Theoretical Aspects of $b \to s \bar{\ell}\ell$ Decays

TL;DR

This work probes whether long-distance charm rescattering can mimic a sizable universal shift in the Wilson coefficient $C_9$ that governs b→sℓℓ transitions, potentially explaining tensions in exclusive decays. It builds a hadronic model anchored in heavy-hadron chiral perturbation theory, extends it with form factors to cover the full $q^2$ range, and calibrates it against experimental data for the decay B0 → K0 ℓℓ, incorporating monopole and dipole photon-vertex topologies and a multiplicity factor for higher resonances. The results show absorptive long-distance contributions of order a few percent to $C_9$, with a characteristic sign flip between low and high $q^2$, and three interference scenarios yielding δC9 up to about 5% naturally, or potentially ~20% in highly tuned cases at the cost of strong $q^2$-dependence. These findings suggest charm-rescattering is non-negligible for NP fits and highlight the importance of considering hadronic dynamics alongside SMEFT-driven interpretations in the broader landscape of flavor anomalies.

Abstract

Flavor-changing neutral current decays such as $b \to s \bar{\ell} \ell$ are highly suppressed in the Standard Model (SM) and therefore provide sensitive tests for new physics. Persistent tensions between SM predictions and experimental results in branching ratios and angular observables can be explained by a shift of the Wilson coefficient $C_9$ of the effective operator $O_9$ by $\sim 20 \%$ relative to the SM value. This shift could arise from a non-standard short-distance contribution or from an inaccurate description of long-distance dynamics, particularly charm rescattering contributions. We therefore investigate charm rescattering contributions in $B^0 \to K^0 \bar{\ell}\ell$ using a model of fundamental hadronic degrees of freedom inspired by heavy-hadron chiral perturbation theory and improved by appropriate form factors as well as experimental data. Our analysis shows that such effects, with a high degree of fine-tuning, could shift $C_9$ by $\sim 20\%$, at the cost of introducing a more pronounced $q^2$ dependence, whereas experimental data are consistent with a $q^2$-independent shift of $C_9$ with the current experimental uncertainties. In the most natural scenario, we find these effects to be of the order of $\sim 5\%$. Connections with other flavor anomalies further illustrate the strong discovery potential of $b \to s \bar{\ell} \ell$ modes.

Figures (3)

• Figure 1: Independent determinations of $C_9$ from data LHCb:2020lmfLHCb:2016yklCMS:2023klkLHCb:2014cxe. The black points illustrate the determinations in the low- and high-$q^2$ regions for the different decay amplitudes. The grey band is the result of the fit assuming a universal $C_9$ over the full spectrum. The red band indicates the SM value.
• Figure 2: Ratio of the dispersive (dashed and dash-dotted lines) and absorptive (solid line) parts of the monopole (top) and dipole (bottom) matrix element over the absolute value of the short-distance matrix element in the low-$q^2$ (left) and high-$q^2$ (right) regions.
• Figure 3: Combined results of monopole and dipole long-distance contributions plotted as $|\delta C_9|/|C_9^{\text{eff}}|$, where $\delta C_9$ is the contribution from charm rescattering triangle diagrams. The dark gray bands give the "natural" results, the light gray bands give the partially tuned results, and the dashed lines give the fully tuned results.