Operators for scattering of particles with spin

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, VN and NN scattering, where P, V and N denote pseudoscalar meson, vector meson and nucleon. The projection method leads to one or several operators $O_{\Gamma,r,n}$ that transform according to a given irreducible representation $\Gamma$ 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 $\lambda_{1,2}$ 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 $(J,P,\lambda_{1,2})$ or $(J,L,S)$ are constructed and then subduced to the irreps $\Gamma$ of the discrete lattice group. The results indicate which linear combinations $O_{\Gamma,r,n}$ 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.Comment: 7 pages, talk presented at the 34th International Symposium on Lattice Field Theory, 24-30 July 2016, Southampton, U

Nucleon- J/ψ and nucleon- ηc scattering in Pc pentaquark channels from lattice QCD

The lattice QCD simulation of NJ/psi and N eta(c) scattering is performed at m(n) similar or equal to 266 MeV in channels with all possible J(P). This includes J(P) = 3/2(+/-) and 5/2(+/-) 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 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/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 noninteracting limit due nonzero spins of J/psi and N, and we establish all of them in the spectra