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.

Figure 1

Some diagrams of leading order in $1/N$ for processes involving pions and other mesons. Plain lines indicate quarks; wavy lines indicate gluons; dashed lines indicate pions; and crosses indicate insertions of quark bilinears.

Figure 2

Some diagrams of leading order in $1/N$ for baryon structure. Notation same as Fig. 1.