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Phases

Phases

One can add a phase \phi to the parametrisation of a field \Phi (Weyl spinor or scalar) in SARAH via

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

By doing that, SARAH replaces in the Lagrangian

\Phi \to \phi \Phi

Phases in RGE calculation

By default, SARAH does not include those phases in the calculation of RGEs.
To change this behaviour set SetOptions[PrepareRGEs, ComplexPhases -> True] before running CalcRGEs[].

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_{\tilde{g}} is related to the gaugino mass parameter M_3 by M_{\tilde{g}} = \phi_{\tilde{g}}^2 M_3. Thus, for instance SPheno calculates M_{\tilde{g}}, \phi_{\tilde{g}} from

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

  1. 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 SU(2) doublet. In addition, it is common to write the phase as e^{i \phi} in contrast to phases for fermions.

  2. Models with vector-like fermions: in models which come with vector-like fermions M_T,\, t,\, \bar{t} (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