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

TL;DR

This paper analyzes quantum electrodynamics (QED) corrections to the decay process A0A0A0A0A0A0A0 at a detailed double-differential level, focusing on divergence cancellations and implications for experimental measurements.

Contribution

It provides a comprehensive analytical framework for QED corrections in A0A0A0 decays, including divergence cancellation and treatment of hard-collinear logs, applicable to various semileptonic decays.

Findings

Soft divergences cancel at the differential level.

Hard-collinear logs A0A0A0 are sizeable in the invariant mass distribution.

Analytic computations are adaptable to other semileptonic decays.

Abstract

We present a detailed analysis of QED corrections to $\bar{B} \to \bar{K} \ell^+ \ell^-$ decays at the double-differential level. Cancellations of soft and collinear divergences are demonstrated analytically using the phase space slicing method. Whereas soft divergences are found to cancel at the differential level, the cancellation of the hard-collinear logs $\ln m_\ell$ require, besides photon-inclusiveness, a specific choice of kinematic variables. In particular, hard-collinear logs in the lepton-pair invariant mass distribution ($q^2$), are sizeable and need to be treated with care when comparing with experiment. Virtual and real amplitudes are evaluated using an effective mesonic Lagrangian. Crucially, we show that going beyond this approximation does not introduce any further infrared sensitive terms. All analytic computations are performed for generic charges and are therefore adaptable to semileptonic decays such as $B \to D \ell \bar \nu$.