Abstract
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.
Highlights
The study of the exotic hadronic states, which cannot fit into the conventional meson and baryon [1,2], has become one of the central topics at the precision frontier of the hadron physics
Borrowing the research experience of the hidden-charm molecular tetraquark states [3,4], we can make a realistic study of the doubly charmed molecular tetraquark candidates composed of the charmed meson in H-doublets and the charmed meson in T-doublets
For the S-wave DDÃ2 state with IðJPÞ 1⁄4 1ð2−Þ, there do not exist the bound state solution until we increase the cutoff parameter to be around 2.2 GeV, even if we take into account the contribution of the S-D wave mixing effect and
Summary
The study of the exotic hadronic states, which cannot fit into the conventional meson and baryon [1,2], has become one of the central topics at the precision frontier of the hadron physics. The experimental collaborations reported the more and more observations of charmoniumlike states with higher mass [10], which results in the discussion of whether they can be regarded as the hidden-charm molecular tetraquark states by checking the interactions of an S-wave charmed meson and a P-wave anticharmed meson [3,4]. The study of the interactions between the charmed meson in H-doublets and the charmed meson in T-doublets is the natural extension of former studies of the interactions involving two S-wave charmed mesons [12,13,14] (see Fig. 1), which has inspired the observation of the doubly charmed þ cc state to some extent [11] These possible doubly charmed molecular tetraquark states were considered with the light vector meson exchange in Ref.
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