The Triangle Anomaly in Triple-Regge Limits

TL;DR

This paper investigates the triangle anomaly in reggeon interactions within the triple-Regge limit, revealing how the massless quark triangle anomaly manifests as an infra-red divergence and affects reggeon vertex properties.

Contribution

It introduces a systematic dispersion relation formalism to analyze anomaly contributions in reggeon interactions and explores their implications for color parity and signature conservation.

Findings

Anomaly appears as a chirality-violating infra-red divergence.

Physical anomaly contributions are linked to unphysical discontinuities.

Anomaly cancels in elementary quark or gluon scattering at lowest order.

Abstract

Reggeized gluon interactions due to a single quark loop are studied in the full triple-regge limit and in closely related helicity-flip helicity-pole limits. Triangle diagram reggeon interactions are generated that include local axial-vector effective vertices. It is shown that the massless quark triangle anomaly is present as a chirality-violating infra-red divergence in the interactions generated by maximally non-planar Feynman diagrams. An asymptotic dispersion relation formalism is developed which provides a systematic counting of anomaly contributions. The asymptotic amplitude is written as a sum over dispersion integrals of triple discontinuities, one set of which is unphysical and can produce chirality transitions. The physical-region anomaly appears in the generalized real parts, determined by multi-regge theory, of the unphysical discontinuities. The amplitudes satisfy a signature conservation rule that implies color parity is not conserved by vertices containing the anomaly. In the scattering of elementary quarks or gluons the signature and color parity of the exchanged reggeon states are such that the anomaly cancels. At lowest-order, it cancels in individual diagrams after the transverse momentum integrations are performed.