Tensor Resonance in $J/\psi J/\psi$ Scattering from Lattice QCD

TL;DR

This study uses lattice QCD to analyze $J/$ scattering, revealing a near-threshold virtual state and a resonance consistent with observed exotic states, advancing understanding of quark interactions.

Contribution

First lattice QCD calculation of $J/$ scattering amplitudes with detailed resonance and virtual state analysis at different pion masses.

Findings

Identified a near-threshold virtual bound state in the $^1S_0$ channel.

Observed a resonance in the $^5S_2$ channel consistent with $X(6600)$.

Resonance parameters show little dependence on sea pion mass.

Abstract

The $S$-wave scattering amplitudes of $J/\psi J/\psi$ with quantum numbers $J^{PC} = 0^{++}$ and $2^{++}$ are determined up to 6600\,MeV using lattice QCD calculations at $m_\pi \approx 420$ and 250\,MeV. The ${}^1S_0$ $J/\psi J/\psi$ system exhibits a near-threshold attractive interaction, resulting in a virtual bound state with a binding energy of approximately 30-40\,MeV. In contrast, the ${}^5S_2$ $J/\psi J/\psi$ system exhibits a repulsive interaction near threshold. These behaviors are primarily dominated by the quark rearrangement effect. Most notably, a resonance is observed in the ${}^5S_2$ $J/\psi J/\psi$ channel, with a mass around 6540\,MeV and a width of approximately 540\,MeV. The extracted mass and width are consistent with the $X(6600)$ (or $X(6400)$) observed by the ATLAS and CMS collaborations, and show little dependence on the sea pion mass.