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

TL;DR

This paper investigates whether the observed deficits in $b o s \, \ell\ell$ decays are due to New Physics or unknown hadronic effects, proposing observables to distinguish these scenarios using inclusive and exclusive decay data.

Contribution

It introduces novel ratios of exclusive to inclusive decay modes that can differentiate between New Physics and hadronic effects, measurable by LHCb without normalization to $J/\psi K^{(*)}$.

Findings

Preliminary data slightly favors New Physics over hadronic explanations.

Comparison of inclusive and summed exclusive modes at high $q^2$ disfavors constant hadronic effects.

Projections suggest upcoming measurements can clarify the origin of the observed deficits.

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 $B\to K^{(*)}\ell\ell$ 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 $J/\psi K^{(*)}$ 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.