$D^\star_{s1}(2700)^\pm$ and $D^\star_{sJ}(2860)^\pm$ revisited within the $^3P_0$ model

TL;DR

This paper revisits the nature of $D^ ext{star}_{s1}(2700)^ ext{pm}$ and $D^ ext{star}_{sJ}(2860)^ ext{pm}$ mesons using the $^3P_0$ decay model, exploring different mixing schemes and parameters to interpret their quantum states.

Contribution

It provides a detailed analysis of the decay properties of these mesons within the $^3P_0$ model, considering various mixing scenarios and parameter choices to clarify their possible quantum configurations.

Findings

$D^ ext{star}_{s1}(2700)^ ext{pm}$ likely not a pure $2^3S_1$ state.

$D^ ext{star}_{sJ}(2860)^ ext{pm}$ may be a $1^3D_3$ state.

Mixing schemes significantly affect the interpretation of these states.

Abstract

The strong decays of $D^\star_{s1}(2700)^\pm$ and $D^\star_{sJ}(2860)^\pm$ are investigated within the $^3P_0$ model. It is found that the interpretation of these two states depends on the mixing schemes and the ways of choices of the harmonic oscillator parameter $\beta$. If $D^\star_{s1}(2700)^\pm$ and $D^\star_{sJ}(2860)^\pm$ are two pure states, $D^\star_{s1}(2700)^\pm$ seems impossibly the $2^3S_1$ $D_s$, but may be the $1^3D_1$ $D_s$. $D^\star_{sJ}(2860)^\pm$ may be the $1^3D_3$. If there is mixing between the $2^3S_1$ and $1^3D_1$, $D^\star_{s1}(2700)^\pm$ may be the mixed $1^-$ state with a small mixing angle in the case of a special $\beta$ for each meson, and $D^\star_{sJ}(2860)^\pm$ is the orthogonal partner of $D^\star_{s1}(2700)^\pm$; $D^\star_{s1}(2700)^\pm$ may also be the mixed $1^-$ state with a large mixing angle based on a universal $\beta$ for all mesons, and $D^\star_{sJ}(2860)^\pm$ seems impossibly the orthogonal partner of $D^\star_{s1}(2700)^\pm$. Other uncertainties related to the choices of constituent quark masses and phase spaces are also explored.