Bₒ, ₃^0 J/ψμ^+μ^- Decays in QCD Factorization

Motivated by the first LHCb searches for the rare Bₒ, ₃^0 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 Bₒ^0 J/ψμ^+μ^- and B₃^0 J/ψμ^+μ^-, integrated over the dimuon invariant mass squared q² from 1\, GeV² to (m₁_ₒ, ₃-m₉/⏧) ², can reach, respectively, up to 2. 2110^-9 and 7. 6910^-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 (Bₒ^0 J/ψμ^+μ^-) |ₐℂ ₁\, ₆₄ₕℂ=2. 8810^-10 and B (B₃^0 J/ψμ^+μ^-) |ₐℂ ₁\, ₆₄ₕℂ=1. 0710^-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.