On the Unification of Couplings in the Minimal Supersymmetric Standard Model

TL;DR

This study analyzes gauge and Yukawa coupling unification in the MSSM at two loops, introducing the effective threshold scale $T_{SUSY}$ to parametrize SUSY-breaking corrections to gauge couplings. It derives an explicit form for $T_{SUSY}$ in terms of sparticle masses and demonstrates its dominant sensitivity to Higgsino and gaugino sectors, while showing a milder dependence on squarks and sleptons. The work connects unification conditions to the top Yukawa sector, infrared fixed-point behavior, and perturbativity bounds, yielding constraints on the sparticle spectrum and predictions for $M_t$ and $m_h$ as functions of $ aneta$ and threshold parameters. It also highlights correlations between $ ext{α}_3(M_Z)$, $T_{SUSY}$, and Yukawa couplings, with implications for experimental tests and future refinements including high-scale threshold corrections.

Abstract

The unification of gauge and Yukawa couplings within the minimal supersymmetric standard model is studied at the two loop level. We derive an expression for the effective scale, $T_{SUSY}$, which characterizes the supersymmetric particle threshold corrections to the gauge couplings, and demonstrate that $T_{SUSY}$ is only slightly dependent on the squark and slepton masses, and strongly dependent on the Higgsino masses as well as on the mass ratio of the gauginos of the strong and weak interactions. Moreover, the value of the top quark Yukawa coupling necessary to achieve the unification of bottom and tau Yukawa couplings is also governed by $T_{SUSY}$, and it yields predictions for the top quark mass which are close to the quasi infrared fixed point results associated with the triviality bounds on this quantity. From the requirement of perturbative consistency of the top quark Yukawa sector of the theory, we obtain constraints on the allowed splitting of the supersymmetric spectrum, which, for certain values of the running bottom quark mass, are stronger than those ones coming from the experimental constraints on the strong gauge coupling.