Higher Order Corrections and Unification in the Minimal Supersymmetric Standard Model: SOFTSUSY3.5.0

TL;DR

This paper investigates the impact of three-loop and leading two-loop threshold corrections on gauge and Yukawa unification in the MSSM, refining predictions for the Higgs mass, dark matter, and collider observables.

Contribution

It introduces higher order corrections into SOFTSUSY, improving the precision of MSSM spectrum calculations and uncertainty estimates compared to previous public tools.

Findings

Higher order corrections alter unification scale couplings by up to 1%.

Theoretical uncertainties in dark matter and collider predictions are significantly affected.

SOFTSUSY now includes these corrections for more accurate MSSM spectrum predictions.

Abstract

We explore the effects of three-loop minimal supersymmetric standard model renormalisation group equation terms and some leading two-loopthreshold corrections on gauge and Yukawa unification: each being one loop higher order than current public spectrum calculators. We also explore the effect of the higher order terms (often 2-3 GeV) on the lightest CP even Higgs mass prediction. We illustrate our results in the constrained minimal supersymmetric standard model. Neglecting threshold corrections at the grand unified scale, the discrepancy between the unification scale $\alpha_s$ and the other two unified gauge couplings changes by 0.1$\%$ due to the higher order corrections and the difference between unification scale bottom-tau Yukawa couplings neglecting unification scale threshold corrections changes by up to 1$\%$. The difference between unification scale bottom and top Yukawa couplings changes by a few percent. Differences due to the higher order corrections also give an estimate of the size of theoretical uncertainties in the minimal supersymmetric standard model spectrum. We use these to provide estimates of theoretical uncertainties in predictions of the dark matter relic density (which can be of order one due to its strong dependence on sparticle masses) and the LHC sparticle production cross-section (often around 30$\%$). The additional higher order corrections have been incorporated into SOFTSUSY, and we provide details on how to compile and use the program. We also provide a summary of the approximations used in the higher order corrections.