The lattice QCD simulation of NJ=ψ and Nη c scattering is performed at m π ≃ 266 MeV in channels with all possible J P. This includes J P ¼ 3=2 AE and 5=2 AE where LHCb discovered P c ð4380Þ and P c ð4450Þ 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 noninteracting 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 the 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=ψðpÞNð−pÞ eigenstates are expected in the noninteracting limit due nonzero spins of J=ψ and N, and we establish all of them in the spectra.

We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for P N , P V , V N and N N scattering, where P , V and N denote pseudoscalar, vector and nucleon. Explicit expressions for operators are given for all irreducible representations at lowest two relative momenta. Each hadron has a good helicity in the first method. The hadrons are in a certain partial wave L with total spin S in the second method. These enable the physics interpretations of the operators obtained from the general projection method. The correct transformation properties of the operators in all three methods are proven. The total momentum of two hadrons is restricted to zero since parity is a good quantum number in this case.

Operators for simulating the scattering of two particles with spin are constructed. Three methods are shown to give the consistent lattice operators for PN, PV , V N and NN scattering, where P, V and N denote pseudoscalar meson, vector meson and nucleon. The projection method leads to one or several operators O Γ,r,n that transform according to a given irreducible representation Γ and row r. However, it gives little guidance on which continuum quantum numbers of total J, spin S, orbital momentum L or single-particle helicities λ 1,2 will be related with a given operator. This is remedied with the helicity and partial-wave methods. There first the operators with good continuum quantum numbers (J, P, λ 1,2 ) or (J, L, S) are constructed and then subduced to the irreps Γ of the discrete lattice group. The results indicate which linear combinations O Γ,r,n of various n have to be employed in the simulations in order to enhance couplings to the states with desired continuum quantum numbers. The total momentum of two hadrons is restricted to zero since parity P is a good quantum number in this case.34th annual "International Symposium on Lattice Field Theory"

Two pentaquarks P + c were discovered by LHCb collaboration as peaks in the proton-J/ψ invariant mass. We perform the lattice QCD study of the scattering between J/ψ meson and nucleon in the channels with, 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/ψ. Energies and eigenstates are extracted for the NJ/ψ 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/ψ channel with other two-hadron channels.

Operators for simulating the scattering of two particles with spin are constructed. Three methods are shown to give the consistent lattice operators for PN, PV , V N and NN scattering, where P, V and N denote pseudoscalar meson, vector meson and nucleon. The projection method leads to one or several operators O Γ,r,n that transform according to a given irreducible representation Γ and row r. However, it gives little guidance on which continuum quantum numbers of total J, spin S, orbital momentum L or single-particle helicities λ 1,2 will be related with a given operator. This is remedied with the helicity and partial-wave methods. There first the operators with good continuum quantum numbers (J, P, λ 1,2 ) or (J, L, S) are constructed and then subduced to the irreps Γ of the discrete lattice group. The results indicate which linear combinations O Γ,r,n of various n have to be employed in the simulations in order to enhance couplings to the states with desired continuum quantum numbers. The total momentum of two hadrons is restricted to zero since parity P is a good quantum number in this case.