Stimulated by the newly reported doubly-charmed tetraquark state $T_{cc}^+$ by LHCb, we carry out a systematic investigation of the $S$-wave interactions between the charmed meson ($D,,D^{*}$) in $H$-doublet and the charmed meson ($D_{1},,D_{2}^{*}$)
in $T$-doublet by adopting the one-boson-exchange model. Both the $S$-$D$ wave mixing effect and the coupled channel effect are taken into account. By performing a quantitative calculation, we suggest that the $S$-wave $D^{*} D_{1}$ states with $I(J^{P})=0(0^{-},,1^{-})$ and the $S$-wave $D^{*}D_{2}^{*}$ state with $I(J^{P})=0(1^{-})$ should be viewed as the most promising candidates of the doubly-charmed molecular tetraquark states, and the $S$-wave $DD_{1}$ state with $I(J^{P})=0(1^{-})$, the $S$-wave $DD_{2}^{*}$ state with $I(J^{P})=0(2^{-})$, and the $S$-wave $D^{*}D_{2}^{*}$ state with $I(J^{P})=0(2^{-})$ are the possible doubly-charmed molecular tetraquark candidates. With the accumulation of experimental data at Run III and after High-Luminosity-LHC upgrade, these predicted doubly-charmed molecular tetraquark states can be accessible at LHCb in the near future.
Very recently, the LHCb Collaboration at the Large Hadron Collider at CERN observed new resonance $X(4630)$. The $X(4630)$ is decoded as a charmoniumlike molecule with hidden-strange quantum number well in the one boson exchange mechanism. Especially
, the study of its hidden-charmed decays explicitly shows the dominant role of $J/psiphi$ among all allowed hidden-charmed decays of $X(4630)$, which enforces the conclusion of $X(4630)$ as a charmoniumlike molecule. The discovery of the $X(4630)$ is a crucial step of constructing charmoniumlike molecule zoo.
Inspired by the observations of three $P_c$ states, we systematically investigate interactions between an $S$-wave charmed baryon $mathcal{B}_{c}^{(*)}=Lambda_c/Sigma_c/Sigma_c^{*}$ and an anticharmed meson $bar T=bar D_1/bar D_2^*$ with the one-pion
-exchange potential model and the one-boson-exchange potential model, and search for possible new types of $P_c$ states with the structures of $mathcal{B}_{c}^{(*)}bar T$. Both $S$-$D$ wave mixing and coupled channel effects are considered. Our results suggest that in some $mathcal{B}_{c}^{(*)}bar T$ systems there are ideal candidates of new types of $P_c$ states, i.e., the $Sigma_cbar{D}_1$ state with $I(J^P)=1/2(1/2^+)$, the $Sigma_cbar{D}_2^*$ state with $I(J^P)=1/2(3/2^+)$, the $Sigma_c^*bar{D}_1$ state with $I(J^P)=1/2(1/2^+)$, and the $Sigma_c^*bar{D}_2^*$ states with $I(J^P)=1/2(1/2^+, 3/2^+)$, and we suggest that these predicted new types of $P_c$ states can be detected in the process $Lambda_b^0 to psi(2S) p pi^{-}$. Meanwhile, we also extend our study to the interactions between an $S$-wave charmed baryon and a charmed meson in a $T$ doublet, and we predict a series of double-charm molecular pentaquarks.
