00 = PV.B00(mu2, p2, mH02[i], mH02[j+2]);
297  PiT_WZH += g2sq/cW2*AM_ij*AM_ij*b00;
298  }
299  for (int j=0; j<4; ++j) {
300  a0 = PV.A0(mu2, mH02[j]);
301  PiT_WZH += g2sq/4.0/cW2*a0;
302  }
303 
304  /* W-boson - charged-Goldstone-boson loop*/
305  b0 = PV.B0(mu2, p2, Mw2, Mw2);
306  PiT_WZH += - 2.0*g2sq*sW2*sW2*Mz*Mz*b0;
307 
308  /* Z-boson - Higgs loops */
309  double CR_i;
310  for (int i=0; i<2; ++i) {
311  CR_i = mySUSY.v1()*ZR(0,i) + mySUSY.v2()*ZR(1,i);
312  b0 = PV.B0(mu2, p2, Mz*Mz, mH02[i]);
313  /* Mw^2/v^2 is substituted for g2^2/4 compared to the expression in the
314  * paper, in order to ensure the cancellation of the UV divergences in
315  * the case where Mw is not the tree-level value. */
316  PiT_WZH += - g2sq*Mw2/mySUSY.v()/mySUSY.v()/cW2/cW2*CR_i*CR_i*b0;
317  }
318 
319  /* W-boson loops */
320  a0 = PV.A0(mu2, Mw2);
321  b0 = PV.B0(mu2, p2, Mw2, Mw2);
322  b00 = PV.B00(mu2, p2, Mw2, Mw2);
323  /* typo in the paper: a0^2 --> a0 in the first term */
324  PiT_WZH += 2.0*g2sq*cW2*(2.0*a0 + (2.0*p2 + Mw2)*b0 + 4.0*b00);
325 
326  /* Sum of all contributions */
327  gslpp::complex PiT = PiT_f + PiT_sf + PiT_ch + PiT_WZH;
328 
329  return ( PiT/16.0/M_PI/M_PI );
330 }

◆ PiThat_W_0()

double EWSUSY::PiThat_W_0 ( const double  Mw_i) const

The renormalized transverse W-boson self-energy at zero momentum transefer in the 't Hooft-Feynman gauge.

Parameters
[in]muThe renormalization scale \(\mu\).
[in]Mw_iThe W-boson mass \(M_W\).
Returns
\(\hat{\Pi}_W^T(0)\) in the 't Hooft-Feynman gauge.

Definition at line 726 of file EWSUSY.cpp.

727 {
728  /* Renormalization scale (varied for checking the cancellation of UV divergences */
729  double mu = Mw_i * RenormalizationScaleFactor;
730 
731  double Mz = mySUSY.getMz();
732  double cW = Mw_i/Mz;
733  double cW2 = cW*cW;
734  double sW2 = 1.0 - cW2;
735  double sW = sqrt(sW2);
736 
737  double PiThat = 0.0;
738 
739  /* W self-energy */
740  PiThat += PiT_W(mu, 0.0, Mw_i).real();
741 
742  /* W-mass counter term */
743  double delMw2 = PiT_W(mu, Mw_i*Mw_i, Mw_i).real();
744  PiThat -= delMw2;
745 
746  /* counter term for e: (del e)/e */
747  double dele_over_e = PiTp_A(mu, 0.0, Mw_i).real()/2.0
748  + sW/cW*PiT_AZ(mu, 0.0, Mw_i).real()/Mz/Mz;
749  PiThat += 2.0*Mw_i*Mw_i*dele_over_e;
750 
751  /* counter term for sW: (del sW)/sW */
752  double delSw_overSw = - cW2/2.0/sW2
753  *( PiT_W(mu, Mw_i*Mw_i, Mw_i).real()/Mw_i/Mw_i
754  - PiT_Z(mu, Mz*Mz, Mw_i).real()/Mz/Mz );
755  PiThat -= 2.0*Mw_i*Mw_i*delSw_overSw;
756 
757  /* remaining counter terms,
758  * usually denoted by 2/(sW*cW)*PiT_AZ(0)/Mz/Mz. */
759  PiThat += - 2.0*Mw_i*Mw_i/(sW*cW)*PiT_AZ(mu, 0.0, Mw_i).real()/Mz/Mz;
760 
761  return PiThat;
762 }

