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

Nonanalyticity of QCD with a θ term at θ=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 χ in pure SU(3) gauge theory. We obtain an upper bound for the symmetry breaking order parameter and, as a by-product, the value χ=[173.4(±0.5)(±1.2)(-0.2+1.1) MeV]4 at β=6 (a≅0.1 Fermi). The errors are the statistical error from our data, the one derived from the value used for ΛL and an estimate of the systematic error, respectively