Helicity operators for mesons in flight on the lattice

TL;DR

This paper develops helicity-based operators for mesons with non-zero momentum on the lattice, enabling better identification of meson states and aiding resonance studies in lattice QCD.

Contribution

It introduces a new set of meson interpolating fields respecting lattice symmetries, derived from helicity operators, improving state identification at finite momentum.

Findings

Operators produce spectra close to diagonal in helicity

Superpositions rapidly isolate single-meson states

Effective for constructing meson-meson operators at finite momentum

Abstract

Motivated by the desire to construct meson-meson operators of definite relative momentum in order to study resonances in lattice QCD, we present a set of single-meson interpolating fields at non-zero momentum that respect the reduced symmetry of a cubic lattice in a finite cubic volume. These operators follow from the subduction of operators of definite helicity into irreducible representations of the appropriate little groups. We show their effectiveness in explicit computations where we find that the spectrum of states interpolated by these operators is close to diagonal in helicity, admitting a description in terms of single-meson states of identified J^{PC}. The variationally determined optimal superpositions of the operators for each state give rapid relaxation in Euclidean time to that state, ideal for the construction of meson-meson operators and for the evaluation of matrix elements at finite momentum.