Operators for scattering of particles with spin

Abstract

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.

arXiv comment7 pages, talk presented at the 34th International Symposium on Lattice Field Theory, 24-30 July 2016, Southampton, UK

References in corpus (9)

• Toward the excited meson spectrum of dynamical QCD
• Two-particle multichannel systems in a finite volume with arbitrary spin
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• Resonance properties from the finite-volume energy spectrum
• Two-Nucleon Higher Partial-Wave Scattering from Lattice QCD
• Helicity operators for mesons in flight on the lattice
• Multiparticle States and the Hadron Spectrum on the Lattice
• Lattice operators for scattering of particles with spin
• Partial-wave and helicity operators for the scattering of two hadrons in lattice QCD