Gauge fixing
As explained in app. [GaugeFixing], the general form of a gauge fixing term in R_{ξ}gauge is
\mathscr{L}_{GF} =  \frac{1}{2 R_\xi} \sum_a f^a^2
with some gauge fixing functions f^{a}.
Implementation in SARAH
If ghost vertices were to be calculated by SARAH 3.1 or earlier versions, it has been necessary to define the gauge fixing terms in R_{ξ} gauge. However, since version 3.2 SARAH derives these terms automatically using the calculated kinetic terms of the Lagrangian. To this end, the condition is applied that the mixing between scalar particles and vector bosons vanishes. Afterwards, the derived gauge fixing terms are used to calculate the ghost interactions. Since it can happen in models with an extended gauge sector that several Goldstone bosons are a mixture of the same gauge eigenstate, for each massive vector boson, the corresponding Goldstone boson has to be defined
{{ Description > "ZBoson",
...
Goldstone > Ah[{1}]}},
...
{{ Description > "Z'Boson",
...
Goldstone > Ah[{2}]}},
The user can check the gauge fixing terms derived by SARAH be looking at
DEFINITION[$EIGENSTATES][GeneratedGaugeFixing]
The general form of the gauge fixing term is:
DEFINITION[$EIGENSTATES][GeneratedGaugeFixing] = {{Function, Prefactor}, ... };
Here, Function
is the f of eq. ([gfstructure]), and the corresponding factor is Prefactor
. If the gauge fixing functions involve derivatives of gauge bosons,
Der["Gauge Boson"]
is used.
Examples

The gauge fixing term for the color group in R_{ξ} gauge is: $\mathscr{L}{GF} =  \frac{1}{2 \xi_g} \partial\mu g ^2$
The corresponding expression in SARAH reads
DEFINITION[GaugeES][GeneratedGaugeFixing]= {{Der[VG], 1/(2 RXi[G])},...};

The gauge fixing term corresponding to the ZBoson after EWSB is (see app. [GFewsb]). $\mathscr{L}{GF} =  \frac{1}{2 \xi_Z} \left( \partial^\mu Z\mu + \xi_Z M_Z G^0 \right)^2$
The corresponding Goldstone boson is in SARAH the first generation of the CPOdd Higgs. Therefore, the gauge fixing term obtained by SARAH are
DEFINITION[EWSB][GeneratedGaugeFixing]= {(2*Der[VZ]  (sigmad*vd  sigmau*vu)*RXi[Z]* (g1*ZZ[1, 2]  g2*ZZ[2, 2]))/2, 1/(2*RXi[Z])}
Here, ZZ is the γ − Z mixing matrices which can be expressed by the Weinberg angle. Therefore, this expression is equivalent to the input used in older version of SARAH
DEFINITION[EWSB][GaugeFixing]= {{Der[VZ] + Mass[VZ] RXi[Z] Ah[{1}],  1/(2 RXi[Z])},...};