B∗Bπ(γ) couplings and D∗ → Dπ(γ)-decays within a 1M-expansion in full QCD

Abstract To leading order in α s , we evaluate the leading and non-leading 1 M b corrections to the B ∗ Bπ and B ∗ Bγ couplings using QCD spectral moment sum rules in the full theory. We find that, for large M b and contrary to the heavy-to-light B → π(ϱ)l v form factors, which are dominated by the soft light quark vacuum condensate, these couplings are governed by the hard perturbative graph, like other heavy-to-heavy transitions. We also find that for the B ∗ → Bγ , the 1 M b correction is mainly due to the perturbative and light quark condensate contributions originating from the graphs involving the heavy quark part of the electromagnetic current, which are essential for explaining the large charge dependence in the observed D ∗− → D − γ and D ∗0 → D 0 γ decays. Our best numerical predictions without any free parameters for the B ∗ - meson are: g B ∗− B 0 π − ⋍ 14±4 , Γ B ∗− →B − γ ⋍ (0.10±0.03) keV and the large charge dependence of the ratio: Γ B ∗− →B − γ Γ B ∗0 →B 0 γ ⋍2.5 . For the D ∗ - meson , we find: Γ D ∗− →D 0 π − ⋍ 1.54Γ D ∗0 →D 0 π 0 ⋍ (8±5) keV, Γ D ∗− → D − γ ⋍ (0.09 −0.07 +0.40 ) keV aand Γ D ∗0 →D 0 γ ⋍ (3.7±1.4) keV, where the branching ratios agree within the errors with the present data, while the total widths Γ D ∗0 →all ⋍ (11±4) keV and Γ D ∗− →all ⋍ (12±7) keV are much smaller than the present experimental upper limits.