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---
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title: Boundary conditions in SPheno
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permalink: /Boundary_conditions_in_SPheno/
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---
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[Category:SPheno](/Category:SPheno "wikilink")
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Sets of Boundary conditions
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---------------------------
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For a [high-scale SPheno version](/Low_or_High_scale_SPheno_version "wikilink") it is possible to define boundary conditions at three different scales:
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- **Electroweak scale (*M*<sub>*Z*</sub>)**: `BoundaryEWSBScale`
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- **Renormalisation (or SUSY) scale**: `BoundaryRenScale` / `BoundarySUSYScale`
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</li>
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(both are equivalent and it is a matter of taste what to use)
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- **GUT scale**: `BoundaryHighScale`
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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:
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BoundaryEWSBScaleRunningDown = ...
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For cases not using a RGE running up to the high scale the boundary conditions are set via
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- `BoundaryLowScaleInput`
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Moreover, if thresholds are present, boundary conditions can be set at the threshold scale via
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- `BoundaryConditionsUp`
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- `BoundaryConditionsDown`
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See also [Models with Thresholds in SPheno](/Models_with_Thresholds_in_SPheno "wikilink")
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Format of the boundary conditions
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---------------------------------
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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:
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BoundaryXYZ = {
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{Parameter1,Condition1},
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{Parameter2,Condition2},
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...
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}
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The condition can be
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- …an input parameter from `MODSEL` or `EXTPAR`, e.g.
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{MassB, m12};
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- …a block in the SLHA input file, e.g.
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{Yv, LHInput[Yv]};
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- …a function of different parameters, e.g.
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{TYd, Azero*Yd};
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- …a diagonal matrix by using the keyword `DIAGONAL`, e.g.
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{md2, DIAGONAL m0^2};
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- …matrix multiplications or the inverse of a matrix, e.g.
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{X, MatMul2[A,InverseMatrix[B], FortranFalse]};
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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`).
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- …a self defined function
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{X, Func[A,B,C]};
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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 :
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- <span>fGMSB\[X\]</span>:
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$\\begin{aligned}
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\\nonumber f(x) &=& \\frac{1+x}{x^2} \\left(\\ln(1+x) - 2 \\text{Li}_2(\\frac{x}{1+x})
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+ \\frac{1}{2} \\text{Li}_2(2 \\frac{x}{1+x}) \\right) + \\\\
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&& \\frac{1-x}{x^2} \\left(\\ln(1-x) - 2 \\text{Li}_2(\\frac{x}{x-1}) + \\frac{1}{2}
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\\text{Li}_2 (2 \\frac{x}{x-1})\\right)\\end{aligned}$
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- <span>gGMSB\[X\]</span>:
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$g(x) = \\frac{1+x}{x^2} \\ln(1+x) + \\frac{1-x}{x^2} \\ln(1-x)$
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Example
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-------
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The GUT conditions in the CMSSM are
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BoundaryHighScale={
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{T[Ye], Azero*Ye},
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{T[Yd], Azero*Yd},
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{T[Yu], Azero*Yu},
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{mq2, DIAGONAL m0^2},
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{ml2, DIAGONAL m0^2},
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{md2, DIAGONAL m0^2},
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{mu2, DIAGONAL m0^2},
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{me2, DIAGONAL m0^2},
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{mHd2, m0^2},
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{mHu2, m0^2},
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{MassB, m12},
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{MassWB, m12},
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{MassG, m12}
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};
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Several sets of boundary conditions
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-----------------------------------
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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.
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BoundarySUSYScale = Table[{},{2}];
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BoundaryGUTScale = Table[{},{2}];
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BoundarySUSYScale[[/1|1]] = {{KappaNMSSM, KappaInput},
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{LambdaNMSSM, LambdaInput}};
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BoundaryGUTScale[[/1|1]] = {};
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BoundarySUSYScale[[/2|2]] = {};
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BoundaryGUTScale[[/2|2]] = {{KappaNMSSM, KappaInput},
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{LambdaNMSSM, LambdaInput}};
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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:
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Block MODSEL #
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2 X # This uses the X. set of boundary conditions.
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The default value is 1.
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Overwriting boundary conditions when running SPheno
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---------------------------------------------------
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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.
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#### Example
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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:
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Block MSOFTIN #
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1 100. # M1 (GUT)
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2. The matrix for the soft-masses squared for the right-up squarks shall have a different entry for the (3,3) element:
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Block MSU2 #
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1 1 1.00E6 # Mu2(1,1)
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2 2 1.00E6 # Mu2(2,2)
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3 3 2.00E5 # Mu2(3,3)
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Note, in the same way one could add flavour violating entries at the GUT scale.
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See also
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-------- |
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\ No newline at end of file |