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

Abstract

We give a systematical study on the recently reported excited charm and charm-strange mesons with potential $1^{-}$ spin-parity, including the $D_{s1}^{\ast }(2700{)}^{+}$, $D_{s1}^{\ast }(2860{)}^{+}$, $D^{\ast }(2600{)}^0$, $D^{\ast }(2650{)}^0$, $D_1^{\ast }(2680{)}^0$ and $D_1^{\ast }(2760{)}^0$. 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 $8.7_{-3.2}^{+3.9}$ degrees. The predicted decay ratio $\frac{\mathcal{B}(D^{\ast }K)}{\mathcal{B}(DK)}$ for $D_{s1}^{\ast }(2860)$ is $0.62_{-0.12}^{+0.22}$.~$D^{\ast }(2600{)}^0$ can also be explained as the $2^3{S}_1$ predominant state with a mixing angle of $-(7.5_{-3.3}^{+4.0})$ degrees. Considering the mass range, $D^{\ast }(2650{)}^0$ and $D_1^{\ast }(2680{)}^0$ 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 $D_1^{\ast }(2760{)}^0$ 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 $\frac{\mathcal{B}(D\pi )}{\mathcal{B}(D^{\ast }\pi )}$ are necessary.

Comments: 18 pages, 3 figures