◆ PiTp_A()

gslpp::complex EWSUSY::PiTp_A ( const double  mu,
const double  p2,
const double  Mw_i 
) const

The derivative of the transverse part of the photon self-energy with respect to \(p^2\), \(\Pi_{\gamma}^{T\prime}(p^2)\), in the 't Hooft-Feynman gauge.

Parameters
[in]muThe renormalization scale \(\mu\).
[in]p2The momentum squared \(p^2\).
[in]Mw_iThe W-boson mass \(M_W\).
Returns
\(\Pi_{\gamma}^{T\prime}(p^2)\) renormalized at the scale \(\mu\) in the 't Hooft-Feynman gauge.
References
Eq. (A.17) in [Chankowski, Pokorski and Rosiek, NPB 423 (1994) 437].

Definition at line 643 of file EWSUSY.cpp.

644 {
645  double mu2 = mu*mu;
646  double e2 = 4.0*M_PI*mySUSY.getAle();
647  double e = sqrt(e2);
648  double Nc = mySUSY.getNc();
649 
650  /* variables depending on Mw_i */
651  double Mw2 = Mw_i*Mw_i;
652  double mHp2[2] = {mySUSY.getMHp()*mySUSY.getMHp(), Mw2}; /* H^+_i = (H^+, G^+) */
653 
654  gslpp::complex PiTp_f = gslpp::complex(0.0, 0.0, false);
655  gslpp::complex PiTp_sf = gslpp::complex(0.0, 0.0, false);
656  gslpp::complex PiTp_ch = gslpp::complex(0.0, 0.0, false);
657  gslpp::complex PiTp_WZH = gslpp::complex(0.0, 0.0, false);
658  gslpp::complex b0, b0p, b00p;
659 
660  /* SM fermion loops */
661  gslpp::complex cV_Aee = - e;
662  gslpp::complex cA_Aee = 0.0;
663  gslpp::complex cV_Add = - e/3.0;
664  gslpp::complex cA_Add = 0.0;
665  gslpp::complex cV_Auu = 2.0/3.0*e;
666  gslpp::complex cA_Auu = 0.0;
667  for (int I=0; I<3; ++I) {
668  /* charged leptons */
669  PiTp_f += dFA(mu, p2, m_l[I], m_l[I], cV_Aee, cV_Aee, cA_Aee, cA_Aee);
670 
671  /* down-type quarks */
672  PiTp_f += Nc*dFA(mu, p2, m_d[I], m_d[I], cV_Add, cV_Add, cA_Add, cA_Add);
673 
674  /* up-type quarks */
675  PiTp_f += Nc*dFA(mu, p2, m_u[I], m_u[I], cV_Auu, cV_Auu, cA_Auu, cA_Auu);
676  }
677 
678  /* charged-slepton loops */
679  for (int n=0; n<6; ++n) {
680  b00p = PV.B00p(mu2, p2, Mse2[n], Mse2[n]);
681  PiTp_sf += 4.0*e2*b00p;
682  }
683 
684  /* down-type squark loops */
685  for (int n=0; n<6; ++n) {
686  b00p = PV.B00p(mu2, p2, Msd2[n], Msd2[n]);
687  PiTp_sf += 4.0*e2*Nc/3.0/3.0*b00p;
688  }
689 
690  /* up-type squark loops */
691  for (int n=0; n<6; ++n) {
692  b00p = PV.B00p(mu2, p2, Msu2[n], Msu2[n]);
693  PiTp_sf += 4.0*e2*Nc*2.0/3.0*2.0/3.0*b00p;
694  }
695 
696  /* chargino loops */
697  gslpp::complex cV_Aii = e;
698  gslpp::complex cA_Aii = 0.0;
699  for (int i=0; i<2; ++i)
700  PiTp_ch += dFA(mu, p2, mC[i], mC[i], cV_Aii, cV_Aii, cA_Aii, cA_Aii);
701 
702  /* charged-Higgs loops */
703  for (int i=0; i<2; ++i) {
704  b00p = PV.B00p(mu2, p2, mHp2[i], mHp2[i]);
705  PiTp_WZH += 4.0*e2*b00p;
706  }
707 
708  /* W-boson loops */
709  /* The Mw_i*Mw_i*b0p term, adding the corresponding contribution from
710  * the W-G loop below, differs from the one in the paper. */
711  b0 = PV.B0(mu2, p2, Mw2, Mw2);
712  b0p = PV.B0p(mu2, p2, Mw2, Mw2);
713  b00p = PV.B00p(mu2, p2, Mw2, Mw2);
714  PiTp_WZH += 2.0*e2*( (2.0*p2 + Mw2)*b0p + 2.0*b0 + 4.0*b00p);
715 
716  /* W-boson - charged-Goldstone-boson loop */
717  //b0p = PV.B0p(mu2, p2, Mw2, Mw2); /* Same as the above */
718  PiTp_WZH += - 2.0*e2*Mw2*b0p;
719 
720  /* Sum of all contributions */
721  gslpp::complex PiTp = PiTp_f + PiTp_sf + PiTp_ch + PiTp_WZH;
722 
723  return ( PiTp/16.0/M_PI/M_PI );
724 }

