$P$-wave charmonium contribution to hidden-charm states from reanalysis of lattice QCD data

Abstract

We reanalyze, considering the contribution of $P$-wave charmonia, lattice data for the $D\bar{D}$-$D_s{\bar{D}}_s$ coupled-channel of S. Prelovsek et al. [JHEP 06, 035 (2021)] and $D{\bar{D}}^{\ast }$ systems of S. Prelovsek et al. [Phys. Rev. Lett. 111, 192001 (2013)] with $m_{\pi }\simeq 280$ and $266$ MeV, and $L=24a/32a$ ($a\simeq 0.09$ fm) and $L=16a$ ($a\simeq 0.1239(13)$ fm), respectively. The hidden-charm states with $J^{PC}=0^{++}$, $1^{++}$, and $2^{++}$ quantum numbers are then searched for. For $0^{++}$, the analysis reveals three poles in the $D\bar{D}$-$D_s{\bar{D}}_s$ coupled-channel amplitude, corresponding to three states. Two of these poles, located near the $D\bar{D}$ and $D_s{\bar{D}}_s$ thresholds, can be interpreted as mostly molecular states. A third pole above the $D_s{\bar{D}}_s$ threshold is originated from the $P$-wave ${\chi }_{c0}(2P)$ charmonium state. The number of poles found in the $D\bar{D}$-$D_s{\bar{D}}_s$ system is the same as that found in the original lattice analysis though the position of the third pole changes sizeably. In the $1^{++}$ sector, we find two poles in the complex energy plane. The first one is related to the molecular $X(3872)$ state, with a compositeness exceeding $90\%$, while the second one, stemming from the ${\chi }_{c1}(2P)$ charmonium, appears above the $D{\bar{D}}^{\ast }$ threshold and it likely corresponds to the recently discovered ${\chi }_{c1}(4010)$ state. In the $2^{++}$ sector, we also report two poles and find that the dressed ${\chi }_{c2}(2P)$ is lighter than the $D^{\ast }{\bar{D}}^{\ast }$ molecular state, with the dynamics of the latter closely related to that of the heavy-quark spin-symmetry partner of the $X(3872)$. Our exploratory study of the $1^{++}$ and $2^{++}$ sectors offers valuable insights into their dynamics, but given that the fits that we carry out are underconstrained, more lattice data are required to draw robust conclusions.

arXiv comment25 pages, 15 figures. Version to appear in Phys. Rev. D

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