Abstract
The on-shell matrix elements, or couplings {g}_{H{H}^{ast}left({H}_1right)upgamma} , describing the B{(D)}_q^{ast } → B(D)qγ and B1q → Bqγ (q = u, d, s) radiative decays, are determined from light-cone sum rules at next-to-leading order for the first time. Two different interpolating operators are used for the vector meson, providing additional robustness to our results. For the D*-meson, where some rates are experimentally known, agreement is found. The couplings are of additional interest as they govern the lowest pole residue in the B(D) → γ form factors which in turn are connected to QED-corrections in leptonic decays B(D) → ℓ overline{nu} . Since the couplings and residues are related by the decay constants {f}_{H^{ast}left({H}_1right)} and {f}_{H^{ast}left({H}_1right)}^T , we determine them at next-leading order as a by-product. The quantities left{{f}_{H^{ast}}^T,{f}_{H_1}^Tright} have not previously been subjected to a QCD sum rule determination. All results are compared with the existing experimental and theoretical literature.
Highlights
In this paper, we consider the on-shell couplings gHH∗γ and gHH1γ, for B(D)∗q → B(D)qγ and B1q → Bqγ where q = u, d, s, from light-cone sum rules (LCSR) [1, 2].1 Our own interest in these couplings is two-fold
In this work we have determined the couplings of photons to heavy-light quark mesons (2.3) from light-cone sum rules at next-to-leading order in αs at the twist-1,2 level, at leading order in twist-3, and partial twist-4.14 We have investigated the effect of various duality regions and have found the impact to be small
The residues related to the B → γ form factors, as in (2.4) and (2.5), are given in table 6
Summary
Our own interest in these couplings is two-fold They describe the decay H∗(H1) → Hγ; secondly they appear as residues of the m2H∗(H1)-pole for the H → γ form factor e.g. This Lagrangian can be used at small recoil and has to be supplemented by higher order couplings away from it As mentioned earlier, another point of interest in the couplings arises from their relation to pole-residues of the B → γ form factors [3] (and cf appendix A).. The computation of the correlation function is the same as for the B → γ form factor; we refer the reader to [3] for details of the calculation and turn to the double dispersion relation
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