Is "just-so" Higgs splitting needed for t-b-τ Yukawa unified SUSY GUTs?
Abstract
Recent renormalization group calculations of the sparticle mass spectrum in the Minimal Supersymmetric Standard Model (MSSM) show that t-b-τ Yukawa coupling unification at M 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 GUT, dubbed "just-so Higgs splitting" (HS) in the literature, which apparently violates the SO(10) gauge symmetry. Here, we investigate three alternative effects: i). SO(10) D-term splitting, ii). inclusion of right hand neutrino in the RG calculation, and iii). first/third generation scalar mass splitting. By combining all three effects (the DR3 model), we find t-b-τ Yukawa unification at M 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.