QED in $\bar B \to \bar K \ell^+\ell^-$ LFU ratios: Theory versus Experiment, a Monte Carlo Study

Abstract

Using analytic results obtained in a meson effective theory, that includes all infrared sensitive logs, we build a dedicated Monte Carlo framework to describe QED corrections in $\bar B \to \bar K \ell^+\ell^-$ for a generic form factor. For the neutral mode $\bar B^0 \to \bar K^0 \ell^+\ell^-$, we perform a detailed numerical comparison versus those obtained with the general-purpose photon-shower tool PHOTOS. The comparison indicates a good agreement, at the few per-mil level, when focusing on the rare mode only. In addition, our framework allows us to investigate the impact of the charmonium resonances. Interference effects, not described by PHOTOS in the experimental analysis, are found to be small in the dilepton invariant mass region $q^2 < 6 \textrm{GeV}^2$, which is used to determine $R_{K^{(*)}}$. Using a semi-analytic framework we assess the full, rare and resonant, mode. Based thereupon, we discuss strategies to check the subtraction of the resonant mode, which has a sizeable impact at $q^2 \approx 6 \textrm{GeV}^2$ in the electron mode.