







title: Models with another gauge group at the SUSY scale




permalink: /Models_with_another_gauge_group_at_the_SUSY_scale/













[Category:SPheno](/Category:SPheno "wikilink")








Important Note













This functionality was replaced in SARAH 4.9.0 by the new option








DEFINITION[MatchingConditions]








see [Matching to the SM in SPheno](/Matching_to_the_SM_in_SPheno "wikilink").








General













Some SUSY models have the distinct feature that they gauge group at the SUSY scale doesn’t consist of *S**U*(3)<sub>*C*</sub> × *S**U*(2)<sub>*L*</sub> × *U*(1)<sub>*Y*</sub>. This is for instance the case in leftright models in which *U*(1)<sub>*R*</sub> × *U*(1)<sub>*B* − *L*</sub> 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 <span>gYaux</span>. This is done by adding








AuxiliaryHyperchargeCoupling = True;








in <span>SPheno.m</span>. 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 GUTnormalized 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, <span>g1RBLFactor</span> is the ratio of *g*<sub>*R*</sub>/*g*<sub>*Y*</sub><sup>*a**u**x*</sup> 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}




};








See also




 



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