FlexibleEFTHiggs

Table of Contents

1 Overview
2 FlexibleEFTHiggs spectrum generator
3 MSSM example for FlexibleEFTHiggs
4 References

1 Overview

By default, FlexibleSUSY creates a "full model" spectrum generator, where the pole mass spectrum is calculated at the 1- or 2-loop level in the MS-bar/DR-bar scheme in the full model.

FlexibleEFTHiggs [1609.00371], [1710.03760] is an approach of FlexibleSUSY, to perform the 1-loop calculation of the lightest Higgs pole mass of the given BSM model in an effective field theory (EFT), which is assumed to be the Standard Model. FlexibleEFTHiggs combines the features of full model calculation (the inclusion of all logarithmic and non-logarithmic Higgs mass contributions) with the ones of an EFT (the resummation of leading and sub-leading logarithms to all orders). In FlexibleEFTHiggs, the quartic Higgs coupling of the Standard Model is determined at the SUSY scale by requiring that the lightest CP-even Higgs pole mass in the full model is equarl to the Standard Model Higgs pole mass.

FlexibleEFTHiggs is exact at the 1-loop level. In particular, all power-suppressed 1-loop terms of the order O(v^2/M^2), where M is the scale of heavy new non-Standard Model particles, are correctly taken into account. In addition, leading and sub-leading logarithms of the scale M are resummed to all orders. At the 2-loop level, FlexibleEFTHiggs misses only non-logarithmic BSM contributions.

2 FlexibleEFTHiggs spectrum generator

In order to create a FlexibleEFTHiggs spectrum generator for a given model, SARAH model files and a FlexibleSUSY model file must be provided, just as in the case of a "full model" spectrum generator.

In the FlexibleSUSY model file, the FlexibleEFTHiggs variable must be set to True:

FlexibleEFTHiggs = True;

In FlexibleEFTHiggs, the matching of the full model to the Standard Model is performed at the SUSYScale (except, if the value of the matching scale is overwritten by setting the FlexibleEFTHiggs[19] to a non-zero value).

The low-scale constaint is completely ignored, i.e. the variables LowScale, LowScaleFirstGuess, LowScaleInput and InitialGuessAtLowScale have no effect.

The model parameters must be set in the SUSY-scale or high-scale constraint. Initial values for the model parameters can be given in the InitialGuessAtSUSYScale or InitialGuessAtHighScale variables.

note If OnlyLowEnergyFlexibleSUSY = True, then the high-scale constraint is ignored. In this case, only the SUSY-scale constraint is available in FlexibleEFTHiggs.

The Standard Model gauge and Yukawa couplings as well as the SM-like VEV of the full model are calculated automatically using a full 1-loop calculation. Therefore, the SU(3)_C\times SU(2)_L\times U(1)_Y gauge couplings and the up- and down-Quark and lepton Yukawa couplings don't need to be specified in any of the constraints.

In many models the determination of the running Yukawa couplings requires the knowledge of the running VEVs. These VEVs are sometimes related to the SM-like VEV v = \sqrt{v_u^2 + v_d^2}. For example in the MSSM the relation reads,

v_u &= v \sin\beta ,
v_d &= v \cos\beta .

Such a matching condition can be set using the MatchingScaleInput variable, see the corresponding section in FlexibleSUSY model file.

Example: in the MSSM

MatchingScaleInput = {
    {vu, VEV Sin[ArcTan[TanBeta]]},
    {vd, VEV Cos[ArcTan[TanBeta]]}
};

The symbol VEV is a FlexibleSUSY constant which refers to the running SM-like vacuum expectation value in the full model. See FlexibleSUSY model file for the precise definition.

3 MSSM example for FlexibleEFTHiggs

An example for the general MSSM can be found in model_files/MSSMEFTHiggs/FlexibleSUSY.m.in. Below, we show a simplified FlexibleEFTHiggs/MSSM spectrum generator, which takes only three input parameters: The SUSY scale M_\text{S}, the stop mixing parameter X_t, and \tan\beta:

FSModelName = "@CLASSNAME@";
FSEigenstates = SARAH`EWSB;
FSDefaultSARAHModel = MSSM;
OnlyLowEnergyFlexibleSUSY = True;
FlexibleEFTHiggs = True;

MINPAR = {
    {4, Sign[\[Mu]]}
};

EXTPAR = {
    {0, Ms},      (* SUSY scale *)
    {14, Xtt},    (* Xt / Ms *)
    {25, TanBeta}
};

EWSBOutputParameters = { mHd2, mHu2 };

SUSYScale = Ms;

SUSYScaleFirstGuess = Ms;

SUSYScaleInput = {
    {MassB, Ms},
    {MassWB, Ms},
    {MassG, Ms},
    {mq2, UNITMATRIX[3] Ms^2},
    {mu2, UNITMATRIX[3] Ms^2},
    {md2, UNITMATRIX[3] Ms^2},
    {ml2, UNITMATRIX[3] Ms^2},
    {me2, UNITMATRIX[3] Ms^2},
    {\[Mu], Ms},
    {B[\[Mu]], Ms^2/(TanBeta + 1/TanBeta)},
    {T[Yu], Ms/TanBeta Yu},
    {T[Yd], Ms TanBeta Yd},
    {T[Ye], Ms TanBeta Ye},
    {T[Yu][3,3], (Ms/TanBeta + Xtt Ms) Yu[3,3]}
};

InitialGuessAtSUSYScale = SUSYScaleInput;

MatchingScaleInput = {
    {vu, VEV Sin[ArcTan[TanBeta]]},
    {vd, VEV Cos[ArcTan[TanBeta]]}
};

UseHiggs2LoopMSSM = True;
EffectiveMu = \[Mu];