SUSY GUTs with Yukawa unification: A go/no-go study using FCNC processes

We address the viability of exact Yukawa unification in the context of general SUSY GUTs with universal soft-breaking sfermion and gaugino mass terms at the GUT scale. We find that this possibility is challenged, unless the squark spectrum is pushed well above the limits allowed by naturalness. This conclusion is assessed through a global fit using electroweak observables and quark flavour-changing neutral current (FCNC) processes. The problem is mostly the impossibility of accommodating simultaneously the bottom mass and the BR(B→Xsγ)BR(B→Xsγ), after the stringent CDF upper bound on the decay Bs→μ+μ−Bs→μ+μ− is taken into account, and under the basic assumption that the b→sγb→sγ amplitude have like sign with respect to the Standard Model one, as indicated by the B→Xsℓ+ℓ−B→Xsℓ+ℓ− data.With the same strategy, we also consider the possibility of relaxing Yukawa unification to b−τb−τ Yukawa unification. We find that with small departures from the condition tanβ≃50tanβ≃50, holding when Yukawa unification is exact, the mentioned tension is substantially relieved. We emphasize that in the region where fits are successful the lightest part of the SUSY spectrum is basically fixed by the requirements of b−τb−τ unification and the applied FCNC constraints. As such, it is easily falsifiable once the LHC turns on.