Nucleon-$J/\psi$ and nucleon-$\eta_{c}$ scattering in $P_{c}$ pentaquark channels from LQCD

The lattice QCD simulation of $NJ/\psi$ and $N\eta_c$ scattering is performed at $m_\pi\simeq 266~$MeV in channels with all possible $J^P$. This includes $J^P=3/2^\pm$ and $5/2^\pm$ where LHCb discovered $P_c(4380)$ and $P_c(4450)$ pentaquark states in proton$-J/\psi$ 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/\psi $ 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 $J/\psi(p) N(-p)$ eigenstates are expected in the non-interacting limit due non-zero spins of $J/\psi$ and N, and we establish all of them in the spectra.