The 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 $\gamma^{*}\pi^0\gamma$ transition form factor, $G^{\gamma^* \pi^0 \gamma}(Q^2)$, whose normalization is intimately connected with the chiral anomaly and dynamical chiral symmetry breaking (DCSB). To compute such transition, we employ 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 strenght parameter $\xi$. 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 $\xi$ to produce the value of $G^{\gamma^* \pi^0 \gamma}(0)$ 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.