Contribution of vector resonances to the Bd⁰ -> K*⁰ mu+ mu- decay

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The fully differential angular distribution for the rare flavor-changing neutral current decay Bd⁰ -> K*⁰ (-> K- pi+) mu+ mu- is studied. The emphasis is placed on accurate treatment of the contribution from the processes Bd⁰ -> K*⁰ (-> K- pi+) V with intermediate vector resonances V = rho(770), omega(782), phi(1020), J/psi, psi(2S),... decaying into the mu+ mu- pair. The dilepton invariant-mass dependence of the branching ratio, longitudinal polarization fraction fₗ of the K*⁰ meson, and forward-backward asymmetry AFB 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 B⁰ -> K*⁰ J/psi and B⁰ -> K*⁰ psi(2S) decay amplitudes with zero helicity.