Leptoquark on P→ℓ+ν, FCNC and LFV

Motivated by the disagreement between the experimental data and lattice calculations on the decay constant of the Ds meson, we investigate leptoquark (LQ) contributions to the purely leptonic decays of a pseudoscalar (P). We concentrate on the LQs which only couple to the second-generation quarks before the electroweak symmetry breaking and we discuss in detail how flavor symmetry breaking effects are brought into the extension of the Standard Model after the spontaneous symmetry breaking. We show that the assumption of the hermiticity for the fermion mass matrices cannot only reproduce the correct Cabibbo-Kobayashi-Maskawa and Maki-Nakagawa-Sakata matrices, but also reduce the number of independent flavor mixing matrices and lead to VfR=VfL with L (R) denoting the chirality of the f-type fermion. Accordingly, it is found that the decays Ds,d→ℓ+ν, B+→τ+ν and Bc→ℓ+ν have a strong correlation in parameters. We predict that the decay constant of the Bc meson calculated by the lattice could be less than the experimental data by 23%. Intriguingly, the resultant upper limits of branching ratios for D→μ+μ− and τ→μ(π0,η,η′,ρ,ω) are found to be around 5.1×10−7 and (2.6,1.5,0.6,7.4,4.8)×10−8, which are below and close to the current experimental upper bounds, respectively.