◆ SetRosiekParameters()

void EWSUSY::SetRosiekParameters ( )

Sets parameters in Rosiek's notation.

Rosiek SLHA
\(Y_u\) \(Y_U\)
\(Y_d\) \(-Y_D\)
\(Y_\ell\) \(-Y_E\)
Rosiek SLHA
\(A_u\) \(-\hat{T}_U^T\)
\(A_d\) \(\hat{T}_D^T\)
\(A_\ell\) \(\hat{T}_E^T\)
Rosiek SLHA
\(Z_-\) \(U^\dagger\)
\(Z_+\) \(V^\dagger\)
\(Z_N\) \(N^\dagger\)
Rosiek SLHA
\(Z_U\) \(R_u^\dagger\)
\(Z_D\) \(R_d^T\)
\(Z_\nu\) \(R_\nu^\dagger\)
\(Z_L\) \(R_e^T\)

\(Z_R=\left(\begin{array}{cc} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{array}\right)\), \(Z_H=\left(\begin{array}{cc} \sin\beta & -\cos\beta \\ \cos\beta & \sin\beta \end{array}\right)\).

Definition at line 39 of file EWSUSY.cpp.

40 {
41  Yu = mySUSY.getYu();
42  Yd = - mySUSY.getYd();
43  Yl = - mySUSY.getYe();
44 
45  Au = - mySUSY.getTUhat().transpose();
46  Ad = mySUSY.getTDhat().transpose();
47  Al = mySUSY.getTEhat().transpose();
48 
49  Zm = mySUSY.getU().hconjugate();
50  Zp = mySUSY.getV().hconjugate();
51  ZN = mySUSY.getN().hconjugate();
52 
53  ZU = mySUSY.getRu().hconjugate();
54  ZD = mySUSY.getRd().transpose();
55  ZL = mySUSY.getRl().transpose();
56  Zne = mySUSY.getRn().hconjugate();
57 
58  double sinAlpha = mySUSY.getSaeff().real(); /* Correct? */
59  double cosAlpha = sqrt(1.0 - sinAlpha*sinAlpha); /* -Pi/2 < alpha < 0 */
60  ZR.assign(0,0, cosAlpha);
61  ZR.assign(0,1, - sinAlpha);
62  ZR.assign(1,0, sinAlpha);
63  ZR.assign(1,1, cosAlpha);
64 
65  ZH.assign(0,0, mySUSY.getSinb());
66  ZH.assign(0,1, - mySUSY.getCosb());
67  ZH.assign(1,0, mySUSY.getCosb());
68  ZH.assign(1,1, mySUSY.getSinb());
69 
70  /* particle masses */
71  for (int I=0; I<3; ++I) {
72  /* up-type quarks */
73  m_u[I] = mySUSY.getMyEWSMcache()->mf(mySUSY.getQuarks((QCD::quark)(2*I)), mySUSY.getMz(), FULLNNLO);
74  /* down-type quarks */
75  m_d[I] = mySUSY.getMyEWSMcache()->mf(mySUSY.getQuarks((QCD::quark)(2*I + 1)), mySUSY.getMz(), FULLNNLO);
76  /* charged leptons */
77  m_l[I] = mySUSY.getLeptons((QCD::lepton)(2*I + 1)).getMass();
78  }
79  /* H^0_i = (H^0, h^0, A^0, G^0) */
80  mH02[0] = mySUSY.getMHh()*mySUSY.getMHh();
81  mH02[1] = mySUSY.getMHl()*mySUSY.getMHl();
82  mH02[2] = mySUSY.getMHa()*mySUSY.getMHa();
83  mH02[3] = mySUSY.getMz()*mySUSY.getMz(); /* mass squared of the neutral Goldstone boson */
84  for (int k=0; k<6; ++k) {
85  Msu2[k] = mySUSY.getMsu2()(k);
86  Msd2[k] = mySUSY.getMsd2()(k);
87  Mse2[k] = mySUSY.getMse2()(k);
88  }
89  for (int k=0; k<3; ++k)
90  Msn2[k] = mySUSY.getMsn2()(k);
91  for (int i=0; i<2; ++i)
92  mC[i] = mySUSY.getMch()(i);
93  for (int j=0; j<4; ++j)
94  mN[j] = mySUSY.getMneu()(j);
95 }

◆ Sigma_nu_0()

gslpp::complex EWSUSY::Sigma_nu_0 ( const double  mu,
const QCD::lepton  I,
const QCD::lepton  J,
const double  Mw_i 
) const

The SUSY neutrino self-energy at zero momentum transfer in the 't Hooft-Feynman gauge.

Parameters
[in]muThe renormalization scale \(\mu\).
[in]IA neutrino.
[in]JA neutrino.
[in]Mw_iThe W-boson mass \(M_W\).
Returns
\(\Sigma_\nu(0,I,J)\) in the 't Hooft-Feynman gauge.
References
Eq. (A.24) in [Chankowski, Dabelstein, Hollik, Mosle, Pokorski and Rosiek, NPB 417 (1994) 101].

Definition at line 1088 of file EWSUSY.cpp.

