Large |Vub|: A challenge for the Minimal Flavour Violating MSSM

Under the assumption of Minimal Flavour Violation (MFV), the Unitarity Triangle (UT) can be determined by using only angle measurements and tree-level observables. In this respect, the most accurate quantities today available are sin 2 beta_{psi Ks}, |Vcb| and |Vub|. Among the latter, |Vub| is at present the quantity suffering from largest systematic uncertainties, given the discrepancy between the inclusive and the exclusive determinations. We show with a numerical fit how sensitively the MFV-UT determination depends on the choice of |Vub|. In addition, we focus on the implications of the inclusive value for |Vub|, which favors two non-SM like solutions in the rhobar - etabar plane. We study in detail the possibility of reproducing such solutions within the MFV MSSM. Our findings indicate that the case for the MFV MSSM is in this respect quite problematic, unless the non-perturbative parameters xi and BK are significantly different from those obtained by lattice methods. As a byproduct, we point out that scenarios with 200 GeV <~ MA <~ 500 GeV and tan beta =~ 50 that predict a significant suppression for Delta Ms in correlation with an enhancement for BR(Bs --> mu^+ mu^-) have to be fine-tuned in order not to violate the new combined bound on the latter decay mode from the CDF and D0 collaborations. Relatively large correlated effects can however still occur for negative values of mu and large values for MA >~ 500 GeV, increasing with increasing tan beta >~ 30.