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

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.