The newly observed state $D_{s0}(2590)^{+}$

TL;DR

This paper investigates the decay properties of the newly observed $D_{s0}(2590)^{+}$ meson using a relativistic wave function approach, finding discrepancies with theoretical predictions and questioning its classification as a conventional $D_s(2^1S_0)^+$ state.

Contribution

The study introduces a model-independent overlap integral parameter and analyzes decay ratios to assess the nature of $D_{s0}(2590)^{+}$, challenging previous assumptions about its structure.

Findings

Decay width highly sensitive to the meson's mass.

Existing models underestimate the overlap integral compared to experimental data.

Current data suggests $D_{s0}(2590)^{+}$ may not be a conventional $D_s(2^1S_0)^+$ meson.

Abstract

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 newly observed $D_{s0}(2590)^{+}$ with supposing it 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 studied the overlap integral over the wave functions of initial and final states, here we parameterized it as $X$ which is model-independent, and the ratio $\Gamma/{|{\vec P_f}|^3}$, both 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 smaller than experimental data $0.585^{+0.015}_{-0.035}$ and $4.54^{+0.25}_{-0.52}$ MeV$^{-2}$. Further compared with $X^{ex}_{D^*(2010) \to D\pi}=0.540\pm0.009$, 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 it is early to say $D_{s0}(2590)^{+}$ is the conventional $D_s(2^1S_0)^+$ meson.