1090 {
1091  int intI, intJ;
1092  switch (I) {
1093  case StandardModel::NEUTRINO_1:
1094  case StandardModel::NEUTRINO_2:
1095  case StandardModel::NEUTRINO_3:
1096  intI = ((int)I - StandardModel::NEUTRINO_1)/2;
1097  break;
1098  default:
1099  throw std::runtime_error("EWSUSY::Sigma_nu(): Wrong argument!");
1100  }
1101  switch (J) {
1102  case StandardModel::NEUTRINO_1:
1103  case StandardModel::NEUTRINO_2:
1104  case StandardModel::NEUTRINO_3:
1105  intJ = ((int)J - StandardModel::NEUTRINO_1)/2;
1106  break;
1107  default:
1108  throw std::runtime_error("EWSUSY::Sigma_nu(): Wrong argument!");
1109  }
1110 
1111  gslpp::complex Sigma = gslpp::complex(0.0, 0.0, false);
1112  double muIR = mu; /* fictional scale, since B0p(0,m1,m2) is IR finite */
1113  gslpp::complex b0p, b0;
1114 
1115  /* charged-slepton - chargino loops */
1116  for (int k=0; k<6; ++k)
1117  for (int i=0; i<2; ++i) {
1118  b0p = PV.B0p(muIR*muIR, 0.0, Mse2[k], mC[i]*mC[i]);
1119  b0 = PV.B0(mu*mu, 0.0, Mse2[k], mC[i]*mC[i]);
1120  Sigma += 0.5*L_nLC(intI, k, i, Mw_i)*L_nLC(intJ, k, i, Mw_i).conjugate()
1121  *( (Mse2[k] - mC[i]*mC[i])*b0p - b0 );
1122  }
1123 
1124  /* sneutrino - neutralino loops */
1125  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
1126  for (int j=0; j<4; ++j) {
1127  b0p = PV.B0p(muIR*muIR, 0.0, Msn2[K], mN[j]*mN[j]);
1128  b0 = PV.B0(mu*mu, 0.0, Msn2[K], mN[j]*mN[j]);
1129  Sigma += 0.5*L_nsnN(intI, K, j, Mw_i)*L_nsnN(intJ, K, j, Mw_i).conjugate()
1130  *( (Msn2[K] - mN[j]*mN[j])*b0p - b0 );
1131  }
1132 
1133  return ( Sigma/16.0/M_PI/M_PI );
1134 }

◆ v()

gslpp::complex EWSUSY::v ( const double  mu,
const QCD::lepton  M,
const QCD::lepton  J,
const double  Mw_i 
) const
Parameters
[in]muThe renormalization scale \(\mu\).
[in]MA charged lepton.
[in]JA neutrino.
[in]Mw_iThe W-boson mass \(M_W\).
Returns
\(v(M,J)\).
References
Eq. (A.19) in [Chankowski, Dabelstein, Hollik, Mosle, Pokorski and Rosiek, NPB 417 (1994) 101].

Definition at line 958 of file EWSUSY.cpp.

