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Sparticle mass spectra from SU(5) SUSY GUT models with $b-τ$ Yukawa coupling unification

Supersymmetric grand unified models based on the gauge group SU(5) often require in addition to gauge coupling unification, the unification of b-quark and $τ$-lepton Yukawa couplings. We examine SU(5) SUSY GUT parameter space under the condition of $b-τ$ Yukawa coupling unification using 2-loop MSSM RGEs including full 1-loop threshold effects. The Yukawa-unified solutions break down into two classes. Solutions with low tanβ~3-11 are characterized by gluino mass ~1-4 TeV and squark mass ~1-5 TeV. Many of these solutions would be beyond LHC reach, although they contain a light Higgs scalar with mass <123 GeV and so may be excluded should the LHC Higgs hint persist. The second class of solutions occurs at large tanβ~35-60, and are a subset of $t-b-τ$ unified solutions. Constraining only $b-τ$ unification to ~5% favors a rather light gluino with mass ~0.5-2 TeV, which should ultimately be accessible to LHC searches. While our $b-τ$ unified solutions can be consistent with a picture of neutralino-only cold dark matter, invoking additional moduli or Peccei-Quinn superfields can allow for all of our Yukawa-unified solutions to be consistent with the measured dark matter abundance.