Abstract :
Using the QCD hybrid (moments-Laplace) sum rule, we show semi-analytically that, in the limit Mb → ∞, the q2 and Mb behaviours of the heavy-to-light exclusive (B → ϱ(π) semileptonic as well as the B → ϱγ rare) decay-form factors are universally dominated by the contribution of the soft light-quark condensate rather than that of the hard perturbative diagram. This phenomenon can invalidate the Mb-behaviour of the form factor from the conventional light cone approach. To leading order in 1Mb, the form factors behave as while they reproduce the HQET expectations at qmax2. The QCD-analytic q2 behaviour of the A1B form factor differs significantly from the naïve polar form, as it decreases for increasing q2. The other form factors increase slowly with q2 (they can be fitted by a polar form) as their q2-dependence is only contained in the non-leading terms in 1Mb. However, due to the previous non-leading q2-dependent terms, our results indicate that it is misleading to combine the polar form of the form factor with the HQET result at qmax2, in order to deduce the Mb-behaviour of the form factor at q2 = 0. Numerically, we extract with a good accuracy the ratios: VB(0)A1B(0) ⋍ A2B(0)A1B(0) ⋍ 1.11 ± 0.01, and A1B(0)F1B(0) ⋍ 1.18 ± 0.06; combined with the “world average” value of f+B(0) or/and F1B(0), these ratios lead to the decay rates: ΓB → πeν ⋍ (4.3 ± 0.7) × |Vub|2 × 1012 s−1, ΓB → ϱeνΓB → πeν ⋍ 0.9 ± 0.2, and to the ratios of the ϱ-polarised rates: Γ+Γ− ⋍ 0.20 ± 0.01, α≡2ΓLΓT − 1 ⋍ − (0.60±0.01).
