The_renormalisation_scale_in_SPheno

The renormalisation scale in SPheno

General

The renormalisation scale at which SPheno performs the loop calculations to the mass spectrum can be defined in SPheno.m via

RenormalizationScale=...

As argument either a fixed value can be given or a function of parameters of the considered model or of calculated tree-level masses. In addition, if a high-scale SPheno version is considered, an approximative scale must be given via

RenormalizationScaleFirstGuess=...

This choice for the scale is used only in the first iteration.

Example

In the MSSM, it is common to use the mean of the stop masses are scale. If one can be sure that the two stops are the lightest and heaviest of the six up squarks are, the brief definition RenormalizationScale = MSu[1]*MSu[6];

is possible. For the general case, the long form
```
RenormalizationScale = Sqrt[(mq2[3, 3] + (vu^2*conj[Yu[3, 3]]*Yu[3, 3])/2)*(mu2[3, 3] + (vu^2*conj[Yu[3, 3]]*Yu[3, 3])/2)
-((vd*\[Mu]*conj[Yu[3, 3]] - vu*conj[T[Yu][3, 3]])*(vd*conj[\[Mu]]*Yu[3, 3] - vu*T[Yu][3, 3]))/2];
```
is the safe choice.
For a first evaluation of the RGEs, before any mass has been calculated and SPheno hasn’t any glue about the renormalization scale, an approximated scale as function of the CMSSM parameters can be defined via RenormalizationScaleFirstGuess = m0^2 + 4 m12^2;

Fixing the scale via the Les Houches file

Independent of the settings for RenormalizationScale there are two possibilities to fix the scale via the Les Houches input file of SPheno

SPA conventions: If SPA conventions are turned on via Block SPhenoInput # SPheno specific input ... 2 0 # SPA conventions

the scale is always put to 1 TeV.
Fixed value: One can fix the numerical value of the renormalisation scale via Block MODSEL # ... 12 VALUE # Renormalisation scale

where VALUE is an integer or real.

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