Semileptonic decays of $D$ and $D_s$ mesons in the relativistic quark model

TL;DR

This paper calculates the form factors for semileptonic decays of D and D_s mesons using a relativistic quark model, providing results that align well with experimental data and offering detailed decay rate predictions.

Contribution

It introduces a systematic relativistic quark model approach to compute form factors for D and D_s meson decays, including relativistic effects and wave function transformations.

Findings

Form factors are accurately calculated across the full q^2 range.

Results agree well with experimental data at q^2=0.

Decay rates and asymmetries are predicted with detailed comparison to other models.

Abstract

The form factors parameterizing the weak $D$ and $D_s$ transitions to light pseudoscalar and vector mesons are calculated in the framework of the relativistic quark model based on the quasipotential approach. The special attention is paid to the systematic account of the relativistic effects including transformation of the meson wave function from the rest to moving reference frame and contributions of the intermediate negative-energy states. The form factors are expressed through the overlap integrals of the meson wave functions, which are taken from previous studies of meson spectroscopy. They are calculated in the whole range of the transferred momentum $q^2$. Convenient parameterization of the form factors which accurately reproduces numerical results is given. The obtained values of the form factors and their ratios at $q^2=0$ agree well with the ones extracted form the experimental data. On the basis of these form factors and helicity formalism, differential and total semileptonic decay rates of $D$ and $D_s$ mesons as well as different asymmetries and polarization parameters are calculated. The detailed comparison of the obtained results with other theoretical calculations and experimental data is given.