Efficient operators for studying higher partial waves

TL;DR

This paper introduces an efficient multi-hadron operator for extracting finite-volume spectra of higher partial waves in lattice QCD, reducing computational costs by requiring only two propagator inversions at fixed physical separation.

Contribution

The authors develop a new coordinate-space operator that simplifies the extraction of irreducible representations in lattice spectra, improving computational efficiency for studying higher partial waves.

Findings

Successfully isolated spectra of specific irreducible representations in a lattice QCD simulation.

Demonstrated the method's efficiency on a $24^3 imes 48$ lattice with heavy pion mass.

Validated the approach through a proof-of-principle study of the $ ho$ meson system.

Abstract

An extended multi-hadron operator is developed to extract the spectra of irreducible representations in the finite volume. The irreducible representations of the cubic group are projected using a coordinate-space operator. The correlation function of this operator is computationally efficient to extract lattice spectra. In particular, this new formulation only requires propagator inversions from two distinct locations, at fixed physical separation. We perform a proof-of-principle study on a $24^3 \times 48$ lattice volume with $m_\pi\approx 900$~MeV by isolating the spectra of $A^+_1$, $E^+$ and $T^+_2$ of the $\pi\pi$ system with isospin-2 in the rest frame.