Bottom-Tau Unification in Supersymmetric Model with Anomaly-Mediation

TL;DR

This paper investigates the unification of bottom and tau Yukawa couplings within a supersymmetric model featuring anomaly-mediated gaugino masses and gravitino-scale scalar masses, emphasizing precise RG calculations and threshold effects.

Contribution

It provides a detailed analysis of Yukawa unification in a specific SUSY framework, including RG effects and threshold corrections, highlighting conditions for unification.

Findings

Bottom Yukawa at GUT scale is about 70% of tau Yukawa without hierarchy.

Sizable threshold corrections are needed for unification.

Results imply possible sfermion mass suppression or threshold effects.

Abstract

We study the Yukawa unification, in particular, the unification of the Yukawa coupling constants of $b$ and $\tau$, in the framework of supersymmetric (SUSY) model. We concentrate on the model in which the SUSY breaking scalar masses are of the order of the gravitino mass while the gaugino masses originate from the effect of anomaly mediation and hence are one-loop suppressed relative to the gravitino mass. We perform an accurate calculation of the Yukawa coupling constants of $b$ and $\tau$ at the grand unified theory (GUT) scale, including relevant renormalization group effects and threshold corrections. In particular, we study the renormalization group effects, taking into account the mass splittings among sfermions, gauginos, and the standard model particles. We found that the Yukawa coupling constant of $b$ at the GUT scale is about $70\ \%$ of that of $\tau$ if there is no hierarchy between the sfermion masses and the gravitino mass. Our results suggest sizable threshold corrections to the Yukawa coupling constants at the GUT scale or significant suppressions of the sfermion masses relative to the gravitino mass.