Identifying $D_{sJ}^*(2860)$ as a four resonance states through strong decay analysis

Abstract: Experimentally observed excited strange charmed mesons $D_{s0}^*(2317)^{\pm}$, $D_{s1}(2460)^{\pm}$, $D_{s1}(2536)^{\pm}$, $D_{s2}^*(2573)^{\pm}$, $D_{s1}^*(2700)^{\pm}$, $D_{s1}^*(2860)^{\pm}$, $D_{s3}^*(2860)^{\pm}$, and $D_{sJ}(3040)^{\pm}$ are identified tentatively according to their spin, parity, and masses. Using the heavy quark effective theory in the leading order approximation, we study their strong decays to ground state charmed mesons plus light pseudoscalar mesons. The branching ratios are classified, $(D_{s0}^*(2317), D_{s1}(2460))$ as $(1^3P_0, 1P_1)$ and $(D_{s1}(2536), D_{s2}^*(2573))$ as $(1P_1^{\prime}, 1^3P_2)$, in heavy quark doublets. The $D_{s1}^*(2700)$ as $2^3S_1$ and its spin partner, $2^1S_0$ is still missing in the experiment. Its strong decay behavior is predicted. The assignment of $D_{sJ}^*(2860)$ as four resonance states $D_{s1}^*(2860)$, $D_{s2}^*(2860)$, $D_{s2}^{*\prime}(2860)$, $D_{s3}^*(2860)$ is favored, where for $D_{s3}^*(2860)^{\pm}$ the mass should be expected to higher than 2.86 GeV. The $D_{sJ}(3040)$ is more likely to be 2$P_1$ state. We construct the Regge trajectories of experimentally observed strange charmed mesons in $(M^2, J)$ and $(M^2, n_r)$ planes, which estimate the masses of $1^3D_3$, $1^3F_4$, $1D_2$, $1^1F_3$, $1D_2^{\prime}$, $1F_3^{\prime}$, $3^3S_1$, and $3P_1$ states with fixing the slopes and intercepts of the Regge lines. Moreover, the strong decay rates and the branching ratios of these higher excited states are also examined, which distinguished the dominant decay channels for these higher excited states. Our results could provide some important clues in LHCb, BESIII, KEK-B, and the forthcoming Belle II and $\overline{\mbox{\sffamily P}}${\sffamily ANDA} experiments.