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 Bd,s-meson decay amplitudes in the heavy quark expansion by including the perturbative resummation of enhanced logarithms of mb/ΛQCD at the next-to-leading-logarithmic 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 at mathcal{O}left({alpha}_s^0right) by virtue of the operator identities due to the classical equations of motion. The higher-twist contributions to the Bd,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 current-current 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 Bd,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 Bd,s→ γγ 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.
Highlights
Decay amplitudes at subleading power where the resolved photon corrections parameterized by the corresponding light-cone distribution amplitudes (LCDAs) will be indispensable for the complete theoretical description
Employing the QCD factorization formalism, the double radiative Bd, s → γγ decay amplitudes have been computed at next-to-leading order (NLO) in the strong coupling and at leading power in the heavy quark expansion [16], where the two-loop b → (s, d) γ matrix elements of QCD penguin operators evaluated in [17, 18] were not taken into account and the factorization-scale independence for the obtained matrix elements γγ|Heff |Bd, s were not completely achieved at O(αs)
We further present the detailed expressions of the complete NLO QCD corrections to the b → sγ matrix elements obtained in [17] and the renormalization-group evolution functions emerged in the next-to-leading logarithmic (NLL) resummation improved factorization formulae of the double radiative Bq-meson decay amplitudes at leading power in appendices A and B, respectively
Summary
Applying the classical equations of motion [42], the effective weak Hamiltonian for b → qγγ can be reduced to the one for the radiative b → qγ transitions at leading order in the Fermi coupling GF [43]. Employing the unitarity relations of the CKM matrix elements, the relevant effective weak Hamiltonian can be written as. 2.2 The helicity and transversity form factors The exclusive radiative Bq → γγ decay amplitude can be expressed as. ∗ 2 correspond to the polarization vectors of the collinear and anti-collinear photons, respectively. In analogy to the radiative leptonic Bq → γdecays [47], the hadronic matrix element (2.3) at the lowest non-vanishing order in the electromagnetic interactions can be further brought into the following form. Applying the transversality conditions for the photon polarization vectors and the QED. The transversity decay amplitudes of Bq → γγ corresponding to the linearly polarized (anti)-collinear photon states can be constructed along the line of the analogous analysis for the charmless non-leptonic B → V V decays [48]. The left-handedness of the weak interaction Lagrangian and the helicity conservation for the strong interaction at high energy implies the well-known hierarchy structure
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