Phases

One can add a phase ϕ to the parametrisation of a field Φ (Weyl spinor or scalar) in SARAH via

DEFINITION[EIGENSTATES][Phases]=
{    {FIELD, NAMEofPHASE}
    };

By doing that, SARAH replaces in the Lagrangian

Φ → ϕ ⋅ Φ

Examples

1. The gluino in the CP conserving MSSM. The standard phsae for the gluino is added by DEFINITION[EWSB][Phases]= { {fG, PhaseGlu} };

   With this definition, the physical gluino mass M_g̃ is related to the gaugino mass parameter M₃ by M_g̃ = ϕ_g̃²M₃

   Thus, for instance SPheno for instance calculates M_g̃, ϕ_g̃ from

   $\begin{aligned} M_{\tilde{g}} &=& |M_3| \\ \phi_{\tilde{g}} &=& \sqrt{|M_3|/M_3} \end{aligned}$

2. The CP violating MSSM: the relative phases between the two Higgs doublets can be defined as follows

   DEFINITION[GaugeES][Phases]=
   {    {SHup, Exp[I eta]},
        {SHu0, Exp[I eta]}
       };

   Note, that is necessary to define the phases for both components of the S**U(2) doublet. In addition, it is common to write the phase as e^i**ϕ in contrast to phases for fermions.

3. Models with vector-like fermions: in models which come with vector-like fermions M_Tt′t̄′ (FT,FTp) one has to define a phase for just one-component: DEFINITION[GaugeES][Phases]= { {FT, PhaseT} }; ... DEFINITION[EWSB][DiracSpinors]={ ..., {Tp -> {FT,FTp} }

   The physical mass of the Dirac spinor is |M_T| and the phase is calculated from |M_T|/M_T.

See also