Coupled-channel $D^{\ast }{K}^{\ast }-D_s^{\ast }\rho$ interactions and the origin of $T_{c\bar{s}0}(2900)$

Abstract

Motivated by the recent observation of $T_{c\bar{s}0}(2900{)}^0$ and $T_{c\bar{s}0}(2900{)}^{++}$ in the $D_s\pi$ invariant mass distributions, we investigate $D^{\ast }{K}^{\ast }$ interactions in a coupled-channel approach. We show that the relativistic corrections could be significant for the energy far away from the threshold. Within the hidden local symmetry formalism, a sizable attraction interaction is found in the $J=0$ isospin triplet sector that can form a bound or a virtual state, which is consistent with the experimentally observed $T_{c\bar{s}0}(2900)$. By reproducing a $D_s^{\ast }\rho$-$D^{\ast }{K}^{\ast }$ bound/virtual state with the pole mass equal to that of the $T_{c\bar{s}0}(2900)$ measured by LHCb in the sector $(I,J)=(1,0)$, we determine the unknown parameter in the loop function, and then search for possible poles in the sectors of $I=1$, $J=1,$ 2 and $I=0$, $J=0$, 1, 2. The predicted resonances provide a useful reference for the future experimental studies of the $(C,S)=(1,1)$ systems and can be also helpful to unravel the nature of the $T_{c\bar{s}0}(2900)$.10

Comments: 10 pages, 6 figures, 3 tables