Lattice calculation of the ${\eta }_c{\eta }_c$ and $J\mathrm{/}\psi J\mathrm{/}\psi$ s-wave scattering length

We calculate the s-wave scattering length in the $0^{+}$ sector of ${\eta }_c{\eta }_c$ and the $2^{+}$ sector of $J\mathrm{/}\psi J\mathrm{/}\psi$ 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{ü}scher finite size method. We observe sizable discretization effects and the results after a continuum extrapolation are $a_{{\eta }_c{\eta }_c}^{0^{+}}=-0.104(09)$ fm and $a_{J\mathrm{/}\psi J\mathrm{/}\psi }^{2^{+}}=-0.165(16)$ 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.