Reliable Semiclassical Computations in QCD

TL;DR

This paper investigates the reliability of semiclassical methods in QCD at zero temperature, establishing criteria for their validity based on operator product expansion and analyzing instanton effects.

Contribution

It provides a systematic criterion for when semiclassical QCD computations are reliable, especially distinguishing cases based on the number of flavors relative to colors.

Findings

Semiclassical calculations are valid for N_f > N.

Instanton effects are exponentially suppressed at large N.

A test for lattice QCD computations in the chiral limit is proposed.

Abstract

We revisit the question of whether or not one can perform reliable semiclassical QCD computations at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of a semiclassical calculation. For $N_f>N$, a systematic computation is possible; for $N_f<N$, it is not. $N_f=N$ is a borderline case. In our analysis, we see explicitly the exponential suppression of instanton effects at large $N$. As an application, we describe a test of QCD lattice gauge theory computations in the chiral limit.