Probing <i>D</i> _<i>s</i> ^*-meson longitudinal twist-2 LCDA*

Abstract In this study, we continue an investigation of the semileptonic decays . First, we derive the moments of the -meson longitudinal leading-twist light-cone distribution amplitude (LCDA) based on QCD sum rules within the background field theory framework. Considering the contributions of the vacuum condensates up to dimension-six, its first ten non-zero -moments at the initial scale are , , , , , , , , , and . We also construct the -meson longitudinal leading-twist LCDA by using the light-cone harmonic oscillator model. Then, using the above moments, we fix the model parameters and using the least squares method and apply them to calculate transition form factors and that are derived using the QCD light-cone sum rules. In the large recoil region, we obtain , and . These form factors are then extrapolated to the allowed whole physical -region through the simplified series expansion. Finally, we obtain the branching fractions for the two decay channels of , and . In addition, we present the CKM matrix element by matching the LHCb Collaboration branching fraction, yielding a value of .