Using_SPheno_for_two loop_masses

Using SPheno for two-loop masses

SARAH automatically writes the necessary Fortran routines in the SPhenooutput to calculate the two-loop Higgs corrections. There are five flags which can be used in the Les Houches input file to adjust the properties of the two-loop calculation

Block SPhenoInput #
...
  7  ... # Skip two loop masses
  8  ... # Choose two-loop method
  9  ... # Gaugeless limit
 10  ... # Safe mode
...      #
400  ... # Step-size for purely-numerical method
401  ... # Step-size for semi-analytical method

The following values are possible:

SPhenoInput[7]:
- 0: Don’t skip two-loop masses
- 1: Skip two-loop masses
SPhenoInput[8]:
- 1: Effective potential two-loop calculation with purely numerical derivation
- 2: Effective potential two-loop calculation with analytical derivation of loop functions
- 3: Diagrammatic two-loop calculation functions (default)
- 9: Use hardcoded routines available for some models
SPhenoInput[9]:
- 0: Turn off gauge-less limit
- 1: Use gauge-less limit (default)
SPhenoInput[10]:
- 0: Turn off the safe-mode (default)
- 1: Use safe-mode
SPhenoInput[400]: a real number (default: 0.5)
SPhenoInput[401]: a real number (default: 0.001)

Note that the hard-coded two-loop routines are not included by default in the SPhenooutput of SARAH. To include them, in the SPheno.m file the flag

Use2LoopFromLiterature = True;

has to be set.

The flags SPhenoInput[400] and SPhenoInput[401] can be used to check numerical stability of the derivation. If the step size is choosen to be too small or large the numerical derivation might suffer from some instabilites. We found that the initial step size for derivation with the fully numerical method usually needs a larger initial step-size for the considered VEV especially for heavy SUSY spectra. The reason is that the potential is of O(M_SUS**Y⁴) and the overall value only changes slightly when the VEVs are varied. The second method usually operates acceptably with a smaller initial step size because objects of at most order O(M_SUS**Y², M_Z²) are derived numerically. In addition, we make the approximation that in the purely numerical approach mass squareds in the loop which are smaller than 10⁻⁵ times the largest mass squared in the loop is taken to be zero. For the semi-analytical approach we take a limit of 10⁻⁸.

Safe-Mode and beyond

For the effective potential calculation, there is a “safe mode” for SPheno via flag 10: in this case SPhenostarts with a large initial step size which is decreased automatically. It checks for what range of the initial step size the results are numerically stable by comparing the results obtained with different inital step sizes. If no stable range is found an error is returned. In the unlikely case that both methods suffer from numerical instabilities the chances are good that the diagrammatic works. Another, less recommended, possibility is to increase the numerical precision by passing from double to quadruple precision. For this purpose, the Makefile located in SPheno-3.3.0/src must be changed. The line

PreDef = -DGENERATIONMIXING  -DONLYDOUBLE

should be replaced by

PreDef = -DGENERATIONMIXING  -DQUADRUPOLE

Afterwards the entire SPhenocode must be recompiled via

 make cleanall
 make Model=$MODEL

This will slow down the numerical evaluation significantly. However, have not found an example for resonable SUSY masses where this was necessary.

GitLab