First lattice study of low-energy charmonium-hadron interaction

We study the scattering lengths of charmonia (J/ψ and ηc) with light hadrons (π, ρ, and N) by the quenched lattice QCD simulations on 243×48, 323×48, and 483×48 lattices with the lattice spacing a 0.068fm. The scattering length is extracted by using the Lüscher's phase-shift formula together with the measurement of the energy shift ΔE of two hadrons on the lattice. We find that there exist attractive interactions in all channels, J/ψ(ηc)-π, J/ψ(ηc)-ρ, and J/ψ(ηc)-N: The s-wave J/ψ-π (ηc-π) scattering length is determined as 0.0119±0.0039fm (0.0113±0.0035fm) and the corresponding elastic cross section at the threshold becomes 0.018-0.010+0.013mb (0.016-0.008+0.011mb). Also, the J/ψ-N (ηc-N) spin-averaged scattering length is 0.71±0.48fm (0.70±0.66fm), which is at least an order of magnitude larger than the charmonium-pion scattering length. The volume dependence of the energy shifts is also investigated to check the expected 1/L3 behavior of ΔE at a large spatial size L.