Abstract
We present a detailed study of ΔF = 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 ±, Z 0 and Higgs so that FCNC processes receive contributions from tree level Z 0 and Higgs exchanges and W ± bosons couple to right-handed quarks. In a particular version of this model in which the Yukawa matrix λD in the heavy down fermion sector is unitary, λU = and M = M VF is fixed, only three real and positive definite parameters describe New Physics (NP) contributions to all ΔF = 2 and ΔF = 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 \( B_{s,d}^0-\overline{B}_{s,d}^0 \) mixings are found to be very small. While in principle NP contributions to ε K and ΔF = 1 processes could be large, the correlation between ε K and K L → μ + μ − eliminates basically NP contributions to ε K and right-handed current contributions to ΔF = 1 FCNC observables. We find CMFV structure in B s,d decays with \( \mathcal{B}\left( {{B_{s,d }}\to {\mu^{+}}{\mu^{-}}} \right) \) uniquely enhanced for M = 3 TeV by at least 35% and almost up to a factor of two over their SM values. Also \( \mathcal{B}\left( {{K^{+}}\to {\pi^{+}}\nu \overline{\nu}} \right) \) and \( \mathcal{B}\left( {{K_L}\to {\pi^0}\nu \overline{\nu}} \right) \) 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, \( {S_{{\psi {K_S}}}} \) ≈ 0.72, S ψϕ ≈ 0.04 and 4.2 × 10−9 ≤ \( \mathcal{B}\left( {{B_s}\to {\mu^{+}}{\mu^{-}}} \right) \) ≤ 5.0 × 10−9 for M = 3 − 4 TeV.
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Buras, A.J., Girrbach, J. & Ziegler, R. Particle-antiparticle mixing, CP violation and rare K and B decays in a minimal theory of fermion masses. J. High Energ. Phys. 2013, 168 (2013). https://doi.org/10.1007/JHEP04(2013)168
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DOI: https://doi.org/10.1007/JHEP04(2013)168