Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD

TL;DR

This paper develops and tests a comprehensive set of multi-hadron operators with definite momentum for lattice QCD spectrum calculations, enabling more reliable extraction of excited state masses above multi-hadron thresholds.

Contribution

It introduces a systematic construction of spatially-extended single-hadron and two-hadron operators with symmetry projections, and demonstrates their effectiveness in lattice QCD simulations.

Findings

Reliable estimates of complex correlation functions achieved

Successful evaluation of glueball and mixing operators

Effective handling of challenging scalar channel computations

Abstract

Multi-hadron operators are crucial for reliably extracting the masses of excited states lying above multi-hadron thresholds in lattice QCD Monte Carlo calculations. The construction of multi-hadron operators with significant coupling to the lowest-lying multi-hadron states of interest involves combining single hadron operators of various momenta. The design and implementation of large sets of spatially-extended single-hadron operators of definite momentum and their combinations into two-hadron operators are described. The single hadron operators are all assemblages of gauge-covariantly-displaced, smeared quark fields. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. Tests of these operators on 24^3 x 128 and 32^3 x 256 anisotropic lattices using a stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing are presented. The method provides reliable estimates of all needed correlations, even those that are particularly difficult to compute, such as eta eta -> eta eta in the scalar channel, which involves the subtraction of a large vacuum expectation value. A new glueball operator is introduced, and the evaluation of the mixing of this glueball operator with a quark-antiquark operator, pi-pi, and eta-eta operators is shown to be feasible.