Reassessing the discovery potential of the $B \to K^{*} \ell^+\ell^-$ decays in the large-recoil region: SM challenges and BSM opportunities (1412.3183v3)

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.

• The paper introduces a novel framework that separates model-independent and nonperturbative QCD effects in the angular analysis of B → K* ll decays.
• It identifies a favored negative shift in the Wilson coefficient C9 and uses optimized observables like P5' to probe potential NP effects.
• The analysis outlines clear strategies for employing lepton-universality observables to disentangle SM challenges from BSM opportunities.

Overview of the Potential Discovery in $B \to K^{*} \ell^+\ell^-$ Decays

The paper "Reassessing the discovery potential of the $B \to K^{*} \ell^+\ell^-$ decays in the large-recoil region: SM challenges and BSM opportunities" by S. Jäeger and J. Martin Camalich presents a comprehensive analysis of the potential to identify signals of New Physics (NP) in $B \to K^{*} \ell^+\ell^-$ decays, focusing on several key anomalies and theoretical uncertainties in the Standard Model (SM). The authors critically evaluate the current challenges and opportunities offered by BSM physics in these decay modes, with specific attention to the implications of various experimental anomalies observed by the LHCb and other collaborations.

Methodological Approach

The authors employ a sophisticated framework for analyzing the angular observables in $B \to K^* \mu^+\mu^-$ and $B \to K^* e^+ e^-$ decays. They advocate for a parameterization of the hadronic matrix elements that separates model-independent information from nonperturbative QCD effects. This approach allows for a transparent decomposition of the decay amplitudes into calculable components and unknown hadronic parameters, which are treated as nuisance parameters in their statistical analysis.

The paper stresses the importance of large-recoil kinematics and explores the sensitivity of various observables to NP, particularly focusing on deviations in Wilson coefficients such as $C_9$ and potential contributions from right-handed currents, indicated by $C_7^\prime$. Furthermore, it emphasizes the use of optimized angular observables like $P_i^{(\prime)}$ and their susceptibility to power corrections beyond the heavy-quark limit.

Numerical Results and Analysis

The paper explores the tensions between LHCb data and SM predictions, notably the observed anomalies in $P_5^\prime$. When assessing these deviations, the authors find a favored negative shift in the $C_9$ Wilson coefficient, suggesting possible NP contributions, albeit with modest statistical significance ($\lesssim2 \sigma$). This nuance underscores the intricacies of attributing such discrepancies solely to NP without thoroughly accounting for theoretical uncertainties.

The analysis of observables such as $P_1$ and $P_3^{CP}$ reveals their robustness as clean probes for detecting right-handed quark currents due to their theoretical suppression in the SM, especially at low $q^2$. Such insights highlight these observables' potential for setting stringent constraints on $C_7^\prime$, enhancing the precision of probing electromagnetic operators.

Implications for Lepton Universality Violation and Future Directions

In light of recent experimental indications of lepton-universality violation (LUV), notably in $B^+\to K^+\ell^+\ell^-$ decays, the paper introduces novel lepton-universality observables. These are shown to be particularly sensitive to potential NP effects, allowing differentiation between various NP scenarios, including those affecting semileptonic operators underpinning $B$ decays.

The work's methodological rigor and extensive numerical analysis provide a fertile ground for future theoretical and experimental studies. It proposes concrete strategies for disentangling potential NP signals from enduring hadronic uncertainties, thus refining the pathways towards discovering new physics beyond the SM. Future developments may further elucidate the interplay between improved nonperturbative calculations and experimental precision, advancing our understanding of rare $B$ decays and testing the limits of the SM.