Impact of Soft Photons on $B\to K\ell^+\ell^-$

Abstract

In this era of precision, it has become necessary to have precise expressions and construct theoretically clean observables to match with the experiments. The $\mathcal{O}(\alpha)$ QED corrections to $B\to K\ell^+\ell^-$ modes are discussed here. The structure of the contact term is fixed by demanding gauge invariance of the real emission amplitude. A fictitious photon mass ($\lambda$) acts as IR regulator, and the results are shown to be independent of it. The QED effects in the individual channel are found to be negative. The electron channel is shown to receive a large correction of $\mathcal{O}(20\%)$. The impact of soft photons on the lepton flavour universality (LFU) ratio ($R_{K}^{\mu e}$) is also discussed.