The Top Quark Mass in Supersymmetric SO(10) Unification

TL;DR

The paper provides a precise top-quark mass prediction within supersymmetric SO(10) unification by enforcing Yukawa unification for the third generation and placing both light Higgs doublets in a single SO(10) multiplet. It develops a two-loop RGE framework with careful threshold matching, analyzes large tanβ effects and potential mb corrections, and demonstrates that a hierarchical SUSY spectrum yields a robust mt prediction in the 170–190 GeV range with small theoretical uncertainties. The approach highlights the interplay between GUT boundary conditions, MSSM running, and radiative corrections, showing that generic GUT thresholds shift mt only modestly unless δmb is sizeable. Extensions to Higgs mixing and higher-generation effects are discussed, indicating the core mt prediction remains tightly constrained under plausible model variations. Overall, the work connects high-scale Yukawa unification to a concrete, testable top-mass prediction in a concrete SUSY GUT framework.

Abstract

The successful prediction of $\sin^2θ_W$ suggests that the effective theory beneath the GUT scale is the two-Higgs MSSM. If we further assume that the unified gauge group contains SO(10), that the two light Higgs doublets lie mostly in a single irreducible SO(10) representation, and that the $t$, $b$ and $τ$ masses originate in renormalizable Yukawa interactions of the form $16_3 O 16_3$, then also the top quark mass can be predicted in terms of the MSSM parameters. To compute $m_t$ we present a precise analytic approximation to the solution of the 2-loop renormalization group equations, and study supersymmetric and GUT threshold corrections and the input value of the $b$ quark mass. The large ratio of top to bottom quark masses derives from a large ratio, $\tanβ$, of Higgs vacuum expectation values. We point out that when $\tanβ$ is large, so are certain corrections to the $b$ quark mass prediction, unless a particular hierarchy exists in the parameters of the model. With such a hierarchy, which may result from approximate symmetries, the top mass prediction depends only weakly on the spectrum. Our results may be applied to any supersymmetric SO(10)-like model as long as $λ_t\simeq λ_b\simeqλ_τ$ at the GUT scale and there are no intermediate mass scales in the desert.