Lattice operators for scattering of particles with spin

Abstract

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 PN, PV, VN and NN 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.

29 pages, updated to match the version published by JHEP. The relation between partial-wave and helicity operators is now provided (Eq. 4.13) and proved (Appendix D). Discussions on the applicability of the constructed operators and higher partial-waves have been extended