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We study the scattering lengths of charmonia (J/psi and eta_c) with lighthadrons (pi, rho and N) by the quenched lattice QCD simulations on 24x24x24x48,32x32x32x48 and 48x48x48x48 lattices with the lattice spacing a = 0.068 fm. Thescattering length is extracted by using the Luscher's phase-shift formulatogether with the measurement of the energy shift Delta E of two hadrons on thelattice. We find that there exist attractive interactions in all channels,J/psi(eta_c)-pi, J/psi(eta_c)-rho and J/psi(eta_c)-N: The s-wave J/psi-pi(eta_c-pi) scattering length is determined as 0.0119+-0.0039 fm (0.0113+-0.0035fm) and the corresponding elastic cross section at the threshold becomes0.018+0.013-0.010 mb (0.016+0.011-0.008 mb). Also, the J/psi-N (eta_c-N)spin-averaged scattering length is 0.71+-0.48 fm (0.70+-0.66 fm), which is atleast an order of magnitude larger than the charmonium-pion scattering length.The volume dependence of the energy shifts is also investigated to check theexpected 1/L^3 behavior of Delta E at a large spatial size L.Comment: 17 pages, 30 figures included, version to appear in Phys. Rev.

First lattice study of low-energy charmonium-hadron interaction