Lattice calculation of the $\eta_c\eta_c$ and $J/\psi J/\psi$ s-wave scattering length

TL;DR

This study computes the s-wave scattering lengths for $ ext{eta}_c ext{eta}_c$ and $ ext{J}/ ext{psi} ext{J}/ ext{psi}$ charmonium pairs using lattice QCD, revealing repulsive interactions after continuum extrapolation.

Contribution

First lattice QCD calculation of these scattering lengths in specific charmonium channels using twisted mass ensembles and finite size method.

Findings

Scattering lengths are negative, indicating repulsive interactions.

Results show sizable discretization effects that are accounted for in continuum extrapolation.

Interaction between charmonia is repulsive in both studied channels.

Abstract

We calculate the s-wave scattering length in the $0^+$ sector of $\eta_c\eta_c$ and the $2^+$ sector of $J/\psi J/\psi$ using three $N_f=2$ twisted mass gauge ensembles with the lattice spacing $a=0.0667,0.085,0.098$ fm, respectively. The scattering lengths are extracted using the conventional L{\"u}scher finite size method. We observe sizable discretization effects and the results after a continuum extrapolation are $a^{0^+}_{\eta_c\eta_c}=-0.104(09)$ fm and $a^{2^+}_{J/\psi J/\psi}=-0.165(16)$ fm. The slight difference of light quark mass is ignored in this study. Our results indicate that the interaction between the two respective charmonia are repulsive in nature in both cases.