Towards the discovery of new physics with lepton-universality ratios of $b\to s\ell\ell$ decays

Abstract: Tests of lepton-universality as rate ratios in $b\to s \ell\ell$ transitions can be predicted very accurately in the Standard Model. The deficits with respect to expectations reported by the LHCb experiment in muon-to-electron ratios of the $B\to K^{(*)}\ell\ell$ decay rates thus point to genuine manifestations of lepton non-universal new physics. In this paper, we analyse these measurements in the context of effective field theory. First, we discuss the interplay of the different operators in $R_K$ and $R_{K^*}$ and provide predictions for $R_{K^*}$ in the Standard Model and in new-physics scenarios that can explain $R_K$. We also provide approximate numerical formulas for these observables in bins of interest as functions of the relevant Wilson coefficients. Secondly, we perform frequentist fits to $R_{K}$ and $R_{K^*}$. The SM disagrees with these measurements at $3.7\sigma$ significance. We find excellent fits in scenarios with combinations of $\mathcal O_{9(10)}^\ell=\bar s\gamma^\mu b_L~\ell\gamma_\mu(\gamma_5) \ell$ operators, with pulls relative to the Standard Model in the region of $4\sigma$. An important conclusion of our analysis is that a lepton-specific contribution to $\mathcal O_{10}$ is essential to understand the data. Under the hypothesis that new-physics couples selectively to the muons, we also present fits to other $b\to s\mu\mu$ data with a conservative error assessment, and comment on more general scenarios. Finally, we discuss new lepton universality ratios that, if new physics is the origin of the observed discrepancy, should contribute to the statistically significant discovery of new physics in the near future.

Analysis of Lepton Universality in $b \to s\ell\ell$ Transitions

The paper under discussion provides a systematic analysis of lepton universality violations in $B$-meson decays via $b \to s\ell\ell$ transitions. The focus is specifically on the lepton-universality ratios $R_K$ and $R_{K^*}$, which are examined in the context of effective field theory to identify potential manifestations of new physics (NP) beyond the Standard Model (SM).

Summary and Key Insights

1. Lepton Universality Violation (LUV): Measurement discrepancies between lepton-flavor ratios $R_K$ and $R_{K^*}$ and their SM predictions suggest possible LUV, an intriguing indicator that may point toward new physics. The paper reports that the SM predictions disagree with the measured values at a $3.7\sigma$ level, suggesting that lepton universality may not hold at these decays.

2. Effective Field Theory Context: The study utilizes an effective Hamiltonian approach to model $b \to s\ell\ell$ transitions. It focuses on variations in Wilson coefficients associated with semileptonic operators, particularly $\mathcal{O}{9}^\ell$ and $\mathcal{O}{10}^\ell$, as these are capable of explaining observed anomalies in $R_K$ and $R_{K^*}$.

3. Wilson Coefficients and New Physics: The analysis finds that modifications to $\mathcal{O}{9(10)}^\ell$ operators, particularly those affecting muons, can reconcile the experimental discrepancies when $\delta C_9^\mu \approx -1$ or $\delta C{10}^\mu \approx +1$. Such values suggest NP scenarios that distinctly affect muonic channels, thereby hinting towards LUV.

4. Frequentist Fits and Statistical Analysis: The paper employs frequentist statistical techniques to fit the measured values against theoretical predictions. Exceptional fits are found when modifying $\mathcal{O}{9(10)}^\mu$ operators, with statistical significance indicating that new lepton-specific contributions to $\mathcal{O}{10}$ are crucial.

5. Influence of Angular Observables: The research delves into $CP$-averaged angular observables in $B\to K^*\mu\mu$ decays. These observables exhibit $\mathcal{O}(4\sigma)$ tensions with SM expectations, further corroborating the evidence for NP. The analysis underlines that NP scenarios can naturally account for discrepancies in angular distributions, specifically when NP selectively couples to muons.

6. Predictions and Prospect for Future Measurements: The paper introduces new ratios such as $R_6$, which offer a more refined probe into NP contributions and membership into LUV. These come with clear predictions within the context of the SM and various NP scenarios, demonstrating their capability to further constrain or validate theoretical models when experimental measurements become available.

Implications and Future Directions

The findings presented in this paper provide a persuasive case for NP affecting lepton universality in $b \to s\ell\ell$ transitions. It emphasizes the significance of further experimental investigations to either confirm or refute these predicted anomalies. The study also sets the stage for more refined tests of LUV through newly proposed observables, which hold the potential to offer insight into the underlying dynamics at play.

Future developments in AI, including advanced modeling and simulations, could greatly enhance the analysis of complex particle interactions and the interpretation of experimental data. As more precise instrumentation becomes available at facilities such as the LHCb and Belle II, these theoretical frameworks will be crucial in the sustained effort to decipher the components of physics beyond the Standard Model.