Instanton Effects in Three Flavor QCD

TL;DR

This paper explores the role of small instantons in three-flavor QCD, extending previous findings to include real QCD, and discusses their implications for lattice computations and the u quark mass.

Contribution

It extends the analysis of instanton effects to N_f = N theories, including real QCD, and proposes their use for calibrating lattice calculations and testing the u quark mass.

Findings

Correlation functions vanish in perturbation theory but get dominant instanton contributions.

Instanton effects can be used to calibrate lattice computations at small quark mass.

Discussion of the u quark mass and its potential zero value on the lattice.

Abstract

Recently it was shown that in QCD-like theories with $N_f > N$, where $N_f$ is the number of light flavors and $N$ is the number of colors, there are correlation functions that vanish in perturbation theory and at short distances receive dominant, calculable contributions from small instantons. Here we extend the set of such objects to theories with $N_f = N$, which includes real QCD, and discuss their application as a calibration of lattice computations at small quark mass. We revisit the related issue of the $u$ quark mass and its additive renormalization by small instantons, and discuss an alternative test of $m_u=0$ on the lattice.