Flavour anomalies after the $R_{K^*}$ measurement

Abstract: The LHCb measurement of the $\mu/e$ ratio $R_{K^*}$ indicates a deficit with respect to the Standard Model prediction, supporting earlier hints of lepton universality violation observed in the $R_K$ ratio. We show that the $R_K$ and $R_{K^*}$ ratios alone constrain the chiralities of the states contributing to these anomalies, and we find deviations from the Standard Model at the $4\sigma$ level. This conclusion is further corroborated by hints in the theoretically challenging $b\to s\mu^+\mu^-$ distributions. Theoretical interpretations in terms of $Z'$, lepto-quarks, loop mediators, and composite dynamics are discussed. We highlight their distinctive features in terms of chiralities and flavour structure relevant for the observed anomalies.

• The paper reveals significant deviations in Rₖ* ratios from SM predictions, with nearly 4σ discrepancies indicating lepton flavour universality violation.
• It evaluates multiple theoretical frameworks, including Z' bosons, leptoquarks, loop processes, and composite models to explain b → sℓ⁺ℓ⁻ anomalies.
• The study underscores the need for refined experiments and models to explore potential new physics beyond the Standard Model.

Flavour Anomalies after the $R_{K^*}$ Measurement

In this study, the authors explore recent observations in the decay ratios $R_K$ and $R_{K^*}$, which show significant deviations from the Standard Model (SM) predictions and suggest lepton flavour universality violation. The measurement of the $\mu/e$ ratio $R_{K^*}$ by the LHCb collaboration reveals a deficit compared to the SM's prediction, aligning with earlier observed anomalies in the $R_K$ ratio.

Key Observations and Results

Recent analyses detail the $R_{K^*}$ ratio: $$R_{K^*} = \frac{\mathrm{BR}(B \to K^*\mu^+\mu^-)}{\mathrm{BR}(B \to K^*e^+e^-)}$$

The experimental measurements within specific di-lepton invariant mass bins show:

• For $0.045< q^2 < 1.1\,^2$: $R_{K^*} = 0.660^{+0.110}_{-0.070} \pm 0.024$
• For $1.1 < q^2 < 6\,^2$: $R_{K^*} = 0.685^{+0.113}_{-0.069} \pm 0.047$

In contrast, SM predictions are:

• For $0.045 < q^2 < 1.1\,^2$: $R^{SM}_{K^*} = 0.906 \pm 0.028$
• For $1.1 < q^2 < 6\,^2$: $R^{SM}_{K^*} = 1.00 \pm 0.01$

These discrepancies are evident and remain statistically significant, indicating about a $4\sigma$ level deviation from the SM.

Theoretical Interpretations

The study considers several theoretical frameworks to explain the observed anomalies:

• $Z'$ Bosons: Models with an extra $Z'$ gauge boson can provide a neutral current interaction affecting left-handed $b$ and $s$ quarks and left-handed leptons. This framework can naturally accommodate the anomalies in $b \to s\ell^+\ell^-$ transitions.
• Lepto-quarks: These additional scalar or vector particles can mediate the anomalous decays at tree level. Scalar triplet lepto-quarks are highlighted as a viable solution consistent with observed data, as they modify the effective chiral operators required to match experimental observations.
• Loop Mediated Processes: The authors also explore models involving loop-level contributions through new particles coupling to quarks and leptons with relatively large Yukawa couplings.
• Composite Models: Extensions of the SM with composite Higgs models are discussed, where new strong dynamics produce the observed anomalies. These involve additional techni-scalars and techni-fermions.

Implications and Future Directions

These findings have profound implications for flavor physics, suggesting potential pathways for new physics beyond the SM. The lepton flavour universality violation observed could be a hint towards new particle interactions, potentially related to dark matter connections or deviations within the neutrino sector.

Future experimental measurements, with reduced statistical and systematic uncertainties, are anticipated to further clarify the nature of these anomalies. Moreover, these observations encourage the development of models that provide a unified explanation for such anomalies, including connections to other sectors impacted by tiny deviations in flavour universality predictions.

Conclusion

The findings gradually reshaping our understanding of beyond-SM physics could direct future theoretical and experimental efforts in particle physics. The consistent evidence urging a reconsideration of fundamental aspects of flavor physics invites diverse theoretical interpretations and guides new research strategies in confronting observed phenomena at high energies.