# Study of the excited $1^-$ charm and charm-strange mesons

## TL;DR

This paper systematically studies excited charm and charm-strange mesons with potential 1^- spin-parity, using Bethe-Salpeter methods to analyze their decay properties and mixing schemes, providing insights into their structure and experimental signatures.

## Contribution

It introduces a detailed Bethe-Salpeter framework analysis of excited charm mesons, proposing specific mixing schemes and decay ratios to identify their quantum states.

## Key findings

- Two 1^- charm-strange mesons fit a 2^3S_1-1^3D_1 mixing scheme.
- Predicted decay ratio for D*_{s1}(2860) is approximately 0.62.
- D^*(2600)^0 likely a 2^3S_1 state with a small mixing angle.

## Abstract

We give a systematical study on the recently reported excited charm and charm-strange mesons with potential $1^-$ spin-parity, including the $D^*_{s1}(2700)^+$, $D^*_{s1}(2860)^+$, $D^*(2600)^0$, $D^*(2650)^0$, $D^*_1(2680)^0$ and $D^*_1(2760)^0$. The main strong decay properties are obtained by the framework of Bethe-Salpeter (BS) methods. Our results reveal that the two $1^-$ charm-strange mesons can be well described by the further $2^3\!S_1$-$1^3\!D_1$ mixing scheme with a mixing angle of $8.7^{+3.9}_{-3.2}$ degrees. The predicted decay ratio $\frac{\mathcal{B}(D^*K)}{\mathcal{B}(D~K)}$ for $D^*_{s1}(2860)$ is $0.62^{+0.22}_{-0.12}$.~$D^*(2600)^0$ can also be explained as the $2^3\!S_1$ predominant state with a mixing angle of $-(7.5^{+4.0}_{-3.3})$ degrees. Considering the mass range, $D^*(2650)^0$ and $D^*_1(2680)^0$ are more likely to be the $2^3\!S_1$ predominant states, although the total widths under both the $2^3\!S_1$ and $1^3\!D_1$ assignments have no great conflict with the current experimental data. The calculated width for LHCb $D^*_1(2760)^0$ seems about 100 \si{MeV} larger than experimental measurement if taking it as $1^3\!D_1$ or $1^3\!D_1$ dominant state $c\bar u$. The comparisons with other calculations and several important decay ratios are also present. For the identification of these $1^-$ charm mesons, further experimental information, such as $\frac{\mathcal{B}(D\pi)}{\mathcal{B}(D^*\pi)}$ are necessary.