Reassessing the discovery potential of the $B \to K^{*} \ell^+\ell^-$ decays in the large-recoil region: SM challenges and BSM opportunities

TL;DR

This paper critically analyzes the potential of $B o K^* \, \ell^+\ell^-$ decays in the large-recoil region to distinguish Standard Model physics from New Physics, focusing on anomalies, right-handed currents, and lepton universality violations, with implications for future measurements.

Contribution

It introduces a model-independent parameterization of hadronic matrix elements and assesses the robustness of angular observables against QCD effects, proposing new observables for NP detection.

Findings

Angular observables are sensitive to long-distance QCD effects.

A fit suggests a possible NP contribution with $\,\delta C_9 \simeq -1.5$, but with limited statistical significance.

Certain observables like $P_1$ and $P_3^{CP}$ are highly sensitive to right-handed currents at low $q^2$.

Abstract

We critically examine the potential to disentangle Standard Model (SM) and New Physics (NP) in $B \to K^* \mu^+\mu^-$ and $B\to K^* e^+ e^-$ decays, focusing on $(i)$ the LHCb anomaly, $(ii)$ the search for right-handed currents, and $(iii)$ lepton-universality violation. Restricting ourselves to the large-recoil region, we advocate a parameterisation of the hadronic matrix elements that separates model-independent information about nonperturbative QCD from the results of model calculations. We clarify how to estimate corrections to the heavy-quark limit that would generate a right-handed (virtual) photon in the $b\to s\gamma$ contribution to the decay. We then apply this approach to the discussion of various sets of observables of increasing theoretical cleanness. First, we show that angular observables in the optimized $P_i^{(\prime)}$ basis are, in general, not robust against the long-distance QCD effects. While a fit to data favours a NP contribution to the semileptonic operators of the type $\delta C_9\simeq-1.5$, this comes at a relatively small statistical significance of $\lesssim2 \sigma$, once power corrections are properly accounted for. Second, two of these observables, $P_1$ and $P_3^{CP}$ are particularly clean at very low $q^2$ and sensitive probes of right-handed quark currents. We discuss their potential to set stringent bounds on the Wilson coefficient $C_7^\prime$, especially using data of the electronic mode. Finally, in light of the recent hint of lepton-universality violation in $B^+\to K^+\ell\ell$, we introduce and investigate new lepton-universality observables involving angular observables of the muonic and electronic modes and their zero crossings, and show that, if the effect is of the size suggested by experiment, these can clearly distinguish between different NP explanations in terms of underlying semileptonic operators.