Weak form factors for heavy meson decays: an update

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 analytical properties and satisfy all general requirements of QCD in the heavy quark limit. The disadvantages of the quark models, such as ill-defined effective quark masses and not precisely known meson wave functions, are greatly diminished by fitting the quark model form factors to lattice QCD results for the $B\to \rho$ transition form factors at large momentum transfers and to $D\to (K,K^*)l\nu$ experimental decay rates. This allows us to predict numerous form factors for all kinematically accessible $q^2$ values.