  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.
