We determine $J^{ PC}=0^{ ++}$ and $2^{ ++}$ hadron-hadron scattering amplitudes in the charmonium energy region up to 4100 MeV using lattice QCD, a first-principles approach to QCD. Working at $m_\pi\approx 391$ MeV, more than 200 finite-volume energy levels are computed and these are used in extensions of the L\"uscher formalism to determine infinite-volume coupled-channel scattering amplitudes. We find that this energy region contains a single $\chi_{ c0}$ and a single $\chi_{ c2}$ resonance. Both are found as pole singularities on the closest unphysical Riemann sheet, just below 4000 MeV with widths around 70 MeV. The largest couplings are to kinematically-closed $D^* \bar{ D}^*$ channels in $S$-wave, and couplings to several decay channels consisting of pairs of open-charm mesons are found to be large and significant in both cases. Above the ground state $\chi_{ c0}$, no other scalar bound-states or near-$D\bar{ D}$ threshold resonances are found, in contrast to several theoretical and experimental studies.
Categories: hep-lat hep-ph