On the Standard Model predictions for $R_K$ and $R_{K^*}$

Abstract: We evaluate the impact of radiative corrections in the ratios $\Gamma[B\to M \mu^+\mu^-]/\Gamma[B\to M e^+e^-]$ when the meson $M$ is a $K$ or a $K^*$. Employing the cuts on $m^2_{\ell\ell}$ and the reconstructed $B$-meson mass presently applied by the LHCb Collaboration, such corrections do not exceed a few $\%$. Moreover, their effect is well described (and corrected for) by existing Montecarlo codes. Our analysis reinforces the interest of these observables as clean probe of physics beyond the Standard Model.

• The paper demonstrates that QED radiative corrections, primarily from collinear photon emission, can induce a positive shift of around 3% in LFU ratios R_K and R_K* under specific kinematic cuts.
• It employs meticulous Monte Carlo simulations that cancel perturbative and non-perturbative QCD effects, ensuring high-precision theoretical predictions.
• The study reinforces the role of LFU ratios as sensitive probes for new physics, consistent with recent experimental hints from LHCb.

Overview of "On the Standard Model predictions for $R_K$ and $R_{K^*}$"

The paper by Bordone, Isidori, and Pattori critically evaluates the Standard Model (SM) predictions for the Lepton Flavor Universality (LFU) ratios $R_K$ and $R_{K^*}$. These ratios serve as precise probes for new physics beyond the SM. Intriguingly, recent experimental data from the LHCb experiment suggest deviations in these LFU ratios from their expected SM values, prompting a thorough investigation into the theoretical predictions and corrections that could account for such observations.

Key Aspects and Methodology

The primary focus is on determining the impact of QED radiative corrections on the decay width ratios $\Gamma[B\to M \mu^+\mu^-]/\Gamma[B\to M e^+e^-]$ for mesons $M$ such as $K$ and $K^*$. The authors highlight:

• The calculations reveal that radiative corrections, mainly due to collinear photon emission, potentially introduce significant deviations, although the inherent theoretical uncertainties are relatively small—around $1\%$.
• Detailed analysis ensures that perturbative and non-perturbative QCD contributions cancel out, maintaining high precision in theoretical predictions for $R_K$ and $R_{K^*}$.
• The study extensively uses Monte Carlo simulations, which accurately account for these radiative corrections.

Numerical Results and Observations

The authors conduct a meticulous numerical analysis to quantify these radiative corrections, examining various kinematic regimes and cut values on the dilepton invariant mass $q^2$ and the reconstructed $B$-meson mass:

• For the $B \to K e^+e^-$ decays, radiative corrections can reach or exceed $10\%$ for electrons under certain kinematic configurations.
• The effects are less pronounced for muons due to stronger collinear suppression and tighter cut criteria in experimental analyses.
• Importantly, the impact on $R_K$ and $R_{K^*}$, when experimental cuts are applied, results in a calculated positive shift, approximately $3\%$, which is consistent with the experimental findings.

Implications and Future Perspectives

The study reinforces the potential of $R_K$ and $R_{K^*}$ as probes for new physics, given their sensitivity to deviations from SM predictions. Although the current theoretical uncertainties due to QED corrections are minimal, they are non-negligible when considered in context with the precise nature necessary for distinguishing new physics effects.

The findings also emphasize the importance of experimental setups, particularly cut choices, on the inferred values of LFU ratios. As the paper outlines, alignment between theoretical predictions and Monte Carlo simulation outcomes ensures that current experimental analyses, such as those by LHCb, remain robust against theoretical discrepancies from radiative corrections.

In terms of future developments, evolving experimental accuracy and increased data from the LHC could refine these results further. Assessing the LFU ratios over a broader range of kinematic cuts and other decay channels might unveil more profound insights into potential deviations, thereby aiding the broader quest for new physics phenomena beyond the SM.

The approach, methodology, and implications presented in this paper substantiate ongoing validations of the SM while concurrently offering a foundation for future exploration of physics beyond the established paradigm.