





title: Boundary conditions in SPheno



permalink: /Boundary_conditions_in_SPheno/










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






Sets of Boundary conditions










For a [highscale SPheno version](/Low_or_High_scale_SPheno_version "wikilink") it is possible to define boundary conditions at three different scales:






 **Electroweak scale (*M*<sub>*Z*</sub>)**: `BoundaryEWSBScale`



 **Renormalisation (or SUSY) scale**: `BoundaryRenScale` / `BoundarySUSYScale`



</li>



(both are equivalent and it is a matter of taste what to use)






 **GUT scale**: `BoundaryHighScale`






Check the definition of the [the renormalisation scale](/The_renormalisation_scale_in_SPheno "wikilink") and the [GUT scale](/GUT_scale_condition_in_SPheno "wikilink"). In general, all these conditions are applied when running up and down with RGEs. In contrast, there is also the possibility to define a boundary condition at the EW scale which is only applied when running down from the Renormalisation/SUSY scale:






BoundaryEWSBScaleRunningDown = ...






For cases not using a RGE running up to the high scale the boundary conditions are set via






 `BoundaryLowScaleInput`






Moreover, if thresholds are present, boundary conditions can be set at the threshold scale via






 `BoundaryConditionsUp`



 `BoundaryConditionsDown`






See also [Models with Thresholds in SPheno](/Models_with_Thresholds_in_SPheno "wikilink")






Format of the boundary conditions










All boundaries conditions are defined by a two dimensional array. The first entry is the name of the parameter, the second entry is the used condition at the considered scale:






BoundaryXYZ = {



{Parameter1,Condition1},



{Parameter2,Condition2},



...



}






The condition can be






 …an input parameter from `MODSEL` or `EXTPAR`, e.g.



{MassB, m12};






 …a block in the SLHA input file, e.g.



{Yv, LHInput[Yv]};






 …a function of different parameters, e.g.



{TYd, Azero*Yd};






 …a diagonal matrix by using the keyword `DIAGONAL`, e.g.



{md2, DIAGONAL m0^2};






 …matrix multiplications or the inverse of a matrix, e.g.



{X, MatMul2[A,InverseMatrix[B], FortranFalse]};






Note, for the matrix multiplication `MatMul2` has to be used. The third argument controls whether if only diagonal elements (`FortranTrue`) should be considered or not (`FortranFalse`).






 …a self defined function



{X, Func[A,B,C]};









It is also possible to use some self defined function. The Fortran code of that function has to included in the array <span>SelfDefinedFunctions</span> in <span>SPheno.m</span>. It will later on be written to <span>Model_Data.f90</span>. Note, that the standard functions needed for GMSB are already included :






 <span>fGMSB\[X\]</span>:



$\\begin{aligned}



\\nonumber f(x) &=& \\frac{1+x}{x^2} \\left(\\ln(1+x)  2 \\text{Li}_2(\\frac{x}{1+x})



+ \\frac{1}{2} \\text{Li}_2(2 \\frac{x}{1+x}) \\right) + \\\\



&& \\frac{1x}{x^2} \\left(\\ln(1x)  2 \\text{Li}_2(\\frac{x}{x1}) + \\frac{1}{2}



\\text{Li}_2 (2 \\frac{x}{x1})\\right)\\end{aligned}$






 <span>gGMSB\[X\]</span>:



$g(x) = \\frac{1+x}{x^2} \\ln(1+x) + \\frac{1x}{x^2} \\ln(1x)$






Example










The GUT conditions in the CMSSM are






BoundaryHighScale={



{T[Ye], Azero*Ye},



{T[Yd], Azero*Yd},



{T[Yu], Azero*Yu},



{mq2, DIAGONAL m0^2},



{ml2, DIAGONAL m0^2},



{md2, DIAGONAL m0^2},



{mu2, DIAGONAL m0^2},



{me2, DIAGONAL m0^2},



{mHd2, m0^2},



{mHu2, m0^2},



{MassB, m12},



{MassWB, m12},



{MassG, m12}



};






Several sets of boundary conditions










In order to implement different versions of a single model which differ only by the used boundary conditions, <span>BoundaryEWSBScale</span>, <span>BoundarySUSYScale</span>, <span>BoundaryHighScale</span> can be also a nested list, e.g.






BoundarySUSYScale = Table[{},{2}];



BoundaryGUTScale = Table[{},{2}];






BoundarySUSYScale[[/11]] = {{KappaNMSSM, KappaInput},



{LambdaNMSSM, LambdaInput}};



BoundaryGUTScale[[/11]] = {};






BoundarySUSYScale[[/22]] = {};



BoundaryGUTScale[[/22]] = {{KappaNMSSM, KappaInput},



{LambdaNMSSM, LambdaInput}};






In the first case, the input values for *λ* and *κ* are used at the SUSY scale, in the second on at the GUT scale. To communicate to SPheno which set of boundary conditions should be used for a run, flag 2 in <span>MODSEL</span> is used:






Block MODSEL #



2 X # This uses the X. set of boundary conditions.






The default value is 1.






Overwriting boundary conditions when running SPheno










Boundary conditions can be overridden by assigning a value to a parameter in the Les Houches input file. For this purpose, the output block with an additional suffix `IN` is used.






#### Example






1. The bino mass in the CMSSM should be not identical to *M*<sub>1/2</sub> at the GUT scale, but fixed to 100 GeV:



Block MSOFTIN #



1 100. # M1 (GUT)






2. The matrix for the softmasses squared for the rightup squarks shall have a different entry for the (3,3) element:



Block MSU2 #



1 1 1.00E6 # Mu2(1,1)



2 2 1.00E6 # Mu2(2,2)



3 3 2.00E5 # Mu2(3,3)






Note, in the same way one could add flavour violating entries at the GUT scale.






See also



 


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