Partial-wave and helicity operators for the scattering of two hadrons in lattice QCD

TL;DR

This paper develops partial-wave and helicity operators for lattice QCD to identify the spins of two-hadron scattering states, accounting for boundary conditions and symmetry group representations.

Contribution

It introduces a systematic method to construct orthogonal partial-wave and helicity operators for lattice QCD, facilitating spin identification of scattering states.

Findings

Operators for zero and nonzero total momentum are constructed.

Orthogonality of operators is maintained under lattice symmetries.

Spin identification is achieved through dominant parent operators.

Abstract

Partial-wave operators for lattice QCD are developed in order to facilitate the identification of the spins of two-hadron scattering states corresponding to zero total momentum. Taking the periodic boundary conditions for lattice states into account, orthogonal sets of partial-wave operators for orbital angular momentum are identified. When combined with the intrinsic spins of the hadrons, orthogonal sets of parent operators for total angular momentum $J$ and projection $M$ are obtained. The parent operators are subduced to irreducible representations of the octahedral group in order to obtain descendant operators for use in lattice calculations. The descendant operators retain orthogonality with respect to $J$. The spin of a state can be identified by the spin of parent operators that dominate creation of the state. For nonzero total momentum, operators are developed for a range of helicities and they are subduced to irreducible representations corresponding to the different directions of total momentum. Sets of operators that include a sufficient range of helicities allow identification of spin $J$ when a state couples to operators with helicities less than or equal to $J$, but not to operators with higher helicities.