Speaker
Description
By solving the Muskhelishvili-Omnes integral equations, coupled-channel effects are taken into account for the scalar form factors of semi-leptonic $D\to\pi$ and $D\to \bar{K}$ transitions, denoted by $f_0^{D\to\pi}$ and $f_0^{D\to\bar{K}}$, respectively. As inputs, we employ the unitarized amplitudes from chiral effective theory for the intermediate region, while, at high energy, proper asymptotic conditions are imposed. The scalar form factors are expressed in terms of Omnes matrix multiplied by a vector polynomials. We reduce the number of subtraction constants by performing matching to the scalar form factors which are derived in chiral perturbation theory at tree-level. The simulated lattice QCD data for $f_0^{D\to\pi}$ and $f_0^{D\to\bar{K}}$ can be well described simutaneously. We predict the scalar form factors corresponding to $D\to\eta$, $D_s\to \bar{K}$ and $D_s\to \eta$ transitions, which can be checked in future by lattice QCD so as to improve precision determination of the Cabibbo-Kobayashi-Maskawa elements of $|V_{cd}|$ and $|V_{cu}|$. The approach used in this work can be straitforwardly extended to the semi-leptonic decays of $B$ mesons whenever new experimental or lattice QCD data come up for scattering at or above the threshold region.
