On the Impact of Soft Photons on $B\rightarrow K \ell^+ \ell^-$

TL;DR

This paper calculates detailed QED corrections to the $B o K\,\ell^+\ell^-$ decay, showing significant effects especially for electron channels and implications for lepton flavor universality tests.

Contribution

It provides the first comprehensive $\,\mathcal{O}(\alpha)$ QED correction analysis for $B\to K\ell^+\ell^-$ decays, including gauge-invariant real emission and virtual corrections.

Findings

QED effects reduce decay rates by about 20%.

Large corrections observed in electron channels.

Impacts on lepton flavor universality ratio $R^{\mu e}_K$ discussed.

Abstract

We give detailed results of $\mathcal{O}(\alpha)$ QED corrections (both real emission and virtual corrections) to $B\to K\ell^+\ell^-$ modes. Requiring the real emission to be gauge invariant, the structure of the contact term(s) is fixed. The calculation is done with a fictitious photon mass as the IR regulator and results are shown to be independent of it, establishing cancellation of the soft divergences. Results are presented for a choice of photon energy, $k_{max}$, and photon angle $\theta_{cut}$. The QED effects are negative, thereby reducing the rate compared to that without QED effects. Electron channels are shown to receive large corrections ($\mathcal{O}(20\%)$). Impact on lepton flavour universality ratio, $R^{\mu e}_K$ are also discussed.