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.
Categories: hep-ph hep-ex