A Fluctuation Theory of Topological Susceptibility

Abstract

We investigate the long-range statistical correlations, whereby discuss the nature of the undermining interacting/ noninteracting domains and associated phase transitions under variations of the quark mass and the mass scale that corresponds to renormalized pion masses and the dimensions of an ensemble of slab sub-volumes of an arbitrary simulated lattice. The purpose of this paper is to compute the system's stability and its phase structures when it's model parameters vary infinitesimally. In particular, we focus on the stability properties and phases of an arbitrary (2+1) flavor QCD configuration under fluctuations of its parameters. In order to investigate the nature of statistical and systematic errors, and the presence of noises in the system, we explore fluctuation theory equivalences of the slab sub-volume method of computing the topological susceptibility with its low energy ChPT counterpart. Hereby, we find that the ChPT configurations always correspond to a non-interacting statistical basis in the space of the quark mass and the mass scale that corresponds to renormalized pion masses. The second system as an ensemble of finite slab sub-volumes of a simulated lattice turns out to be generically interacting under fluctuations of the slab dimensions. However, it yields an ill-defined degenerate system in the infinitesimal limit of slab parameters. It is worth mentioning that implications of the intrinsic geometric analysis are well suited towards the modeling based understanding of the gluonic topological charge density fluctuations, quark mass dependence and long auto-correlation of the global topology. Finally, we discuss the stability properties of sub-volume simulated lattice improvements towards the understanding of QCD vacua, the behavior of UV divergences, finite-volume effects, statistical precision, simultaneous measurements, and associated quantum channel measurements.