Possible molecular states of ${\bar{D}}^{\ast }{K}^{\ast }$ ($D^{\ast }{K}^{\ast }$) and the new exotic states $X_0(2900)$ and $X_1(2900)$ ($T_{cs0}^a(2900{)}^0$ and $T_{cs0}^a(2900{)}^{++}$)

Abstract

Two iso-singlet hadron states $X_0(2900)$ and $X_1(2900)$ with $J=0$ and 1 respectively, discovered by the LHCb collaboration in 2020, were identified as molecular bound states of ${\bar{D}}^{\ast }{K}^{\ast }$. Recently two structures $T_{cs0}^a(2900{)}^0$ and $T_{cs0}^a(2900{)}^{++}$ have been observed at the hadron spectra, one would suspect if they also are molecular states of $D^{\ast }$ and $K^{\ast }$. As long as they were of the molecular structures of $D^{\ast }{K}^{\ast }$, the hadron states must be in an iso-vector, namely $T_{cs0}^a(2900{)}^0$ and $T_{cs0}^a(2900{)}^{++}$ were $I_3=-1,1$ components of the iso-vector. If it is the case, the corresponding $T_{cs0}^a(2900{)}^{+}$ of ($I=1,I_3=0$) and $T_{cs0}^{{}^{\prime }a}(2900{)}^{+}$ of $I=0,I_3=0$ so far evade experimental observation, but should be found by the future experiments. To testify this ansatz, in this paper we study the possible molecular structures of ${\bar{D}}^{\ast }{K}^{\ast }$ and $D^{\ast }{K}^{\ast }$ within the Bethe-Salpeter (B-S) framework. With reasonable input parameters it is found that ${\bar{D}}^{\ast }{K}^{\ast }$ iso-scalar systems with $J^P=0^{+}$ and $1^{+}$ are solutions. The result supports the ansatz of $X_0(2900)$ ($X_1(2900)$) being molecular states of ${\bar{D}}^{\ast }{K}^{\ast }$. Whereas for the system of $D^{\ast }{K}^{\ast }$ with $I=1$ the corresponding B-S equation has no solution. Thus we can draw a clear conclusion that $T_{cs0}^a(2900{)}^0$ and $T_{cs0}^a(2900{)}^{++}$ should not be bound states of $D^{\ast }$ and $K^{\ast }$. The two structures observed by the LHCb collaboration may be caused by dynamics, such as the well-recognized triangle anomalies or other mechanisms.

Comments: 14 pages, 2 figures and 5 tables. Accepted by PRD. arXiv admin note: text overlap with arXiv:2112.14142