Nucleon-J/ψ and nucleon-η_c scattering in P_c pentaquark channels from LQCD

The lattice QCD simulation of NJ/ψ and Nη_c scattering is performed at m_π≃ 266MeV in channels with all possible J^P. This includes J^P=3/2^± and 5/2^± where LHCb discovered P_c(4380) and P_c(4450) pentaquark states in proton-J/ψ decay. This is the first lattice simulation that reaches the energies 4.3-4.5 GeV where pentaquarks reside. Several decay channels are open in this energy region and we explore the fate of P_c in the one-channel approximation in this work. Energies of eigenstates are extracted for the nucleon-charmonium system at zero total momentum for all quantum numbers, i.e. six lattice irreducible representations. No significant energy shifts are observed. The number of the observed lattice eigenstates agrees with the number expected for non-interacting charmonium and nucleon. Thus, we do not find any strong indication for a resonance or a bound state in these exotic channels within one-channel approximation. This possibly indicates that the coupling of NJ/ψ channel with other two-hadron channels might be responsible for P_c resonances in experiment. One of the challenges of this study is that up to six degenerate J/ψ(p) N(-p) eigenstates are expected in the non-interacting limit due non-zero spins of J/ψ and N, and we establish all of them in the spectra.