Particle-antiparticle mixing, CP violation and rare K and B decays in a minimal theory of fermion masses

We present a detailed study of ∆F = 2 observables and of rare K⁺(K_L) and B_s,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^±, Z₀ and Higgs so that FCNC processes receive contributions from tree level Z⁰ and Higgs exchanges and W ^± bosons couple to right-handed quarks. In a particular version of this model in which the Yukawa matrix λ^D in the heavy down fermion sector is unitary, λ^U = 1 and M = M_VF is fixed, only three real and positive definite parameters describe New Physics (NP) contributions to all ∆F = 2 and ∆F = 1 observables in K and B_s,d systems once the known quark masses and the CKM matrix are correctly reproduced. For M ≥ 1 TeV NP contributions to (Formula presented.) mixings are found to be very small. While in principle NP contributions to εK and ∆F = 1 processes could be large, the correlation between εK and K_L → µ⁺ µ⁻ eliminates basically NP contributions to εK and right-handed current contributions to ∆F = 1 FCNC observables. We find CMFV structure in Bs,d decays with (Formula presented.) uniquely enhanced for M = 3 TeV by at least 35% and almost up to a factor of two over their SM values. Also (Formula presented.) and (Formula presented.) are uniquely enhanced by similar amount but the correlation between them differs from the CMFV one. We emphasize various correlations between K and B_s,d decays that could test this scenario. The model favours γ ≈ 68°, |V_ub| ≈ 0.0037, S_ψKS ≈ 0.72, S_ψφ ≈ 0.04 and (formula presented.) for M = 3 − 4 TeV.