Yukawa coupling unification in supersymmetric models

Abstract

We present an updated assessment of the viability of t-b-tau Yukawa coupling unification in supersymmetric models. For the superpotential Higgs mass parameter mu>0, we find unification to less than 1% is possible, but only for GUT scale scalar mass parameter m_{16}~8-20 TeV, and small values of gaugino mass m_{1/2}<400 GeV. Such models require that a GUT scale mass splitting exists amongst Higgs scalars with m_{H_u}^2<m_{H_d}^2. Viable solutions lead to a radiatively generated inverted scalar mass hierarchy, with third generation and Higgs scalars being lighter than other sfermions. These models have very heavy sfermions, so that unwanted flavor changing and CP violating SUSY processes are suppressed, but may suffer from some fine-tuning requirements. While the generated spectra satisfy b->s gamma and (g-2)_mu constraints, there exists tension with the dark matter relic density unless m_{16}<3 TeV. These models offer prospects for a SUSY discovery at the Fermilab Tevatron collider via the search for chargino_1 neutralino_2 -> 3 leptons events, or via gluino pair production. If mu<0, Yukawa coupling unification to less than 5% can occur for m_{16} and m_{1/2}>1-2 TeV. Consistency of negative mu Yukawa unified models with b->s gamma, (g-2)_mu, and relic density all imply very large values of m_{1/2} typically greater than about 2.5 TeV, in which case direct detection of sparticles may be a challenge even at the LHC.