Semileptonic Decays of $D \to \rho l^+ \nu$ and $D_{(s)} \to K^\ast l^+ \nu$ from Light-Cone Sum Rules

TL;DR

This paper calculates form factors for semileptonic D meson decays to vector mesons using light-cone sum rules, revealing twist dominance patterns and discrepancies with experimental data, highlighting the importance of background effects.

Contribution

It provides leading-order light-cone sum rule predictions for D to vector meson semileptonic decays, including twist contributions and branching ratios, with a detailed analysis of convergence and discrepancies.

Findings

Twist-three contributions dominate some form factors.

Negligible twist-four and twist-five contributions.

Predicted branching ratios differ by 10-20% from experiments.

Abstract

We investigate the semileptonic decays of charmed mesons to light vector mesons within the framework of light-cone sum rules. Our calculation is performed at leading order in QCD coupling, incorporating contributions up to twist-five accuracy from both two-particle and three-particle light-cone distribution amplitudes. Transition form factors are predicted twist by twist to assess the convergence property of the operator product expansion. It is verified that the twist-four and twist-five contributions are indeed negligible for all the decays under consideration. Twist-three dominance is observed for some of the form factors, subject to heavy quark effective field theory interpretation. Branching ratios for the decays $D^+ \to \rho^0 \ell^+\nu_\ell$ , $D_s^+ \to K^{\ast0} \ell^+\nu_\ell$, $D^0 \to K^{\ast-} \ell^+\nu_\ell$ and $D^+ \to \bar{K}^{\ast0} \ell^+\nu_\ell$ are obtained, and a $10\%$--$20\%$ discrepancy from experimental measurements is found. Our finding indicates that the resonant-width and non-resonant QCD backgrounds effects should be potentially significant, implying the necessity to further implement their contributions in future precision studies of the semileptonic charm decays.