Is "just-so" Higgs splitting needed for t-b-\tau Yukawa unified SUSY GUTs?

TL;DR

This paper explores alternative mechanisms to achieve t-b- au Yukawa unification in SUSY GUTs without requiring the problematic 'just-so' Higgs splitting, by combining D-term splitting, right-handed neutrinos, and scalar mass splitting.

Contribution

The study demonstrates that combining D-term splitting, right-handed neutrinos, and third-generation scalar mass splitting can achieve Yukawa unification at M_GUT without violating SO(10) symmetry.

Findings

Yukawa unification achieved at 2.5% level with combined effects

Lighter third-generation and heavy Higgs scalars predicted

Right-handed bottom squark dominance in DR3 model

Abstract

Recent renormalization group calculations of the sparticle mass spectrum in the Minimal Supersymmetric Standard Model (MSSM) show that t-b-\tau Yukawa coupling unification at M_{\rm GUT} is possible when the mass spectra follow the pattern of a radiatively induced inverted scalar mass hierarchy. The calculation is entirely consistent with expectations from SO(10) SUSY GUT theories, with one exception: it seems to require MSSM Higgs soft term mass splitting at M_{\rm GUT}, dubbed "just-so Higgs splitting" (HS) in the literature, which apparently violates the SO(10) gauge symmetry. Here, we investigate three alternative effects: {\it i}). SO(10) D-term splitting, {\it ii}). inclusion of right hand neutrino in the RG calculation, and {\it iii}). first/third generation scalar mass splitting. By combining all three effects (the DR3 model), we find t-b-\tau Yukawa unification at M_{\rm GUT} can be achieved at the 2.5% level. In the DR3 case, we expect lighter (and possibly detectable) third generation and heavy Higgs scalars than in the model with HS. In addition, the light bottom squark in DR3 should be dominantly a right state, while in the HS model, it is dominantly a left state.