Contribution of vector resonances to the $\bar{B}_{d}^{0}\to\bar {K}^{*0}\mu^{+}\mu^{-}$ decay

Abstract

The fully differential angular distribution for the rare flavor-changing neutral current decay \(\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) \mu^{+}\mu^{-} \) is studied. The emphasis is placed on accurate treatment of the contribution from the processes \(\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) V \) with intermediate vector resonances V=ρ(770),ω(782),ϕ(1020),J/ψ,ψ(2S),… decaying into the μ + μ − pair. The dilepton invariant-mass dependence of the branching ratio, longitudinal polarization fraction f L of the \(\bar{K}^{*0}\) meson, and forward–backward asymmetry A FB is calculated and compared with data from Belle, CDF and LHCb. It is shown that inclusion of the resonance contribution may considerably modify the branching ratio, calculated in the SM without resonances, even in the invariant-mass region far from the so-called charmonia cuts applied in the experimental analyses. This conclusion crucially depends on values of the unknown phases of the B 0→K ∗0 J/ψ and B 0→K ∗0 ψ(2S) decay amplitudes with zero helicity.