${\bar{B}}_{s,d}^0\to J/\ddot{I}ˆ\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ Decays in QCD Factorization

Abstract

Motivated by the first LHCb searches for the rare ${\bar{B}}_{s,d}^0\to J/\ddot{I}ˆ\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ decays, we perform a detailed study of these processes within the QCD factorization formalism. Since the transverse size of the $J/\ddot{I}ˆ$ 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 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 ${\bar{B}}_s^0\to J/\ddot{I}ˆ\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ and ${\bar{B}}_d^0\to J/\ddot{I}ˆ\hat{I}{¼}^{+}\hat{I}{¼}^{-}$, integrated over the dimuon invariant mass squared $q^2$ from $1{\mathrm{GeV}}^2$ to $(m_{B_{s,d}}-m_{J/\ddot{I}ˆ}{)}^2$, can reach up to $2.21\times 10^{-9}$ and $7.69\times 10^{-11}$ at the leading order in $\hat{I}{\pm }_s$, respectively. After incorporating the non-factorizable one-loop vertex corrections, these branching ratios are further reduced by about one order of magnitude, with $\mathcal{B}({\bar{B}}_s^0\to J/\ddot{I}ˆ\hat{I}{¼}^{+}\hat{I}{¼}^{-}){|}_{q^2\ge 1{\mathrm{GeV}}^2}=2.88\times 10^{-10}$ and $\mathcal{B}({\bar{B}}_d^0\to J/\ddot{I}ˆ\hat{I}{¼}^{+}\hat{I}{¼}^{-}){|}_{q^2\ge 1{\mathrm{GeV}}^2}=1.07\times 10^{-11}$. 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 $J/\ddot{I}ˆ$ meson, which could be probed by the future LHCb and Belle II experiments with more accumulated data.

40 pages, 10 figures, and 7 tables; more discussions and references added, final version published in the journal