Changes between Version 3 and Version 4 of 2HDM
 Timestamp:
 Feb 16, 2010 11:36:53 PM (9 years ago)
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2HDM
v3 v4 16 16 The 2HDM considered here is based on two SU(2) doublets with the same hypercharge Y=+1. If one imposes only gauge invariance, the most general renormalisable scalar potential can be found in the reference quoted below. This potential has 6 real (mu_(1,2) and lambda_(1,2,3,4)) and four complex parameters (mu_3 and lambda_(5,6,7)). We assume the electromagnetic gauge symmetry is preserved, i.e. , that the vev's of two doublets are aligned in the SU(2) space in such a way that a single SU(2) gauge transformation suffices to rotate them to the neutral components. 17 17 18 The most general form for the Yukawa interactions contains two 3x3 complex Yukawa coupling matrices, noted Delta_i and Gamma_i, expressed in the fermion physical basis, i.e. in the basis where the fermion mass matrix are diagonal. Since the fermion mass matrix is <br />fixed, only the Gamma_i matrices, i.e. the Yukawa couplings of the second Higgs doublet, are required. We choose as free parameters the Gamma_i matrices, while the other Yukawa couplings, the Delta_i matrices, are deduced from the matching with the observed fermion masses. Conventionally, the indices of the elements of these Yukawa matrices refer to the generations of the SU(2) doublet and singlet, respectively18 The most general form for the Yukawa interactions contains two 3x3 complex Yukawa coupling matrices, noted Delta_i and Gamma_i, expressed in the fermion physical basis, i.e. in the basis where the fermion mass matrix are diagonal. Since the fermion mass matrix is fixed, only the Gamma_i matrices, i.e. the Yukawa couplings of the second Higgs doublet, are required. We choose as free parameters the Gamma_i matrices, while the other Yukawa couplings, the Delta_i matrices, are deduced from the matching with the observed fermion masses. Conventionally, the indices of the elements of these Yukawa matrices refer to the generations of the SU(2) doublet and singlet, respectively 19 19 20 20 The 2HDM Lagrangian implemented in !FeynRules is based on the Standard Model default implementation, where the scalar potential and Yukawa interactions have been modified as explained above. An important feature of this model is the freedom to redefine the two scalar fields using arbitrary "horizontal" U(2) transformations acting on the two doublets simultaneously since this transformation leaves the gaugecovariant kinetic energy terms invariant. Since a given set of Lagrangian parameter values is only meaningful for a given basis, let us take advantage of this invariance property to select the Higgs basis (by defining the additional file HiggsBasis.fr) where only one of the two Higgs fields acquires a nonzero vev, namely H_1. Note that the Higgs basis is not univocally defined since a phase reparametrization of H_2 leaves the Higgs basis condition invariant, so that the phase of H_2 can be fixed in such a way that lambda_5 becomes real. Other basis choices can in principle be easily implemented as different extension files for the main Lagrangian file Lag.fr.