Dark matter allowed scenarios for Yukawa-unified SO(10) SUSY GUTs
  Simple supersymmetric grand unified models based on the gauge group SO(10) require --in addition to gauge and matter unification-- the unification of t-b-\tau Yukawa couplings. Yukawa unification, however, only occurs for very special values of the soft SUSY breaking parameters. We perform a search using a Markov Chain Monte Carlo (MCMC) technique to investigate model parameters and sparticle mass spectra which occur in Yukawa-unified SUSY models, where we also require the relic density of neutralino dark matter to saturate the WMAP-measured abundance. We find the spectrum is characterizd by three mass scales: first/second generation scalars in the multi-TeV range, third generation scalars in the TeV range, and gauginos in the \sim 100 GeV range. Most solutions give far too high a relic abundance of neutralino dark matter. The dark matter discrepancy can be rectified by 1. allowing for neutralino decay to axino plus photon, 2. imposing gaugino mass non-universality or 3. imposing generational non-universality. In addition, the MCMC approach finds 4. a compromise solution where scalar masses are not too heavy, and where neutralino annihilation occurs via the light Higgs h resonance. By imposing weak scale Higgs soft term boundary conditions, we are also able to generate 5. low \mu, m_A solutions with neutralino annihilation via a light A resonance, though these solutions seem to be excluded by CDF/D0 measurements of the B_s\to \mu^+\mu^- branching fraction. Based on the dual requirements of Yukawa coupling unification and dark matter relic density, we predict new physics signals at the LHC from pair production of 350--450 GeV gluinos. The events are characterized by very high b-jet multiplicity and a dilepton mass edge around mz2-mz1 \sim 50-75 GeV. 
Howard Baer, Sabine Kraml, Sezen Sekmen and Heaya Summy