960 {
961  int intM, intJ;
962  switch (M) {
963  case StandardModel::ELECTRON:
964  case StandardModel::MU:
965  case StandardModel::TAU:
966  intM = ((int)M - StandardModel::ELECTRON)/2;
967  break;
968  default:
969  throw std::runtime_error("EWSUSY::v(): Wrong argument!");
970  }
971  switch (J) {
972  case StandardModel::NEUTRINO_1:
973  case StandardModel::NEUTRINO_2:
974  case StandardModel::NEUTRINO_3:
975  intJ = ((int)J - StandardModel::NEUTRINO_1)/2;
976  break;
977  default:
978  throw std::runtime_error("EWSUSY::v(): Wrong argument!");
979  }
980 
981  gslpp::complex v = gslpp::complex(0.0, 0.0, false);
982  gslpp::complex b0, ff;
983  gslpp::complex CL_ji, CR_ji; /* chargino-neutralino-W couplings */
984 
985  /* charged-slepton - chargino - neutralino loops */
986  for (int k=0; k<6; ++k)
987  for (int j=0; j<4; ++j)
988  for (int i=0; i<2; ++i) {
989  CL_ji = ZN(1,j)*Zp(0,i).conjugate()
990  - ZN(3,j)*Zp(1,i).conjugate()/sqrt(2.0);
991  CR_ji = ZN(1,j).conjugate()*Zm(0,i)
992  + ZN(2,j).conjugate()*Zm(1,i)/sqrt(2.0);
993  b0 = PV.B0(mu*mu, 0.0, mC[i]*mC[i], mN[j]*mN[j]);
994  ff = f(sqrt(Mse2[k]), mC[i], mN[j]);
995  v += L_nLC(intJ, k, i, Mw_i).conjugate()*L_eLN(intM, k, j, Mw_i)
996  *( sqrt(2.0)*CL_ji*mC[i]*mN[j]*ff
997  - CR_ji/sqrt(2.0)*(b0 - 0.5 + Mse2[k]*ff) );
998  }
999 
1000  /* sneutrino - neutralino - chargino loops */
1001  for (int K=0; K<3; ++K) /* K=0-2 for left-handed sneutrinos */
1002  for (int j=0; j<4; ++j)
1003  for (int i=0; i<2; ++i) {
1004  CL_ji = ZN(1,j)*Zp(0,i).conjugate()
1005  - ZN(3,j)*Zp(1,i).conjugate()/sqrt(2.0);
1006  CR_ji = ZN(1,j).conjugate()*Zm(0,i)
1007  + ZN(2,j).conjugate()*Zm(1,i)/sqrt(2.0);
1008  b0 = PV.B0(mu*mu, 0.0, mC[i]*mC[i], mN[j]*mN[j]);
1009  ff = f(sqrt(Msn2[K]), mC[i], mN[j]);
1010  v += L_nsnN(intJ, K, j, Mw_i).conjugate()*L_esnC(intM, K, i, Mw_i)
1011  *( - sqrt(2.0)*CR_ji*mC[i]*mN[j]*ff
1012  + CL_ji/sqrt(2.0)*(b0 - 0.5 + Msn2[K]*ff) );
1013  }
1014 
1015  /* sneutrino - charged-slepton - neutralino loops */
1016  gslpp::matrix<gslpp::complex> ZneT_ZL = Zne.transpose()*ZL;
1017  for (int i=0; i<6; ++i)
1018  for (int j=0; j<4; ++j)
1019  for (int K=0; K<3; ++K) { /* K=0-2 for left-handed sneutrinos */
1020  b0 = PV.B0(mu*mu, 0.0, Mse2[i], Msn2[K]);
1021  ff = f(mN[j], sqrt(Mse2[i]), sqrt(Msn2[K]));
1022  v += 0.5*L_nsnN(intJ, K, j, Mw_i).conjugate()*L_eLN(intM, i, j, Mw_i)
