Explicit estimate of charm rescattering in $B^0 \to K^0 \bar{\ell} \ell$

TL;DR

This paper provides a detailed estimate of charm rescattering effects in the decay $B^0 o K^0 ar{ell}ell$, showing these long-distance contributions are small and refining the understanding of short-distance physics in this process.

Contribution

The study introduces an explicit, data-driven method to estimate charm rescattering contributions in $B^0$ decays using hadronic effective theory and form factors.

Findings

Long-distance charm rescattering contributions are a few percent of the short-distance amplitude.

The method accurately describes rescattering in the high-$q^2$ region.

Implications for the extraction of the Wilson coefficient $C_9$ are discussed.

Abstract

We analyze $B^0 \to K^0 \bar{\ell}\ell$ long-distance contributions induced by the rescattering of a pair of charmed and charmed-strange mesons. We present an explicit estimate of these contributions using an effective description in terms of hadronic degrees of freedom, supplemented by data on the $B^0 \to D^*D_s (D^*_sD)$ transition in order to reproduce the corresponding discontinuity in the $B^0 \to K^0 \bar{\ell}\ell$ amplitude. The $D^* D_s (D^*_s D) K$ vertex is estimated using heavy-hadron chiral perturbation theory, obtaining an accurate description of the whole rescattering process in the low-recoil (or high-$q^2$) limit. We also present an extrapolation to the whole kinematical region introducing hadronic form factors. The explicit estimate of the leading $D^*D_s (D^*_sD)$ intermediate state leads to a long-distance amplitude which does not exceed a few percent relative to the short-distance one. The consequences of this result for the extraction of the short-distance coefficient $C_9$ are discussed.