$J/\psi$ -nucleon scattering in $P_{c}^{+}$ pentaquarks channel

Two pentaquarks $P_{c}^{+}$ were discovered by LHCb collaboration as peaks in the proton-$J/\psi$ invariant mass. We perform the lattice QCD study of the scattering between $J/\psi$ meson and nucleon in the channels with $J^{P}=\frac{3}{2}^{+},\frac{3}{2}^{-}, \frac{5}{2}^{+}, \frac{5}{2}^{-}$, where $P_{c}^{+}$ was discovered. This is the first lattice simulation that reaches the energies $4.3-4.5~$GeV where pentaquarks reside. The higher partial waves $L>0$ are also explored for the first time. In this study we consider the single-channel approximation for scattering of $NJ/\psi$. Energies and eigenstates are extracted for the $NJ/\psi$ system at the zero total momentum for all six irreducible representations of the lattice irreducible representation. No significant energy shifts are observed. The number of eigenstates agrees with the number expected from non-interacting limit for scattering. This could possibly indicate that the $P_{c}$ resonances seen in experiment are a consequence of a coupling of the $NJ/\psi$ channel with other two-hadron channels.