Probing unknown nonperturbative effects in $b\to s\ell \ell$ with inclusive and exclusive observables

Abstract

In this paper we revisit, from a different perspective, a long-standing question: ``Is the systematic deficit observed in all branching ratios mediated by a $b\to s\mu \mu$ transition due to New Physics, or to a hypothetical constant unknown universal hadronic contribution that mimics New Physics?'' The key observation that allows us to distinguish between these two possibilities is that non-perturbative contributions associated with $c\bar{c}$ loops affect inclusive $B\to X_s\ell \ell$ and exclusive $B\to K^{(\ast )}\ell \ell$ modes differently. In inclusive decays, factorizable contributions are exactly determined from data on $e^{+}{e}^{-}\to \mathrm{hadrons}$, while non-factorizable corrections are described by resolved-photon contributions at low $q^2$ and by local power corrections at high $q^2$. In exclusive decays, by contrast, hypothetical charming-penguin effects, beyond those already included in current uncertainty estimates, could appear, in a worst-case scenario, as a constant, universal contribution that it seems, in principle, indistinguishable from genuine New Physics. We identify two observables, constructed from ratios of exclusive to inclusive modes, that can discriminate between a New Physics contribution and a constant hadronic contribution. Moreover, these ratios can be measured directly by LHCb, as they do not require any normalisation to $J/\psi K^{(\ast )}$ branching fractions from B factories. A preliminary evaluation of these observables with present data shows some preference for the New Physics interpretation. In a complementary test, a comparison between inclusive measurements and the corresponding sum of exclusive modes at high $q^2$ similarly disfavours an explanation based on a constant hadronic contribution. Finally, we provide projections for the new observables based on expected LHCb and Belle II measurements in the near future.

Comments: 24 pages, 5 figures, 4 tables