Precision calculations of the double radiative bottom-meson decays in soft-collinear effective theory

Abstract

Employing the systematic framework of soft-collinear effective theory (SCET) we perform an improved calculation of the leading-power contributions to the double radiative B d, s -meson decay amplitudes in the heavy quark expansion by including the perturbative resummation of enhanced logarithms of m b /Λ QCD at the next-to-leadinglogarithmic accuracy. We then construct the QCD factorization formulae for the subleading power contributions arising from the energetic photon radiation off the constituent light-flavour quark of the bottom meson at tree level. Furthermore, we explore the factorization properties of the subleading power correction from the effective SCET current ξ) by virtue of the operator identities due to the classical equations of motion. The higher-twist contributions to the B d, s → γγ helicity form factors from the two-particle and three-particle bottom-meson distribution amplitudes are evaluated with the perturbative factorization technique, up to the twist-six accuracy. In addition, the subleading power weak-annihilation contributions from both the currentcurrent and QCD penguin operators are taken into account at the one-loop accuracy. We proceed to apply the operator-production-expansion-controlled dispersion relation for estimating the power-suppressed soft contributions to the double radiative B d,s -meson decay form factors, which cannot be factorized into the light-cone distribution amplitudes of the heavy-meson and the resolved photon as well as the hard-scattering kernel calculable in perturbation theory canonically. Phenomenological explorations of the radiative B d, s → γ γ decay observables in the presence of the neutral-meson mixing, including the CP-averaged branching fractions, the polarization fractions and the time-dependent CP asymmetries, are carried out subsequently with an emphasis on the numerical impacts of the newly computed ingredients together with the theory uncertainties from the shape parameters of the HQET bottom-meson distribution amplitudes.

QCD factorization for the four-body leptonic $B$-meson decays

“…where the achieved expressions for the two form factors F 3PHT V, NLP and F 3PHT A, NLP are in accordance with the analogous NLP contributions to the double radiative bottom-meson decays in the kinematic limit n • p → 0 as displayed in Eq. (4.37) in [12].…”

“…Matching the achieved SCET representations (22) and (23) for T , ⊥ νµ onto the general decomposition (12) of the nonlocal matrix element T νµ with the requirement T νµ = T νµ + T ⊥ νµ leads to the desired expressions of the B − u → γ * ν form factors with a hard-collinear photon…”

“…• The "kinematic" power correction from the subleading component of the hard-collinear photon momentum n • p in the hadronic representation of the non-local matrix element T νµ as presented in (12). • The power suppressed local contribution from the energetic photon emission off the heavy bottom-quark field at tree level.…”

“…Following the computational strategy detailed in [12], we start with the tree-level contribution to the QCD correlation function (4) from the diagram 1(a)…”

“…It is therefore advantageous to investigate the four-body leptonic decays B − u → ¯ ν with , ∈ {e, µ} with three charged tracks for the sake of facilitating the experimental reconstruction of the bottom-meson candidates in the hadronic collision environment and circumventing the helicity suppression mechanism applied to the two-body leptonic decays simultaneously. From the QCD perspective, the rare leptonic decays B − u → ¯ ν with the invariant mass of the lepton pair ( ¯ ) of order m b Λ QCD will further provide us with the valuable information on the inverse moment of the twist-two B-meson distribution amplitude in heavy quark effective theory (HQET), which serves as an indispensable ingredient for the theory description of a variety of the exclusive B-meson decay observables [9][10][11][12][13][14][15][16] based upon the heavy quark expansion as well as the dispersion technique. Moreover, the exclusive four-body decays B − u → γ * (→ ¯ ) ν with the four-momentum (p µ ) of the intermediate photon state satisfying p 2 ∼ O(m 2 b ) are apparently of interest for addressing the "notorious" open issue of the systematic uncertainty due to the analytical continuation of the (local) operator product expansion (OPE) from the Euclidean to the Minkowskian domain in the practical applications [17][18][19].…”