The Triangle Anomaly in Triple - Regge Limits

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 U(1) anomaly is present as an infra-red divergence in the interactions generated by maximally non-planar Feynman diagrams. A multi-regge asymptotic dispersion relation formalism is developed which provides a systematic counting of anomaly contributions. The 48 triple discontinuities in the dispersion relation are of two kinds. The first kind are to one-particle inclusive cross-sections. The second kind contains the anomaly and the multi-regge theory has some special features, including a signature conservation rule. It is shown that the anomaly is present only in multiple discontinuities obtained from the maximally non-planar diagrams and that in the scattering of elementary quarks or gluons the signature and color parity of the exchanged reggeon states are such that the anomaly cancels. In more complicated scattering processes the anomaly need not cancel. Color parity is not conserved by vertices containing the anomaly and only anomalous color parity reggeon states are coupled. The extraction of a potential hadronic regge region S-Matrix, via the infra-red divergent amplitudes that appear when an anomalous color parity regggeon condensate is introduced, is briefly discussed. ∗Work supported by the U.S. Department of Energy, Division of High Energy Physics, Contracts W-31-109-ENG-38 and DEFG05-86-ER-40272 †[email protected]