1023  *ZneT_ZL(K, i).conjugate()*(b0 + 0.5 + mN[j]*mN[j]*ff);
1024  }
1025 
1026  return ( v/16.0/M_PI/M_PI );
1027 }
The documentation for this class was generated from the following files:
QCD::TAU
Definition: QCD.h:316
QCD::NEUTRINO_3
Definition: QCD.h:315
EWSUSY::DeltaR_boxLL_SUSY
double DeltaR_boxLL_SUSY(const double Mw_i) const
The LL SUSY box corrections to in the 't Hooft-Feynman gauge.
Definition: EWSUSY.cpp:774
EWSUSY::FA
gslpp::complex FA(const double mu, const double p2, const double mi, const double mj, const gslpp::complex cV_aij, const gslpp::complex cV_bji, const gslpp::complex cA_aij, const gslpp::complex cA_bji) const
Fermionic contribuiton to the transverse part of a gauge-boson self-energy, .
Definition: EWSUSY.cpp:97
EWSUSY::DeltaR_TOTAL_EW1
double DeltaR_TOTAL_EW1(const double Mw_i) const
The total one-loop contribution to in the MSSM.
Definition: EWSUSY.cpp:1147
gslpp::matrix< double >
A class for constructing and defining operations on real matrices.
Definition: gslpp_matrix_double.h:48
EWSUSY::DeltaR_boxLR_SUSY
double DeltaR_boxLR_SUSY(const double Mw_i) const
The LR SUSY box corrections to in the 't Hooft-Feynman gauge.
Definition: EWSUSY.cpp:865
EWSUSY::v
gslpp::complex v(const double mu, const QCD::lepton M, const QCD::lepton J, const double Mw_i) const
Definition: EWSUSY.cpp:958
EWSUSY::PiT_W
gslpp::complex PiT_W(const double mu, const double p2, const double Mw_i) const
The transverse part of the W-boson self-energy, , in the 't Hooft-Feynman gauge.
Definition: EWSUSY.cpp:333
gslpp::complex
A class for defining operations on and functions of complex numbers.
Definition: gslpp_complex.h:35
QCD::NEUTRINO_2
Definition: QCD.h:313
gslpp::log
complex log(const complex &z)
Definition: gslpp_complex.cpp:342
gslpp::matrix
A base class for defining operations on matrices, both real and complex.
Definition: gslpp_matrix_base.h:21
QCD::ELECTRON
Definition: QCD.h:312
gslpp::complex::abs2
double abs2() const
Definition: gslpp_complex.cpp:86
EWSUSY::DeltaR_rem_SM
double DeltaR_rem_SM(const double Mw_i) const
The SM one-loop renormalized vertex and box corrections to in the 't Hooft-Feynman gauge.
Definition: EWSUSY.cpp:764
EWSUSY::PiThat_W_0
double PiThat_W_0(const double Mw_i) const
The renormalized transverse W-boson self-energy at zero momentum transefer in the 't Hooft-Feynman ga...
Definition: EWSUSY.cpp:726
