${\eta }_c{\eta }_c$ and $J/\psi J/\psi$ scatterings from lattice QCD

Abstract

We investigate the $S$-wave ${\eta }_c{\eta }_c$ and $J/\psi J/\psi$ scattering in the $J^{PC}=(0,2{)}^{++}$ channels up to a center-of-mass energy of 6.6~GeV. The calculations are carried out at two unphysical pion masses, $m_{\pi }\approx 420$~MeV and 250~MeV, in $N_f=2$ lattice QCD. For each $m_{\pi }$, we extract the finite-volume energy levels on two lattices with an identical lattice spacing ($a\simeq 0.136\mathrm{fm}$) but different spatial volumes. Since the coupled-channel effects between the ${\eta }_c{\eta }_c$ and $J/\psi J/\psi$ channels are found to be negligible, we analyze the corresponding scattering properties using the single-channel L"{u}scher method. We find that the interactions in these dicharmonium systems are dominated by the quark rearrangement effect. In the $0^{++}$ channel, the near-threshold attraction in $J/\psi J/\psi$ and repulsion in ${\eta }_c{\eta }_c$ can be explained through the Fierz rearrangement. The attractive interaction in the ${}^1{S}_0$ $J/\psi J/\psi$ channel allows for the existence of a near-threshold scalar structure, which may correspond to the $X(6200)$. However, possible left-hand-cut effects due to light-hadron exchange prevent us from precisely determining the pole positions. In the $2^{++}$ channel, while the ${}^5{S}_2$ $J/\psi J/\psi$ system exhibits a repulsive interaction near threshold, the scattering amplitude has a Castillejo-Dalitz-Dyson zero at $\sqrt{s}=6.45\mathrm{GeV}$ and a resonance pole at $\sqrt{s}=[6.543(10)-i,0.548(34)/2]\mathrm{GeV}$ for $m_{\pi }\approx 420\mathrm{MeV}$ and $[6.538(13)-i,0.537(56)/2]\mathrm{GeV}$ for $m_{\pi }\approx 250\mathrm{MeV}$, where the uncertainties are statistical. This resonance may correspond to the $X(6600)$ (or $X(6400)$) reported by the ATLAS and CMS Collaborations. Our result supports its $2^{++}$ assignment, in agreement with the latest spin-parity determination by CMS.