Charmonium-like resonances with $J^{PC}=0^{++},2^{++}$ in coupled $D\bar{D}$, $D_s{\bar{D}}_s$ scattering on the lattice

Abstract

We present the first lattice investigation of coupled-channel $D\bar{D}$ and $D_s{\bar{D}}_s$ scattering in the $J^{PC}=0^{++}$ and $2^{++}$ channels. The scattering matrix for partial waves $l=0,2$ and isospin zero is determined using multiple volumes and inertial frames via Lüscher's formalism. Lattice QCD ensembles from the CLS consortium with $m_{\pi }\simeq 280$ MeV, $a\simeq 0.09$ fm and $L/a=24,32$ are utilized. The resulting scattering matrix suggests the existence of three charmonium-like states with $J^{PC}=0^{++}$ in the energy region ranging from slightly below $2m_D$ up to 4.13 GeV. We find a so far unobserved $D\bar{D}$ bound state just below threshold and a $D\bar{D}$ resonance likely related to ${\chi }_{c0}(3860)$, which is believed to be ${\chi }_{c0}(2P)$. In addition, there is an indication for a narrow $0^{++}$ resonance just below the $D_s{\bar{D}}_s$ threshold with a large coupling to $D_s{\bar{D}}_s$ and a very small coupling to $D\bar{D}$. This resonance is possibly related to the narrow $X(3915)$/${\chi }_{c0}(3930)$ observed in experiment also just below $D_s{\bar{D}}_s$. The partial wave $l=2$ features a resonance likely related to ${\chi }_{c2}(3930)$. We work with several assumptions, such as the omission of $J/\psi \omega$, ${\eta }_c\eta$ and three-particle channels. Only statistical uncertainties are quantified, while the extrapolations to the physical quark-masses and the continuum limit are challenges for the future.

Comments: 41 pages, 16 figures; JHEP version, corrected typo concerning the uncertainty in Fig 5c