Form factor relations for heavy-to-light meson transitions: tests of the Quark Model predictions

In the case of heavy-to-light weak meson transitions, a Quark Model derivation leads to very general relations between the form factors that parametrize the hadronic matrix elements. We investigate to what extent these form factor relations remain a good approximation, beyond the Quark Model. In heavy-to-light pseudoscalar-to-vector meson transitions, a simple argument shows that the V-A structure of the weak interaction leads to a strong suppression of the helicity h=+1 amplitude - an effect that has been confirmed experimentally by the CLEO Collaboration, with a full angular analysis of the B -> K* J/psi decay. We show that the theoretical predictions, in terms of the hadronic form factors, can accommodate the suppression of the h=+1 amplitude, only if the Quark Model relations are verified. Moreover, the form factor relations also allow us to predict the ratio of the two remaining helicity amplitudes, with h=0 and h=-1; here too, there is excellent agreement with the CLEO data for the B -> K* J/psi decay. In the future, similar experimental tests can be carried out, with a few advantages, using the semileptonic decay B -> rho l- nu_l. The Quark Model relations can also be tested against the predictions for the hadronic form factors, from the more powerful theoretical methods of Lattice QCD and Light Cone Sum-Rules. The excellent agreement points once again to the validity of the form factor relations, beyond the Quark Model framework where they were derived.