Soft contribution to B→γℓνℓ and the B-meson distribution amplitude

Abstract

The B → γℓν ℓ decay at large energies of the photon receives a numerically important soft-overlap contribution which is formally of the next-to-leading order in the expansion in the inverse photon energy. We point out that this contribution can be calculated within the framework of heavy-quark expansion and soft-collinear effective theory, making use of dispersion relations and quark-hadron duality. The soft-overlap contribution is obtained in a full analogy with the similar contribution to the γ * γ → π transition form factor. This result strengthens the case for using the B → γℓν ℓ decay to constrain the B-meson distribution amplitude and determine its most important parameter, the inverse moment λ B .1. The decay B → γℓν ℓ at large photon energy E γ is one of the simplest hadronic processes that can be studied using QCD factorization [1,2,3,4]. This method involves the B-meson light-cone distribution amplitude (DA) [5,6,7,8,9,10] as the main nonperturbative input at the leading order in the heavy quark expansion. The B → γℓν ℓ decay 1 is therefore best suited for determining the parameters of the B-meson DA and presents a close analog to the photon-pion transition γ * γ → π with one highly-virtual (Q 2 ) and one real photon, which is used for the determination of the pion DA. The theoretical challenges are also similar, and in both cases are mainly due to the necessity to have a quantitative control over the corrections that are subleading in the expansion parameter, 1/m b ∼ 1/(2E γ ) or 1/Q 2 , and, in general, are not factorizable. The purpose of this letter is to emphasize this connection and suggest a method to calculate the soft contribution to B → γℓν ℓ , which closely follows the technique used in γ * γ → π.A recent summary of the theory status of B → γℓν ℓ can be found in [11]. The decay amplitude1 to distinguish this important decay channel we suggest to call it photoleptonic B-decay.

Factorization and dispersion relations for radiative leptonic B decay

“…An alternative approach to evaluate the power suppressed contributions in B → γ ν was proposed in [6] by employing the dispersion relations and quark-hadron duality, where the "soft" two-particle correction to the B → γ form factors was computed at leading order in the perturbative expansion. The main purpose of this paper is to extend the calculation performed in [6] by computing the subleading power contributions to the B → γ ν amplitude from the two-particle DA φ…”

Search forB+→ℓ+νℓγdecays with hadronic tagging using the full Belle data sample

“…[4] for different true values of λ B . We identify the central value of ξ(Eγ ) with the one obtained for λ B = 300 MeV.…”

“…The soft correction for the light quark ξ(E γ ) constitutes the largest uncertainty in the form factors and it has been calculated in Ref. [4] to a higher precision. The most stringent limits for the decay process have been reported by the BaBar collaboration [5] at 90% confidence level with B(B + → e + ν e γ) < 17 × 10 −6 , B(B + → µ + ν µ γ) < 26 × 10 −6 , B(B + → + ν γ) < 15.6 × 10 −6 , and a partial branching fraction ∆B(B + → + ν γ) < 14 × 10 −6 for photons with energies higher than 1 GeV.…”

Radiative leptonic $$B_c\rightarrow \gamma \ell {\bar{\nu }}$$ B c → γ ℓ ν ¯ decay in effective field theory beyond leading order

“…It is interesting to notice that the counterpart in B sector, B → γ ν, has been widely discussed as regards the understanding of the B meson light-cone distribution amplitudes [59][60][61][62][63]. The small branching fraction of B c → γ ν can be compensated by the high luminosity at the ongoing hadron colliders and the experimental facilities under design.…”