Models with several generations of Higgs doublets

Important Note

This functionality was replaced in SARAH 4.9.0 by the new option

DEFINITION[MatchingConditions]

see Matching to the SM in SPheno.

General

For models in which the SM Yukawa couplings and/or THDM VEVs don't exist, but other Yukawa couplings/VEVs are present which are functions of them, new options for SPheno.m exist:

• DEFINITION[MoreEWvevs]: Can be used to relate new VEVs to the ew VEV
• DEFINITION[UseNonStandardYukwas]: Can be used to turn on the new functionality to relate other Yukwas than the common Yu, Yd, Ye to SM parameters
• DEFINITION[NonStandardYukawas]: names of the new Yukawas
• DEFINITION[NonStandardVEVs1L]: Can be used to turn on the shift in the new VEVs at the one-loop level
• DEFINITION[NonStandardVEVs1Lrelations]: defines the relations to shift the VEVs at one-loop
• AuxiliaryParametersSPheno: contains the initialisation of parameters needed for the above definitions

EXAMPLE: Left-Right SUSY Model with two Higgs bi-doublets:

1. The VEVs of the two generations of bi-doublets are defined by

 DEFINITION[MoreEWvevs] = {
      "vPhiu(1) = (TanBeta*TanBetaU*sqrt(vev2))/(Sqrt(1 + TanBeta**2)*Sqrt(1 + TanBetaU**2))",
      "vPhid(1) = (TanBetaD*sqrt(vev2))/(Sqrt(1 + TanBeta**2)*Sqrt(1 + TanBetaD**2))",
      "vPhiu(2) = (TanBeta*sqrt(vev2))/(Sqrt(1 + TanBeta**2)*Sqrt(1 + TanBetaU**2))",
      "vPhid(2) = sqrt(vev2)/(Sqrt(1 + TanBeta**2)*Sqrt(1 + TanBetaD**2))"
    };

1. The LR symmetric Yukawas are calculated using

  DEFINITION[UseNonStandardYukwas]=True;
  DEFINITION[NonStandardYukawas] = {YQ,YL};

  DEFINITION[NonStandardYukawasRelations] = {
      "YQ(1:3,1:3,1) = -(vu * vPhid(2) * Transpose(Y_u) - vd * vPhiu(2) * Transpose(Y_d))/(vPhid(2) * vPhiu(1) - vPhid(1) * vPhiu(2))",
      "YQ(1:3,1:3,2) = (vu * vPhid(1) * Transpose(Y_u) - vd * vPhiu(1) * Transpose(Y_d))/(vPhid(2) * vPhiu(1) - vPhid(1) * vPhiu(2))",
      "YL(1:3,1:3,1) = ( vd * vPhiu(2) * Transpose(Y_l))/(vPhid(2) * vPhiu(1) - vPhid(1) * vPhiu(2))",
      "YL(1:3,1:3,2) = (- vd * vPhiu(1) * Transpose(Y_l))/(vPhid(2) * vPhiu(1) - vPhid(1) * vPhiu(2))"
    };

1. The shift in the VEVs at the one-loop level are set via

  DEFINITION[NonStandardVEVs1L]=True;
  DEFINITION[NonStandardVEVs1Lrelations] = {
      "tanbQ=sqrt((vPhiu(1)**2+vPhiu(2)**2)/(vPhid(1)**2+vPhid(2)**2))",
      "tanbUQ =  vPhiu(1)/vPhiu(2)",
      "tanbDQ = vPhid(1)/vPhid(2)",
      "vev2 =  (4*((mZ2+dmz2)*(-4*(mZ2+dmz2) + (gBL**2 + gR**2)*vR**2)))/(-4*(g2**2 + gR**2)*mZ2 + (gBL**2*gR**2 + g2**2*(gBL**2 + gR**2))*vR**2)",
      "vPhiu(1) = (TanBQ*TanBUQ*sqrt(vev2))/(Sqrt(1 + TanBQ**2)*Sqrt(1 + TanBUQ**2))",
      "vPhid(1) = (TanBDQ*sqrt(vev2))/(Sqrt(1 + TanBQ**2)*Sqrt(1 + TanBDQ**2))",
      "vPhiu(2) = (TanBQ*sqrt(vev2))/(Sqrt(1 + TanBQ**2)*Sqrt(1 + TanBUQ**2))",
      "vPhid(2) = sqrt(vev2)/(Sqrt(1 + TanBQ**2)*Sqrt(1 + TanBDQ**2))"
    };

1. The new parameters are define via

AuxiliaryParametersSPheno={
      "Real(dp) :: tanbQ, tanBUQ, tanBDQ"
    };

See also