Weak Decays of Excited $B$ Mesons

We investigate the decays of the excited $(b\overline{q})$ mesons as probes of the short-distance structure of the weak $\mathrm{\Delta }B=1$ transitions. These states are unstable under the electromagnetic or strong interactions, although their widths are typically suppressed by phase space. Compared to the pseudoscalar $B$ meson, the purely leptonic decays of the vector $B^{*}$ are not chirally suppressed and are sensitive to different combinations of the underlying weak effective operators. An interesting example is $B_s^{*}\to {\ell }^{+}{\ell }^{-}$, which has a rate that can be accurately predicted in the standard model. The branching fraction is $\mathcal{B}\sim 10^{-11}$, irrespective of the lepton flavor and where the main uncertainty stems from the unmeasured and theoretically not well known $B_s^{*}$ width. We discuss the prospects for producing this decay mode at the LHC and explore the possibility of measuring the $B_s^{*}\to \ell \ell$ amplitude, instead, through scattering experiments at the $B_s^{*}$ resonance peak.