# Models with another gauge group at the SUSY scale

## Important Note

This functionality was replaced in SARAH 4.9.0 by the new option

`DEFINITION[MatchingConditions]`

see Matching to the SM in SPheno.

## General

Some SUSY models have the distinct feature that they gauge group at the SUSY scale doesn’t consist of *S**U*(3)_{C} × *S**U*(2)_{L} × *U*(1)_{Y}. This is for instance the case in left-right models in which *U*(1)_{R} × *U*(1)_{B − L} is just broken around the SUSY scale (see e.g. Ref. and references therein). This special feature has to be taken into account in some calculations. For instance, the calculation of the running couplings at the EW scale assumes that the hypercharge is present.
Therefore, SARAH has to create in this kind of models an auxiliary variable for the hypercharge coupling called gYaux. This is done by adding

`AuxiliaryHyperchargeCoupling = True;`

in SPheno.m. In addition, the user has to define a relation between the existing gauge couplings and the hypercharge coupling. For instance, in the model mentioned above, this relation reads

`ExpressionAuxHypercharge =Sqrt[(gBL*gR - gBLgR*gRgBL)^2/((gBLgR - gR)^2 + (gBL - gRgBL)^2)];`

Note, if kinetic mixing is neglected, this reduces to the more familiar form of `\sqrt{g^2_{BL} g_R/(g_R^2 + g_{BL}^2)}`

. When setting the boundary conditions to relate the gauge couplings, one has to make sure that always the relations for the not GUT-normalized values are used. For instance,

```
BoundaryEWSBScale = {
{gYauxt, Sqrt[5/3]*gYaux},
{gR, g1RBLFactor*gYauxt},
{gRgBLt, 1*gRgBL},
{gBLgRt, Sqrt[2/3]*gBLgR},
{gBLt, (5 gBLgRt gR gRgBLt - Sqrt[6] gRgBLt gYauxt^2
+ Sqrt[(3 gBLgRt^2 - 2 Sqrt[6] gBLgRt gR + 2 gR^2) *
(5 (gR^2 + gRgBLt^2) - 3 gYauxt^2) gYauxt^2])/(5 gR^2 - 3 gYauxt^2)},
{gBL, Sqrt[3/2]*gBLt},
{TanBetaR, TanBetaRinput},
{vChiR, vR*TanBetaR/Sqrt[1 + TanBetaR^2]},
{vChiRb, vR*1/Sqrt[1 + TanBetaR^2]}};
```

Here, g1RBLFactor is the ratio of *g*_{R}/*g*_{Y}^{aux} which has been calculated in the iteration before

```
BoundaryEWSBScaleRunningDown = {
{gBLt, gBL*Sqrt[2/3]},
{gRgBLt, 1*gRgBL},
{gBLgRt, Sqrt[2/3]*gBLgR},
{gYaux, Sqrt[5*(gBLt*gR - gBLgRt*gRgBLt)^2/(3*(gBLt^2 + gBLgRt^2)
+ 2*(gR^2 + gRgBLt^2) - 2*Sqrt[6]*(gR*gBLgRt + gBLt*gRgBLt))]},
{g1RBLFactor, gR/gYaux},
{gYaux, Sqrt[3/5]*gYaux}
};
```