Bari-th/95-214 Heavy-to-light Meson Transitions in Qcd

I discuss QCD sum rules determinations of the form factors governing the decay B ! ( )` . For some of these form factors the computed dependence on the momentum transferred does not agree with the expectation from the nearest pole dominance hypothesis. Relations are observed among the form factors, that seem to be compatible with equations recently derived by B.Stech. The measurement of a number of color suppressed nonleptonic B decay rates could shed light on the accuracy of the calculation of these form factors and on the factorization approximation. Talk presented at the 6th International Symposium on Heavy Flavour Physics Pisa, Italy, June 6 10, 1995 1. Form factors of heavy-to-light meson transitions The exclusive semileptonic B decays to and play a prime role in the measurement of Vub. Let us consider, for example, the spectrum of B0 ! + : d ( B0 ! + ) dq2 = GF 24 3 jVubjjF 1 (q)jj~p (q)j (1) where ~ p (q ) is the pion three-momentum (at xed q) in the B meson rest frame. It is clear that a measurement of d dq would provide us with Vub once the form factor F 1 (q ), de ned by the hadronic matrix element (P = ): < P (p)j q bjB(p) >= (p + p0) F1(q) + M 2 B M P q2 [F0(q ) F1(q)]q (2) (q = p p, F0(0) = F1(0)) is known in the whole accessible range of q: 0 q q max = (MB M ). An equation analogous to (1) holds for B0 ! +  in terms of the form factors V and Ai de ned by the matrix element (P = ): < P (p; )j q (1 5)bjB(p) > = p p 2V (q ) MB +MP i(MB +MP )A1(q) +i A2(q) MB +MP ( p)(p + p0) + i ( p)P q2 q (A3(q ) A0(q)) (3) (A3(0) = A0(0) and A3(q) = MB+MP 2MP A1(q) MB MP 2MP A2(q ) ). Model independent relations can be derived for Fi, V and Ai in the in nite heavy quark mass limit at the point of zero recoil (q max) where and are at rest in the B meson rest frame [1]. For example, when mb !1 the following relations can be worked out for F1 and F0: F 1 (q 2 max) ' g 2f F̂ p MB +M (4) F 0 (q 2 max) ' F̂ f 1 p MB +O(M ) ; (5) eq.(4) describes the dominance of the B pole for F1 at zero recoil ( in the limit mb !1 F̂ is related to fB and fB , g is the rescaled B B strong coupling, and =MB MB); eq.(5) is the Callan-Treiman relation valid in the chiral limit. The above scaling relations, that could be used, e.g., to relate B ! ` to D ! ` at zero recoil, are not su cient to describe the form factors in the physical range of