# Semileptonic and nonleptonic decays of $D$ into tensor mesons with light-cone sum rule

## TL;DR

This paper calculates form factors for D meson decays into tensor mesons using light-cone sum rules, providing predictions for branching ratios that align well with experimental data and improve upon previous models.

## Contribution

It introduces a detailed calculation of D to tensor meson form factors up to twist-4, including all relevant mass terms, and compares the decay predictions with experimental results and other theoretical approaches.

## Key findings

- Semileptonic branching ratios around 10^{-5}.
- Nonleptonic decay predictions agree better with experiments than previous models.
- Provides comprehensive form factor calculations up to twist-4 for D to tensor meson decays.

## Abstract

Form factors of $D$ decays into $J^{PC}=2^{++}$ tensor mesons are calculated in the light-cone sum rules approach up to twist-4 distribution amplitudes of the tensor meson. The masses of the tensor mesons are comparable to that of the charm quark mass $m_c$; therefore all terms including powers of $m_T/m_c$ are kept out in the expansion of the two-particle distribution amplitude $\langle T|\bar q_{1\alpha}(x) \, q_{2\delta}(0)|0\rangle$. Branching ratios of the semileptonic $D \to T\,\mu \,\bar{\nu}_{\mu}$ decays and nonleptonic $D\to T~ P ~(P=K, \pi)$ decays are taken into consideration. A comparison is also made between our results and predictions of other methods and the existing experimental values for the nonleptonic case. The semileptonic branching ratios are typically of the order of $10^{-5}$, and the nonleptonic ones show better agreement with the experimental data in comparison to the Isgur-Scora-Grinstein-Wise predictions.