Aspects of QCD Current Algebra on a Null Plane

Silas R. Beane; Timothy J. Hobbs

doi:10.1016/j.aop.2016.05.015

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arXiv · 1512.00098

Aspects of QCD Current Algebra on a Null Plane

Silas R. Beane·Timothy J. Hobbs

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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.

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Silas R. Beane, Timothy J. Hobbs. 2015-11-30. Aspects of QCD Current Algebra on a Null Plane. https://doi.org/10.1016/j.aop.2016.05.015

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