Finite volume QCD at fixed topological charge

TL;DR

This paper derives formulas to correct for fixed topological charge effects in finite volume QCD, enabling the determination of topological susceptibility from correlation functions within a fixed sector.

Contribution

It introduces a saddle point expansion-based method to relate fixed topological sector measurements to true QCD expectation values, improving topological susceptibility estimation.

Findings

Derived correction formulas for fixed topological charge effects.

Proposed methods to extract topological susceptibility from fixed sector data.

Validated the approach using correlation functions in finite volume QCD.

Abstract

In finite volume the partition function of QCD with a given $\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of a 1/V expansion. Applying this formula, we propose a class of methods to determine the topological susceptibility in QCD from various correlation functions calculated in a fixed topological sector.