Abstract
We present a detailed analysis of QED corrections to overline{B}to overline{K}{mathrm{ell}}^{+}{mathrm{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 mℓ require, besides photon-inclusiveness, a specific choice of kinematic variables. In particular, hard-collinear logs in the lepton-pair invariant mass distribution (q2), 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 overline{B}to Dmathrm{ell}overline{nu } .
Highlights
Rare semileptonic B decays of the type B → K (∗) + − have received significant interest in the last few years because of the hints of Lepton Flavour Universality (LFU) violations reported by the LHCb experiment [1,2,3] and [4] for a review, which could be due to physics beyond the Standard Model (SM)
We go one step further: we focus our attention on the process B → K 1 ̄2, and analyse QED corrections at a fully differential level in terms of the “visible” kinematics
We have performed a complete calculation of these corrections within improved scalar QED, employing a mesonic effective Lagrangian which provides an accurate description of the nonradiative hadronic form factors
Summary
Rare semileptonic B decays of the type B → K (∗) + − have received significant interest in the last few years because of the hints of Lepton Flavour Universality (LFU) violations reported by the LHCb experiment [1,2,3] and [4] for a review, which could be due to physics beyond the Standard Model (SM). Besides trivial kinematic mass effects, the only potential large source of LFU violation present in the SM are hard-collinear singularities in QED. These can induce non-universal corrections of order O(α) ln(m /mB) to the physical decay rates (depending on the definition of the observables), which can be large for light leptons. We show that it is only by using q02, as the relevant kinematic variable, that the differential distribution is free from O(α) ln(m )-terms This does not imply that one cannot perform clean tests of LFU at hadron colliders, but rather that in such cases, the collinear singularities are unavoidable and should be properly corrected for. The appendices contain additional plots, comparison with older work, comments on RK A, amplitudes B, the parametrisation of kinematic variables C, the soft integrals D and the explicit PassarinoVeltman functions E
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
