QED corrections in $$ \overline{B}\to \overline{K}{\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ at the double-differential level

Abstract

We present a detailed analysis of QED corrections to $$ \overline{B}\to \overline{K}{\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ B ¯ → K ¯ ℓ + ℓ − 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 $$ \overline{B}\to D\mathrm{\ell}\overline{\nu } $$ B ¯ → D ℓ ν ¯ .

Radiative decays of heavy-light mesons and the $$ {f}_{H,{H}^{\ast },{H}_1}^{(T)} $$ decay constants

“…The lattice determination g DsD * s γ | [12] = 0.11( 2) is approximately three standard deviations lower than our value g DsD * s γ = 0.60 (19). This is where the breakdown (3.22) is useful.…”

“…, is softened by the derivative term F αβ and avoids unsuppressed large logarithms of the form ln(∆M 2 B /m 2 B ). This is another manifestation, with a different twist, of the finding in [19] (cf. section 3.4 therein) that structure dependent terms do not generate large logarithms.…”

“…3 One might wonder whether the proximity of the B and B * mass leads to any enhanced terms in the soft photon region in diagrams where the photon couples to an external B-meson and a lepton for instance (e.g. diagram top left of figure 3 in [19] where the weak Hamiltonian corresponds to B * → K ). The behaviour of the denominator in the soft region (i.e.…”

New ideas for handling of loop and angular integrals in D-dimensions in QCD

“…(154)-( 159) is a version of three-point partial fractioning. In a recent publication on QED corrections in exclusive B → K + − decay [67], the order ε of the double massive angular integral was explicitly needed to extract collinear logarithms from soft integrals. Private communication with Somogyi is cited to obtain a result.…”

New physics effects in leptonic and semileptonic decays

“…Effects from soft-photon emission in semileptonic B-meson decays have been recently considered in refs [41][42][43],. see also ref [44]…”