Assignment of charmed-strange $D_{s0}(2590)^+$ and $D_{sJ}(3040)^+$

Abstract: Based on analyses of the mass and the strong decay features, $D_{s0}(2590)^+$ observed by LHCb collaboration is identified as a radial excitation of the pseudoscalar $D_s$, and $D_{sJ}(3040)^+$ observed by BaBar collaboration is identified as a radial excitation of $D_{s1}(2536)^\pm$. $D_{s0}(2590)^+$ is possibly a pure $D_{s}(2~^1S_0)$ meson, both basic $D_{s1}(2536)^\pm$ and radially excited $D_{sJ}(3040)^+$ are possibly the mixtures $D_s(nP_1)$ between spin triplet $D_s(n~^3P_1)$ and spin singlet $D_s(n~^1P_1)$. In this arrangement, their masses meet the linear behavior of the radial Regge trajectory very well. In the $^3P_0$ strong decay model, the decay channels of $D_{s0}(2590)^+$ are $D^{*0}K^+$ and $D^{*+}K^0$, the total decay width is predicted with $\Gamma=76.12$ MeV. The main decay channels of $D_{sJ}(3040)^+$ are $D^{0}K^+$/$D^{+}K^0$ and $D^{0}K^{+}$/$D^{*+}K^{*0}$, the total decay width is predicted with $\Gamma=283.46$ MeV. These numerical strong decay results are consistent with the experiment data and support our arrangement. The dimensionless strength creation parameter $\gamma$ plays an important role in the calculation, and $\gamma=9.57$ is fixed through a comparison of the predicted strong decay widths of $D^*_{s2}(2573)$ and $D^*_{s3}(2860)^{\pm}$ with experimental data.