Lattice operators for scattering of particles with spin

TL;DR

This paper develops lattice operators for simulating scattering processes involving particles with spin, providing three consistent methods and explicit expressions for various hadron combinations, enhancing the analysis of hadron interactions.

Contribution

It introduces three methods for constructing lattice operators for hadron scattering with spin, ensuring correct transformation properties and explicit expressions for different irreducible representations.

Findings

Operators are consistent across three methods.

Explicit expressions for all irreducible representations.

Operators correctly transform under symmetry operations.

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.