Lattice calculation of the \(\eta _c\eta _c\) and \(J/\psi J/\psi \) s-wave scattering length

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 pion mass \(300{-}365\) MeV and lattice spacing \(a=0.0667,0.085,0.098\) fm, respectively. The scattering lengths are extracted using the conventional Lüscher 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.