Dominance of the light-quark condensate in the heavy-to-light exclusive decays

Abstract

Using the QCD {\it hybrid} (moments-Laplace) sum rule, we show $semi$-$analytically$ that, in the limit $M_b \rar \infty$, the $q^2$ and $M_b$ behaviours of the heavy-to-light exclusive ($\bar B\rar \rho~(\pi)$ semileptonic as well as the $ B\rar \rho\gamma$ rare) decay--form factors are $universally$ dominated by the contribution of the soft light-quark condensate rather than that of the hard perturbative diagram. The QCD-analytic $q^2$ behaviour of the form factors is a polynomial in $q^2/M^2_b$, which mimics quite well the usual pole parametrization, except in the case of the $A_1^B$ form factor, where there is a significant deviation from this polar form. The $M_b$-dependence of the form factors expected from HQET and lattice results is recovered. We extract with a good accuracy the ratios: $V^B(0)/A^B_1(0) \simeq A^B_2(0)/A^B_1(0) \simeq 1.11\pm 0.01$, and $A^B_1(0)/F^B_1(0) \simeq 1.18 \pm 0.06$; combined with the ``world average" value of $f^B_+(0)$ or/and $F^B_1(0)$, these ratios lead to the decay rates: $\Gamma_{\bar B\rar \pi e\bar \nu} \simeq (4.3 \pm 0.7)