The newly observed state $D_{s0}(2590)^{+}$ and width of $D^*(2007)^0$

We choose the Reduction Formula, PCAC and Low Energy Theory to reduce the $S$ matrix of a OZI allowed two-body strong decay involving a light pseudoscalar, the covariant transition amplitude formula with relativistic wave functions as input is derived. After confirm this method by the decay $D^*(2010)\to D\pi$, we study the state $D^*(2007)$, and the full width $\Gamma_{\rm{th}}(D^*(2007))=53.8\pm0.7$ keV is obtained. Supposing the newly observed $D_{s0}(2590)^{+}$ to be the state $D_s(2^1S_0)^+$, we find its decay width $\Gamma$ is highly sensitive to the $D_{s0}(2590)^{+}$ mass, which result in the meaningless comparison of widths by different models with various input masses. Instead of width, we introduce a model independent quantity $X$ and the ratio $\Gamma/{|{\vec P_f}|^3}$, which are almost mass independent, to give us useful information. The results show that, all the existing theoretical predictions $X_{D_s(2S) \to D^*K}=0.25\sim 0.41$ and $\Gamma/{|{\vec P_f}|^3}=0.81\sim1.77$ MeV$^{-2}$ are much smaller than experimental data $0.585^{+0.015}_{-0.035}$ and $4.54^{+0.25}_{-0.52}$ MeV$^{-2}$. Further compared with $X^{ex}_{D^*(2010) \to D\pi}=0.58$, the current data $X^{ex}_{D_s(2S) \to D^*K}=0.585^{+0.015}_{-0.035}$ is too big to be an reasonable value, so to confirm $D_{s0}(2590)^{+}$ as the state $D_s(2^1S_0)^+$, more experimental studies are needed.