EWSUSY::dFA
gslpp::complex dFA(const double mu, const double p2, const double mi, const double mj, const gslpp::complex cV_aij, const gslpp::complex cV_bji, const gslpp::complex cA_aij, const gslpp::complex cA_bji) const
The derivative of with respect to .
Definition: EWSUSY.cpp:115
gslpp::complex::conjugate
complex conjugate() const
Definition: gslpp_complex.cpp:288
EWSUSY::Sigma_nu_0
gslpp::complex Sigma_nu_0(const double mu, const QCD::lepton I, const QCD::lepton J, const double Mw_i) const
The SUSY neutrino self-energy at zero momentum transfer in the 't Hooft-Feynman gauge.
Definition: EWSUSY.cpp:1088
gslpp::sqrt
complex sqrt(const complex &z)
Definition: gslpp_complex.cpp:385
EWSUSY::PiT_Z
gslpp::complex PiT_Z(const double mu, const double p2, const double Mw_i) const
The transverse part of the Z-boson self-energy, , in the 't Hooft-Feynman gauge.
Definition: EWSUSY.cpp:135
EWSUSY::PiT_AZ
gslpp::complex PiT_AZ(const double mu, const double p2, const double Mw_i) const
The transverse part of the self-energy, , for the mixing between photon and Z boson in the 't Hooft-F...
Definition: EWSUSY.cpp:499
QCD::quark
quark
An enum type for quarks.
Definition: QCD.h:323
EWSUSY::delta_v
gslpp::complex delta_v(const double mu, const QCD::lepton M, const QCD::lepton J, const double Mw_i) const
Definition: EWSUSY.cpp:1029
EWSUSY::DeltaAlphaL5q_SM_EW1
double DeltaAlphaL5q_SM_EW1() const
The SM one-loop leptonic and five-flavour-hadronic corrections to at Z-mass scale.
Definition: EWSUSY.cpp:1178
gslpp::complex::real
const double & real() const
Definition: gslpp_complex.cpp:53
EWSUSY::PiTp_A
gslpp::complex PiTp_A(const double mu, const double p2, const double Mw_i) const
The derivative of the transverse part of the photon self-energy with respect to , ,...
Definition: EWSUSY.cpp:643
FULLNNLO
Definition: OrderScheme.h:38
QCD::NEUTRINO_1
Definition: QCD.h:311
QCD::MU
Definition: QCD.h:314
QCD::lepton
lepton
An enum type for leptons.
Definition: QCD.h:310
EWSUSY::DeltaR_vertex_SUSY
double DeltaR_vertex_SUSY(const double Mw_i) const
The renormalized SUSY vertex corrections to in the 't Hooft-Feynman gauge.
Definition: EWSUSY.cpp:1077
EWSUSY::DeltaR_neutrino_SUSY
double DeltaR_neutrino_SUSY(const double Mw_i) const
The renormalized SUSY neutrino wave-function contribution to in the 't Hooft-Feynman gauge.
Definition: EWSUSY.cpp:1136