Inclusive $\bar{B}\to X_s \ell^+\ell^-$ at the LHC: theory predictions and new-physics reach

Abstract

We present theoretical predictions for observables in inclusive $\bar{B}\to X_s \ell^+\ell^-$ suitable for measurements at hadron colliders through a sum-over-exclusive approach. At low $q^2$ we calculate the branching ratio and three angular observables. At high $q^2$ we provide the branching ratio and the ratio of the $\bar B \to X_s \ell^+\ell^-$ rate with respect to the inclusive $\bar B \to X_u \ell \bar\nu$ rate with the same phase-space cut. We compare our predictions to the $B$ factory measurements and also to an extraction of the experimental rate through a sum-over-exclusive method using branching ratios of the exclusive $\bar B \to K^{(*)}\mu^+\mu^-$ modes measured at LHCb. We find a consistent picture comparing Standard Model theory and experiment. As such, our analysis does not support a recent claim about a deficit in the inclusive branching ratio in the high-$q^2$ region. Finally, we present current model-independent bounds on new physics and emphasize the potential of complementary analyses of $\bar{B}\to X_s \ell^+\ell^-$ at Belle II and the LHC.