Changes between Version 10 and Version 11 of 2HDM
 Timestamp:
 04/16/14 14:53:09 (5 years ago)
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2HDM
v10 v11 9 9 * NIKHEF theory group 10 10 * mherquet@nikhef.nl 11 * Celine Degrande 12 * IPPP Durham 13 * celine.degrande@durham.ac.uk 11 14 12 15 === Description of the model === … … 18 21 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 22 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.23 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 where only one of the two Higgs fields acquires a nonzero vev, namely Phi1. Note that the Higgs basis is not univocally defined since a phase reparametrization of Phi2 leaves the Higgs basis condition invariant. 21 24 22 There are two independent minimization conditions for general 2HDM potential, one relating m_1 to lambda_1 and one relating m_3 to lambda_6. This reduces the number of free parameters in the most general 2HDM to ten (seven real parameters, three complex ones and three minimization conditions). Besides the usual three massless wouldbe Goldstone bosons, the physical spectrum also contains a pair of charged Higgs with a mass directly related to lambda_3 and m_2, so that m_2 can be directly extracted from this mass, given as an external input.25 There are two independent minimization conditions for general 2HDM potential, one relating m_1 to lambda_1 and one relating m_3 to lambda_6. This reduces the number of free parameters in the most general 2HDM to ten (seven real parameters, three complex ones and three minimization conditions). Besides the usual three massless wouldbe Goldstone bosons, the physical spectrum also contains a pair of charged Higgs. 23 26 24 The symmetric matrix squared mass matrix for the three neutral Higgs field is diagonalized by an orthogonal matrix T which describe the relation between the physical scalar fields and the doublet neutral components. Even though this matrix is directly related to the potential parameter, it is still considered as an external input in the current implementation and must be provided by the user.27 The symmetric matrix squared mass matrix for the three neutral Higgs field is diagonalized by an orthogonal matrix T which describe the relation between the physical scalar fields and the doublet neutral components. The three mixing angles defining this orthogonal matrix are externals parameters as the masses of the scalars and lambda_(2,3,7). The other parameters of the potential are internal parameters. 25 28 26 In the current implementation of the 2HDM into !FeynRules, the user has to provide numerical values for all the lambda_i parameters in the Higgs basis, together with the charged Higgs mass. The other parameters of the potential, such as the \mu_i, are then deduced from these inputs. Contrary, the T matrix must be calculated externally. This, together with the change of basis required if the user wants to provide potential parameters and Yukawa coupling values in bases different from the Higgs basis, as it is often the case, can be done using the ''!TwoHiggsCalc'' calculator introduced for the original implementation of the 2HDM in !MadGraph. This code has been modified to produce a parameter file compatible with the present implementation. This calculator can also be used to calculate the required Higgs boson treelevel decay widths. It can be found at27 28 http://cp3wks05.fynu.ucl.ac.be/Calculators/TwoHiggsCalc/index.html29 29 30 30 === References === 31 31 * " ''CP violation'' ", G. Branco, L. Lavoura and J. P. Silva, Clarandon Press, Oxford, 1999. Chapter 22. 32 * "R2 rational terms and ultraviolet counterterms for the 2HDM from automated tools", C. Degrande, to be published. 32 33 33 34 === Model files === 34 35 * [/attachment/wiki/2HDM/2HDM.tar.gz 2HDM.tar.gz]: This archive contains all the model files. Should be expanded in the FR model directory. 35 * [/attachment/wiki/2HDM/HBreal.rst HBreal.rst]: Additionnal restriction file to define all parameters as being real, to be used, for example, with !CalcHEP. 36 * [/attachment/wiki/2HDM/Masslessbuttb.rst Masslessbuttb.rst]: Restriction file to set all the masses of the fermions but the top and bottom quarks to zero. 37 * [/attachment/wiki/2HDM/FlavorSym.rst FlavorSym.rst]: Restriction file to force flavor conservation. 38 * [/attachment/wiki/2HDM/CPconcerving.rst CPconcerving.rst]: Restriction file to conserve CP. It assumes that FlavorSym.rst is loaded first. 36 39 37 === Instructions ===38 39 The modelfile is loaded in the usual way.40 41 Feynman gauge is not supported, only unitary gauge is available.42 40 43 41 === Examples === 44 * [/attachment/wiki/2HDM/2HDM.nb 2HDM.nb] : This is an example Mathematica® notebook that loads the model and calculates Feynman rules. 45 * [/attachment/wiki/2HDM/param_card_FR.dat param_card_FR.dat] : This is an example of LHA parameter file to be used with this model. It also contains the defalut values used for validation. 46 === Validation === 47 * [/attachment/wiki/2HDM/PSPoints.jpg Phase space point comparison with stock version] 48 * [/attachment/wiki/2HDM/TANU.jpg Cross section comparison, for tau/nu_tau initial state] 49 * [/attachment/wiki/2HDM/TATA.jpg Cross section comparison, for tau/tau initial state] 50 * [/attachment/wiki/2HDM/TATAbis.jpg Cross section comparison, for tau/tau initial state (part 2)] 51 * [/attachment/wiki/2HDM/VV.jpg Cross section comparison, for VV initial state] 52 * [/attachment/wiki/2HDM/VSSS.jpg Cross section comparison, for VSSS external legs] 53 54 55 56 == Matrix element generator files == 57 Below we give tarballs containing the model files generated by !FeynRules for the various matrix element generaotrs for which a !FeynRules interface exists. All fermion masses are put to zero, except for the top, the bottom and the Tau lepton masses. Furthermore, in the CalcHep files, the Yukawa matrices are real. All files are in unitary gauge. 42 * [/attachment/wiki/2HDM/THDM.nb THDM.nb] : This is an example Mathematica® notebook that loads the model and calculates Feynman rules. It also show how the NLO counterterms can be computed. 43 * [/attachment/wiki/2HDM/2HDM.nlo 2HDM.nlo] : The file containing the QCD R2 and UV conterterms for the 2HDM. 58 44 59 45