Glueball spectral densities from the lattice

TL;DR

This paper presents a pioneering attempt to extract the scalar glueball spectral density in SU(3) gluodynamics using lattice gauge theory, addressing a key gap in nonperturbative QCD studies.

Contribution

It introduces a novel method to estimate the spectral density of glueballs directly from lattice simulations, which is not accessible through traditional approaches.

Findings

First estimate of scalar glueball spectral density from lattice QCD

Demonstrates feasibility of spectral density extraction in nonperturbative regime

Provides insights into the continuum structure of glueball states

Abstract

The propagator of a physical degree of freedom ought to obey a K\"{a}ll\'{e}n-Lehmann spectral representation, with positive spectral density. The latter quantity is directly related to a cross section based on the optical theorem. The spectral density is a crucial ingredient of a quantum field theory with elementary and bound states, with a direct experimental connection as the masses of the excitations reflect themselves into (continuum) $\delta$-singularities. In usual lattice simulational approaches to the QCD spectrum the spectral density itself is not accessed. The (bound state) masses are extracted from the asymptotic exponential decay of the two-point function. Given the importance of the spectral density, each nonperturbative continuum approach to QCD should be able to adequately describe it or to take into proper account. In this work, we wish to present a first trial in extracting an estimate for the scalar glueball spectral density in SU(3) gluodynamics using lattice gauge theory.