B̄s,d⁰ → J/ψμ⁺μ⁻ Decays in QCD Factorization

Motivated by the first LHCb searches for the rare B̄s,d⁰ → J/ψμ⁺μ⁻ decays, we perform a detailed study of these processes within the QCD factorization formalism. Since the transverse size of the $J/ψ$ meson is small in the heavy quark mass limit, this formalism is generally expected to hold for these decays. We include both the leading- and the next-to-leading-order QCD corrections to the hard-scattering kernels, which are convoluted with the light-cone distribution amplitudes (LCDAs) of the initial- and final-state hadrons. It is numerically found that, depending on the model parameters for the leading-twist B-meson LCDA, the maximum branching ratios of B̄ₛ⁰→ J/ψμ⁺μ⁻ and B̄d⁰ → J/ψμ⁺μ⁻, integrated over the dimuon invariant mass squared q² from 1\,GeV² to (m_Bs,d-mJ/ψ)², can reach, respectively, up to 2.21×10⁻⁹ and 7.69×10⁻¹¹ at the leading order in αₛ. After incorporating the non-factorizable one-loop vertex corrections, these branching ratios are further reduced by about one order of magnitude, with B(B̄ₛ⁰ → J/ψμ⁺μ⁻)|q² ≥ 1\,GeV²=2.88×10⁻¹⁰ and B(B̄d⁰ → J/ψμ⁺μ⁻)|q² ≥ 1\,GeV²=1.07×10⁻¹¹. In addition, we have presented the dimuon invariant mass distributions of the individual and total helicity amplitudes squared, as well as the differential and integrated longitudinal polarization fractions of the $J/ψ$ meson, which could be probed by the future LHCb and Belle II experiments with more accumulated data.