Predicting the Sparticle Spectrum from GUTs via SUSY Threshold Corrections with SusyTC

Abstract

Grand Unified Theories (GUTs) can feature predictions for the ratios of quark and lepton Yukawa couplings at high energy, which can be tested with the increasingly precise results for the fermion masses, given at low energies. To perform such tests, the renormalization group (RG) running has to be performed with sufficient accuracy. In supersymmetric (SUSY) theories, the one-loop threshold corrections (TC) are of particular importance and, since they affect the quark-lepton mass relations, link a given GUT flavour model to the sparticle spectrum. To accurately study such predictions, we extend and generalize various formulas in the literature which are needed for a precision analysis of SUSY flavour GUT models. We introduce the new software tool SusyTC, a major extension to the Mathematica package REAP, where these formulas are implemented. SusyTC extends the functionality of REAP by a full inclusion of the (complex) MSSM SUSY sector and a careful calculation of the one-loop SUSY threshold corrections for the full down-type quark, up-type quark and charged lepton Yukawa coupling matrices in the electroweak-unbroken phase. Among other useful features, SusyTC calculates the one-loop corrected pole mass of the charged (or the CP-odd) Higgs boson as well as provides output in SLHA conventions, i.e. the necessary input for external software, e.g. for performing a two-loop Higgs mass calculation. We apply SusyTC to study the predictions for the parameters of the CMSSM (mSUGRA) SUSY scenario from the set of GUT scale Yukawa relations $y_e/y_d=-1/2$, $y_{\mu }/y_s=6$, and $y_{\tau }/y_b=-3/2$, which has been proposed recently in the context of SUSY GUT flavour models.

54 pages, 12 figures. SusyTC can be downloaded from http://particlesandcosmology.unibas.ch/pages/SusyTC.htm

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• Predicting ${\delta }^{\text{PMNS}}$, ${\theta }_{23}^{\text{PMNS}}$ and fermion mass ratios from flavour GUTs with CSD2
• Employing nucleon decay as a fingerprint of SUSY GUT models using \texttt{SusyTCProton}
• Yukawa ratio predictions in non-renormalizable $\mathrm{SO}(10)$ GUT models
• Comparatively Light Extra Higgs States as Signature of SUSY $\mathrm{SO}(10)$ GUTs with 3rd Family Yukawa Unification
• Quark-lepton mass relations from modular flavor symmetry
• The Minimal Supersymmetric Standard Model with Non-Invertible Selection Rules