$D_{s1}^{\star }(2700{)}^{\pm }$ and $D_{sJ}^{\star }(2860{)}^{\pm }$ revisited within the ${}^3{P}_0$ model

Abstract

The strong decays of $D_{s1}^{\star }(2700{)}^{\pm }$ and $D_{sJ}^{\star }(2860{)}^{\pm }$ are investigated within the ${}^3{P}_0$ 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 $D_{s1}^{\star }(2700{)}^{\pm }$ and $D_{sJ}^{\star }(2860{)}^{\pm }$ are two pure states, $D_{s1}^{\star }(2700{)}^{\pm }$ seems impossibly the $2^3{S}_1$ $D_s$, but may be the $1^3{D}_1$ $D_s$. $D_{sJ}^{\star }(2860{)}^{\pm }$ may be the $1^3{D}_3$. If there is mixing between the $2^3{S}_1$ and $1^3{D}_1$, $D_{s1}^{\star }(2700{)}^{\pm }$ may be the mixed $1^{-}$ state with a small mixing angle in the case of a special $\beta$ for each meson, and $D_{sJ}^{\star }(2860{)}^{\pm }$ is the orthogonal partner of $D_{s1}^{\star }(2700{)}^{\pm }$; $D_{s1}^{\star }(2700{)}^{\pm }$ may also be the mixed $1^{-}$ state with a large mixing angle based on a universal $\beta$ for all mesons, and $D_{sJ}^{\star }(2860{)}^{\pm }$ seems impossibly the orthogonal partner of $D_{s1}^{\star }(2700{)}^{\pm }$. Other uncertainties related to the choices of constituent quark masses and phase spaces are also explored.

7 pages, 5 tables, 12 figures, RevTex