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Pions in Large-$N$ Quantum Chromodynamics

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.