Analyticity in theta on the lattice and the large volume limit of the topological susceptibility

TL;DR

This paper investigates the non-analyticity of QCD with a  term at  by analyzing the large volume limit of topological susceptibility in pure SU(3) gauge theory, providing bounds and precise measurements.

Contribution

It provides an upper bound for the symmetry breaking order parameter and a precise value for the topological susceptibility in pure SU(3) gauge theory at a specific lattice coupling.

Findings

Upper bound for the symmetry breaking order parameter <Q>

Measured topological susceptibility =(173.4.5.2 .1 MeV)^4

Quantified statistical and systematic errors

Abstract

Non-analyticity of QCD with a \theta term at \theta=0 may signal a spontaneous breaking of both parity and time reversal invariance. We address this issue by investigating the large volume limit of the topological susceptibility $\chi$ in pure SU(3) gauge theory. We obtain an upper bound for the symmetry breaking order parameter <Q> and, as a byproduct, the value \chi=(173.4(+/- 0.5)(+/- 1.2)(+1.1 / -0.2) MeV)^4 at \beta=6 (a approx= 0.1 fermi). The errors are the statistical error from our data, the one derived from the value used for \Lambda_L and an estimate of the systematic error respectively.