Instanton Effects in Three Flavor QCD

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.

22 pages, 2 figures. v3: reordered discussion of finite correlators and low energy constants, version published in PRD. v2: amended discussion of calculable vs incalculable effects for $N_f\le N$