Inclusive $\bar B_s\mapsto X_{\bar sc} \ell \bar ν$ decays from lattice QCD: computational strategy and a first physical result

Abstract

We present a strategy to compute the inclusive decay rate for the process $\bar B_s \mapsto X_{\bar sc} \ell \barν$ from first principles in lattice QCD. The physical decay rate is obtained from the interpolation of non-perturbative lattice data, obtained at lighter than physical heavy meson masses ($M_{\bar B_s}^\mathrm{max}=4.3$GeV), with the Operator Product Expansion predictions, which become exact in the limit of infinitely heavy quarks. We also present a new method for the computation of the required lattice four-point correlators, which represents a considerable improvement over the state-of-the-art on the subject. We show the effectiveness of the strategy by performing the calculation on a subset of the available $n_f=2+1+1$ physical-point Extended Twisted Mass Collaboration (ETMC) gauge ensembles. Our current determination of the inclusive decay rate has a 7% total error, that is dominated by uncertainties due to the relatively limited configuration ensembles considered herein, and can be significantly reduced in the near future.