Double pole structures of $X_1(2900)$ as the $P$-wave ${\bar{D}}^{\ast }{K}^{\ast }$ resonances

Abstract

We reveal the double pole structures of the manifestly exotic tetraquark state $X_1(2900)$ in the scenario of $P$-wave ${\bar{D}}^{\ast }{K}^{\ast }$ dimeson resonance. We find that the observed enhancement signal associated with $X_1(2900)$ in $B^{+}\to D^{+}{D}^{-}{K}^{+}$ by LHCb contains two $P$-wave poles denoted as $T_{cs1-}(2900)$ and $T_{cs1-}^{\prime }(2900)$, respectively. After considering the channel couplings among the $\bar{D}K$, ${\bar{D}}^{\ast }K$, $\bar{D}{K}^{\ast }$ and ${\bar{D}}^{\ast }{K}^{\ast }$ and the width of the $K^{\ast }$ meson, the masses and widths of the $S$-wave pole $T_{cs0+}(2900)$ and two $P$-wave poles $T_{cs1-}(2900)$ and $T_{cs1-}^{\prime }(2900)$ coincide with those of the $X_0(2900)$ and $X_1(2900)$ remarkably, which provides strong support for identifying $X_0(2900)$ and $X_1(2900)$ as ${\bar{D}}^{(\ast )}{K}^{(\ast )}$ dimeson states. Furthermore, we extensively calculate all $S$-wave and $P$-wave ${\bar{D}}^{(\ast )}{K}^{(\ast )}$ systems up to $J=3$ and predict four new isoscalar charmed-strange dimeson-type tetraquark states: an $S$-wave state $T_{cs1+}(2900)$ with quantum number $J^P=1^{+}$, three $P$-wave states $T_{cs1-}(2760)$ with $J^P=1^{-}$, $T_{cs0-}(2760)$ with $J^P=0^{-}$ and $T_{cs2-}(2900)$ with $J^P=2^{-}$. These near-threshold poles can be searched for at LHCb, Belle II and BESIII.

12 pages, 5 figures and 4 tables