We calculate the form factors for weak decays of B (s) and D (s) mesons to light pseudoscalar and vector mesons. To reveal the intimate connection between different decay modes and to be able to perform the calculations in the full physical q 2 -region we use a relativistic dispersion approach based on the constituent quark picture. This approach gives the form factors as relativistic double spectral representations in terms of the wave functions of the initial and final mesons. The form factors have the correct analytic properties and satisfy general requirements of nonperturbative QCD in the heavy quark limit.The disadvantages of quark models related to ill-defined effective quark masses and not precisely known meson wave functions are reduced by fitting the quark model parameters to lattice QCD results for the B → ρ transition form factors at large momentum transfers and to the measured total D → (K, K * )lν decay rates. This allows us to predict numerous form factors for all kinematically accessible q 2 values.

We study the accuracy of the bound-state parameters obtained with the method of dispersive sum rules, one of the most popular theoretical approaches in nonperturbative QCD and hadron physics. We make use of a quantum-mechanical potential model since it provides the only possibility to probe the reliability and the accuracy of this method: one obtains the bound-state parameters from sum rules and compares these results with the exact values calculated from the Schrödinger equation. We investigate various possibilities to fix the crucial ingredient of the method of sum rules -the effective continuum threshold -and propose modifications which lead to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method. Although the rigorous control of systematic uncertainties in the method of sum rules remains unfeasible, the application of the proposed procedures in QCD promises a considerable increase of the actual accuracy of the extracted hadron parameters.

Meson decays are considered within the constituent quark model, making use of the dispersion formulation of the model: Starting with spacelike momentum transfers q, meson transition form factors are expressed as relativistic invariant double spectral representations over the invariant masses of the initial and final QQ pairs. The form factors at timelike momentum transfers are obtained by performing the analytical continuation in q 2 . As a result, the form factors both in the scattering and decay regions are expressed through the light-cone wave functions of the initial and final hadrons. The constituent quark transition form factor is briefly discussed.