  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.
