Helicity operators for mesons in flight on the lattice

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 JPC. Lastly, 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.