|
|
# Phases
|
|
|
|
|
|
One can add a phase ϕ to the parametrisation of a field Φ (Weyl spinor or scalar) in SARAH via
|
|
|
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
|
|
|
```math
|
|
|
\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[]`.
|
|
|
|
|
|
*Φ* → *ϕ* ⋅ *Φ*
|
|
|
|
|
|
Examples
|
|
|
--------
|
|
|
## 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*<sub>*g̃*</sub> is related to the gaugino mass parameter *M*<sub>3</sub> by *M*<sub>*g̃*</sub> = *ϕ*<sub>*g̃*</sub><sup>2</sup>*M*<sub>3</sub>
|
|
|
|
|
|
Thus, for instance [SPheno](/SPheno "wikilink") for instance calculates *M*<sub>*g̃*</sub>, *ϕ*<sub>*g̃*</sub> from
|
|
|
|
|
|
$\\begin{aligned}
|
|
|
M_{\\tilde{g}} &=& |M_3| \\\\
|
|
|
\\phi_{\\tilde{g}} &=& \\sqrt{|M_3|/M_3}
|
|
|
\\end{aligned}$
|
|
|
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](/SPheno "wikilink") calculates $`M_{\tilde{g}}`$, $`\phi_{\tilde{g}}`$ from
|
|
|
```math
|
|
|
\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`
|
|
|
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*<sup>*i**ϕ*</sup> in contrast to phases for fermions.
|
|
|
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.
|
|
|
|
|
|
3. **Models with vector-like fermions**: in models which come with vector-like fermions *M*<sub>*T*</sub>*t*′*t̄*′ (`FT`,`FTp`) one has to define a phase for just one-component:
|
|
|
DEFINITION[GaugeES][Phases]=
|
|
|
{ {FT, PhaseT}
|
|
|
3. **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 $`|M_T|/M_T`$.
|
|
|
|
|
|
The physical mass of the Dirac spinor is |*M*<sub>*T*</sub>| and the phase is calculated from |*M*<sub>*T*</sub>|/*M*<sub>*T*</sub>.
|
|
|
## See also
|
|
|
|
|
|
See also
|
|
|
-------- |
|
|
\ No newline at end of file |
|
|
* [Basic definitions for a supersymmetric model](/Basic_definitions_for_a_non-supersymmetric_model "wikilink")
|
|
|
* [Basic definitions for a non-supersymmetric model](Basic_definitions_for_a_non-supersymmetric_model) |
|
|
\ No newline at end of file |