Chiral anomaly and the pion transition form factor: Beyond the cutoff

Abstract

In the presence of a momentum cutoff, effective theories seem unable to faithfully reproduce the so-called chiral anomaly in the Standard Model. A novel prospect to overcome this related issue is discussed herein via the calculation of the γ*π0γ transition form factor Gγ*π0γ(Q2), whose normalization is intimately connected with the chiral anomaly and dynamical chiral symmetry breaking (DCSB). To compute such transition, we employ a contact interaction model of quantum chromodynamics (QCD) under a modified rainbow ladder truncation, which automatically generates a quark anomalous magnetic moment term, weighted by a strength parameter ξ. This term, whose origin is also connected with DCSB, is interpreted as an additional interaction that mimics the complex dynamics beyond the cutoff. By fixing ξ to produce the value of Gγ*π0γ(0) dictated by the chiral anomaly, the computed transition form factor, as well as the interaction radius and neutral pion decay width, turn out to be comparable with QCD-based studies and experimental data.