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We present a detailed analysis of QED corrections to $\bar{B} \to \bar{K}\ell^+ \ell^-$ decays at the double-differential level. Cancellations of softand collinear divergences are demonstrated analytically using the phase spaceslicing method. Whereas soft divergences are found to cancel at thedifferential level, the cancellation of the hard-collinear logs $\ln m_\ell$require, besides photon-inclusiveness, a specific choice of kinematicvariables. In particular, hard-collinear logs in the lepton-pair invariant massdistribution ($q^2$), are sizeable and need to be treated with care whencomparing with experiment. Virtual and real amplitudes are evaluated using aneffective mesonic Lagrangian. Crucially, we show that going beyond thisapproximation does not introduce any further infrared sensitive terms. Allanalytic computations are performed for generic charges and are thereforeadaptable to semileptonic decays such as $B \to D \ell \bar \nu$.

QED Corrections in $\bar{B} \to \bar{K} \ell^+ \ell^-$ at the Double-Differential Level