Deciphering the long-distance penguin contribution to $\bar B_{d, s} \to γγ$ decays

Abstract

We compute for the first time the long-distance penguin contribution to the double radiative B-meson decays due to the purely hadronic operators acting with the electromagnetic current in the background soft-gluon field from first field-theoretical principles by introducing a novel subleading B-meson distribution amplitude. The numerically dominant penguin amplitude arises from the soft-gluon radiation off the light up-quark loop rather than the counterpart charm-loop effect on account of the peculiar analytical behaviour of the short-distance hard-collinear function. Importantly the long-distance up-quark penguin contribution brings about the substantial cancellation of the known factorizable power correction possessing the same multiplication CKM parameters, thus enabling B d, s → γγ to become new benchmark probes of physics beyond the Standard Model.

Complete analysis on QED corrections to Bq → τ+τ−

“…We will apply the following three-parameter model for leading twist B-meson LCDA as used in [32,[36][37][38][39],…”

Structure-dependent QED effects in exclusive B-meson decays

“…It is worth noting that complex-valued soft functions, defined through operators that contain fields that are separated along different light-cone directions, will become relevant in various processes, in particular for the analysis of power corrections in the 1/m b expansion. In a recent example, such an HQET matrix element has been analyzed in the context of charm-loop contributions to the radiative decay Bd, s → γγ [47]. Interestingly, it has been shown that the support of the appearing three-particle soft function also extends to the negative axis, and the corresponding evolution kernel features the very same distributions H ± as in (79).…”

“…( 39), while the leading expressions for the jet functions J m (u, ω) and J A (u, ω, w) are given in Eqs. (47,48). The leading term for the function M A (w) can be found in Eq.…”

A guide to the QCD light-cone sum rules for b-quark decays

“…[147], we only mention that the power-suppressed soft contribution reveals a destructive interference with the LP effect. Another type of the subleading power contribution to B s, d → γγ from the soft gluon radiation off the quark loop has been recently computed [148] in terms of a factorization approach, with a generalized soft function defined by the HQET matrix element of the non-local operator with quark-gluon fields localized on different light-cone directions.…”

“…Hence OPEand LCSR-based calculations combined with hadronic dispersion relations will remain the only available continuum QCD tool. This combined approach, however, still has the following problems deserving dedicated studies: (i) the calculation in the spacelike q 2 region is strictly speaking not a regular OPE, because the charm loop contribution even at q 2 4m 2 c is complex valued, hence contains intermediate ccsq hadronic states (where q is a spectator quark in the B -meson); (ii) the usual three-particle DAs of B meson are kinematically not well suited for the correlators used for estimating soft-gluon contributions (see recent discussion in [148]). In this situation, an alternative method of calculation is desirable, e.g.…”