High Energy Theorems at Large-N

TL;DR

This paper derives exact sum rules for QCD currents in the large-N limit using chiral symmetry, enabling precise construction of correlators and detailed analysis of pion form factors and scattering amplitudes.

Contribution

It introduces new sum rules for multiple QCD currents at large-N, linking meson properties and correlator behaviors with exact asymptotic relations.

Findings

Derived sum rules for products of QCD currents.

Established asymptotic behavior of QCD correlators.

Provided exact expressions for pion form factors and scattering amplitudes.

Abstract

Sum rules for products of two, three and four QCD currents are derived using chiral symmetry at infinite momentum in the large-N limit. These exact relations among meson decay constants, axialvector couplings and masses determine the asymptotic behavior of an infinite number of QCD correlators. The familiar spectral function sum rules for products of two QCD currents are among the relations derived. With this precise knowledge of asymptotic behavior, an infinite number of large-N QCD correlators can be constructed using dispersion relations. A detailed derivation is given of the exact large-N pion vector form factor and forward pion-pion scattering amplitudes.