New Physics in $b \to s μ^+ μ^-$ after the Measurement of $R_{K^*}$ (1704.07397v3)

Abstract: The recent measurement of $R_{K^*}$ is yet another hint of new physics (NP), and supports the idea that it is present in $b\to s\mu^+\mu^-$ decays. We perform a combined model-independent and model-dependent analysis in order to deduce properties of this NP. Like others, we find that the NP must obey one of two scenarios: (I) $C_9^{\mu\mu}({\rm NP}) < 0$ or (II) $C_9^{\mu\mu}({\rm NP}) = - C_{10}^{\mu\mu}({\rm NP}) < 0$. A third scenario, (III) $C_9^{\mu\mu}({\rm NP}) = - C_{9}^{\prime \mu\mu}({\rm NP})$, is rejected largely because it predicts $R_K = 1$, in disagreement with experiment. The simplest NP models involve the tree-level exchange of a leptoquark (LQ) or a $Z'$ boson. We show that scenario (II) can arise in LQ or $Z'$ models, but scenario (I) is only possible with a $Z'$. Fits to $Z'$ models must take into account the additional constraints from $B^0_s$-${\bar B}^0_s$ mixing and neutrino trident production. Although the LQs must be heavy, O(TeV), we find that the $Z'$ can be light, e.g., $M_{Z'} = 10$ GeV or 200 MeV.

Overview of "New Physics in $b$ after the Measurement of $R_{K^*}$"

This paper conducts a thorough investigation into potential new physics (NP) underlying the observed anomalies in $b \to s \mu^+\mu^-$ transitions, specifically following the measurement of $R_{K^*}$ by the LHCb Collaboration. The measurement of $R_{K^*}$, which denotes the ratio of branching fractions of $B^0 \to K^{*0} \mu^+ \mu^-$ over $B^0 \to K^{*0} e^+ e^-$, reveals discrepancies from the Standard Model (SM) predictions that suggest lepton flavor universality violation.

Key Findings

The authors perform a comprehensive analysis, combining both model-independent and model-dependent approaches, to delineate the characteristics of NP in $b$ decays. They arrive at several conclusions:

1. Scenarios of New Physics: The analysis indicates that NP must adhere to one of two scenarios:
   • Scenario I: $C_9^{\mu\mu}({\rm NP}) < 0$
   • Scenario II: $$C_9^{\mu\mu}({\rm NP}) = - C_{10}^{\mu\mu}({\rm NP}) < 0$$

A third scenario, (III) $$C_9^{\mu\mu}({\rm NP}) = - C_{9}^{\prime \mu\mu}({\rm NP})$$, is ruled out primarily because it leads to theoretical predictions inconsistent with observed experimental results, notably predicting $R_K = 1$, contrary to the experimental data.

1. Model Implications:
   • The simplest NP models, which involve the tree-level exchange of a leptoquark (LQ) or a $Z'$ boson, support scenario (II) for both LQ and $Z'$ models. Scenario (I) is feasible only with $Z'$ boson exchange.
   • LQs are required to be heavy, approximately in the TeV range, while $Z'$ bosons can be either heavy or light, with admissible masses as low as 10 GeV or as minuscule as 200 MeV.

Constraints and Implications

Additional constraints from $B^0_s$-$$mixing and neutrino trident production necessitate specific properties from NP models:</p> <ul> <li>Heavy$$Z'$$models must have a considerable coupling to muons, possibly observable in future experiments concerning neutrino trident production.</li> <li>Light$$Z'$$models, which propose novel opportunities in dark matter and anomalies related to the muon magnetic moment, offer alternate pathways of investigation, potentially addressing discrepancies in other flavor observables.</li> </ul> <h3 class='paper-heading' id='future-directions'>Future Directions</h3> <p>The paper suggests multiple directions for future research:</p> <ul> <li>Exploring the implications of light$$Z'$$models in detail, particularly their effects at low energies which could significantly deviate from high-energy expectations due to the$$q^2$$dependence.</li> <li>Detailed experimental investigations into neutrino trident production might unveil evidence directly pointing to the$$Z'$$coupling strengths posited by these models.</li> <li>Continued theoretical scrutiny of model-independent and model-dependent fits, taking advantage of upcoming high precision flavor data, could further refine or challenge these conclusions.</li> </ul> <p>In summary, the paper carefully delineates potential NP scenarios ascribeable to observed measurements, advocating for continued experimental and model-based exploration into the flavor dynamics governing$$b \to s$ transitions.