Heavy-to-light scalar form factors from Muskhelishvili-Omnes dispersion relations

By solving the Muskhelishvili-Omnes integral equations, the scalar form factors of the semileptonic heavy meson decays D → π anti lν_l, D → anti K anti lν_l, anti B → πl anti ν_l and anti B_s → Kl anti ν_l are simultaneously studied. As input, we employ unitarized heavy meson-Goldstone boson chiral coupled-channel amplitudes for the energy regions not far from thresholds, while, at high energies, adequate asymptotic conditions are imposed. The scalar form factors are expressed in terms of Omnes matrices multiplied by vector polynomials, which contain some undetermined dispersive subtraction constants. We make use of heavy quark and chiral symmetries to constrain these constants, which are fitted to lattice QCD results both in the charm and the bottom sectors, and in this latter sector to the light-cone sum rule predictions close to q² = 0 as well. We find a good simultaneous description of the scalar form factors for the four semileptonic decay reactions. From this combined fit, and taking advantage that scalar and vector form factors are equal at q² = 0, we obtain vertical stroke V_cd vertical stroke = 0.244 ± 0.022, vertical stroke V_cs vertical stroke = 0.945 ± 0.041 and vertical stroke V_ub vertical stroke = (4.3 ± 0.7) x 10^-3 for the involved Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. In addition, we predict the following vector form factors at q² = 0: vertical stroke f₊^D→η(0) vertical stroke = 0.01 ± 0.05, vertical stroke f₊^D_s→K(0) vertical stroke = 0.50 ± 0.08, vertical stroke f₊^D_s→η(0) vertical stroke = 0.73 ± 0.03 and vertical stroke f₊ ^{anti B→η}(0) vertical stroke = 0.82 ± 0.08, which might serve as alternatives to determine the CKM elements when experimental measurements of the corresponding differential decay rates become available. Finally, we predict the different form factors above the q²-regions accessible in the semileptonic decays, up to moderate energies amenable to be described using the unitarized coupledchannel chiral approach. (orig.)