Pions in Large-$N$ Quantum Chromodynamics

TL;DR

This paper develops an effective field theory for quarks, gluons, and pions in large-$N$ QCD, enabling calculations of hadronic phenomena at moderate energies with simplified renormalization properties.

Contribution

It introduces a large-$N$ effective field theory incorporating constituent quark masses, differing from pure QCD, and demonstrates its renormalizability at leading order in $1/N$.

Findings

Effective theory captures qualitative large-$N$ QCD features.

Renormalizable with finite terms at leading order.

Allows calculations at moderate energies.

Abstract

An effective field theory of quarks, gluons, and pions, with the number $N$ of colors treated as large, is proposed as a basis for calculations of hadronic phenomena at moderate energies. The qualitative consequences of the large $N$ limit are similar though not identical to those in pure quantum chromodynamics, but because constituent quark masses appear in the effective Lagrangian, the `t Hooft coupling in the effective theory need not be strong at moderate energies. To leading order in $1/N$ the effective theory is renormalizable, with only a finite number of terms in the Lagrangian.