Glueball masses from ratios of path integrals

TL;DR

This paper introduces a method to compute glueball masses in Yang-Mills theory using ratios of path integrals and a multi-level Monte Carlo scheme, successfully applied to SU(3) at two lattice spacings.

Contribution

It generalizes previous symmetry-based approaches to decompose the partition function, enabling efficient computation of glueball properties with reduced numerical cost.

Findings

Computed the mass of the lightest glueball with vacuum quantum numbers.

Determined the multiplicity of the lightest glueball states.

Performed calculations at two different lattice spacings (0.17 and 0.12 fm).

Abstract

By generalizing our previous work on the parity symmetry, the partition function of a Yang-Mills theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang-Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at two values of the lattice spacing (0.17 and 0.12 fm).