Aspects of QCD Current Algebra on a Null Plane

TL;DR

This paper explores the implications of QCD current algebra on a null plane, deriving sum rules related to chiral symmetry and connecting them to known physical sum rules and Regge limit constraints.

Contribution

It introduces a novel formulation of QCD current algebra on a light-like hyperplane and derives sum rules directly from the algebraic structure, linking them to established physical sum rules.

Findings

Derivation of sum rules from null-plane current algebra.

Connection of sum rules to known physical sum rules like Adler-Weisberger.

Equivalence of sum rules to algebraic constraints on forward S-matrix elements.

Abstract

Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial-vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial-vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler-Weisberger, Gerasimov-Drell-Hearn, Cabbibo-Radicatti and Fubini-Furlan-Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S-matrix elements in the Regge limit.