Identification of $D_{s1}(2933)$ as the $2P_1$ state in the quark model

Abstract

We investigate the internal structure of the newly observed charm-strange meson $D_{s1}(2933{)}^{+}$, which was reported by the LHCb Collaboration in $B^0\to D^{+}{D}^{-}{K}^{+}{\pi }^{-}$, in the quark model by treating it as the $2P_1$ state of the $c\bar{s}$ system. The coupled-channel corrections to the ${}^1{P}_1$--${}^3{P}_1$ mass matrix are evaluated through the two-point self-energy loops involving the $D{K}^{\ast }$, $D^{\ast }K$, $D^{\ast }{K}^{\ast }$, $D_s\varphi$, $D_s^{\ast }\varphi$ and $D_s^{\ast }\eta$ intermediate channels. Requiring the corrected eigenvalue to reproduce the measured mass yields a cutoff scale of about $0.82\mathrm{GeV}$, a $2P_1^{\prime }$ partner state at $3012\mathrm{MeV}$, and a mixing angle of $-12.9^{\circ }$ that deviates significantly from the heavy-quark ideal-mixing angle. Moreover, the predicted three-body branching ratio fraction $R_{\text{th}}=1.98$ for $D_{s1}(2933)\to D^{+}{K}^{+}{\pi }^{-}$ via the $D{K}^{\ast }$ and $D_2^{\ast }K$ intermediate states is consistent with the experimental value $R_{\text{exp}}=1.27_{-0.95}^{+1.29}$ within uncertainties. These results support the assignment of $D_{s1}(2933)$ as the $2P_1$ excited state of the $c\bar{s}$ system with final state interactions.

arXiv commentRevtex, 9 pages, 2 eps figures and 4 tables