The $B_s\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}{\hat{I}}^3$ decay rate at large $q^2$ from lattice QCD

Abstract

We determine, by means of lattice QCD calculations, the local form factors describing the $B_s\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}{\hat{I}}^3$ decay. For this analysis we make use of the gauge configurations produced by the ETM Collaboration with $N_f=2+1+1$ flavour of Wilson-Clover twisted-mass fermions at maximal twist. To obtain the $B_s$ meson form-factors, we perform simulations for several heavy-strange meson masses $m_{H_s}$ in the range $m_{H_s}\in [m_{D_s},2m_{D_s}]$, and extrapolate to the physical $B_s$ meson point $m_{B_s}\simeq 5.367\mathrm{GeV}$ making use of the HQET scaling laws. We cover the region of large di-muon invariant masses $\sqrt{q^2}>4.16\mathrm{GeV}$, and use our results to determine the branching fraction for $B_s\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}{\hat{I}}^3$, which has been recently measured by LHCb in the region $\sqrt{q^2}>4.9\mathrm{GeV}$. The largest contribution to the uncertainty in the partial branching fractions at values of $\sqrt{q^2}<4.8\mathrm{GeV}$ is now due to resonance and other long-distance effects, including those from "charming penguins", which we estimate by summing over the contributions from the $J_P=1^{-}$ charmonium resonances.

42 page, 25 figures, 6 tables