Particle-Antiparticle Mixing, CP Violation and Rare K and B Decays in a Minimal Theory of Fermion Masses

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We present a detailed study of Delta F=2 observables and of rare K+(Kₗ) and Bₛ,d meson decays in a "Minimal Theory of Fermion Masses" (MTFM). In this theory Yukawa couplings are generated through the mixing with heavy vectorlike (VF) fermions. This implies corrections to the SM quark couplings to W, Z and Higgs so that FCNC processes receive contributions from tree level Z and Higgs exchanges and W bosons couple to right-handed quarks. In a particular version of this model in which the Yukawa matrix lambdaᵈ in the heavy down fermion sector is unitary, lambdaᵘ =1 and M = MVF is fixed, only three real and positive definite parameters describe New Physics (NP) contributions to all Delta F=2 and Delta F=1 observables in K and Bₛ,d systems once the known quark masses and the CKM matrix are correctly reproduced. For M>1 TeV NP contributions to Bₛ,d⁰- barBₛ,d⁰ mixings are found to be very small. While in principle NP contributions to epsilonₖ and Delta F=1 processes could be large, the correlation between epsilonₖ and Kₗ->mu+ mu- eliminates basically NP contributions to epsilonₖ and right-handed current contributions to Delta F=1 FCNC observables. We find CMFV structure in Bₛ,d decays with BR(Bₛ,d->mu+ mu-) uniquely enhanced for M=3 TeV by at least 35% and almost up to a factor of two over their SM values. Also BR(K+->pi+ barnu nu) and BR(Kₗ->pi⁰ barnu nu) are uniquely enhanced by similar amount but the correlation between them differs from the CMFV one. We emphasize various correlations between K and Bₛ,d decays that could test this scenario. The model favours gamma=68°, |Vub|=0.0037, Spsi Kₛ=0.72, Spsi phi=0.04 and 4.2*10-9<BR(Bₛ->mu+ mu-)<5.0*10-9 for M=3-4 TeV.