Electroweak High-Energy Scattering and the Chiral Anomaly

The effect of perturbative QCD interactions on the high energy scattering of electroweak vector bosons, when the exchanged channel has pion quantum numbers, is considered. It is shown that transverse momentum diagrams appear that have couplings in which the chiral anomaly appears. As a consequence, there is a large transverse momentum divergence that produces an enhancement of the scattering amplitude by a power of the energy. If there is no cancelation from outside of the transverse momentum diagram framework, then the enhancement is present at O(αs) and involves a single large transverse momentum gluon. In higher orders, soft gluons can accompany the large transverse momentum anomaly process and cancelation of the resulting infra-red divergences is discussed. Odd (anomalous) color parity two gluon exchange, with one gluon carrying finite transverse momentum, also appears at O(αs). Color zero anomalous color parity multigluon exchange first appears at O(αs). The manipulation of a transverse momentum cut-off to replace the ultraviolet anomaly divergence by infra-red divergences that can lead to confinement and chiral symmetry breaking, is briefly discussed. Possible implications for electroweak symmetry breaking are also noted.