Structure of the neutral pion and its electromagnetic transition form factor

TL;DR

This paper calculates the neutral pion's electromagnetic transition form factor across all spacelike momenta using a continuum quantum field theory approach, aligning well with experimental data and connecting nonperturbative and perturbative QCD predictions.

Contribution

It provides a unified, self-consistent calculation of the pion's transition form factor, valence-quark distribution amplitude, and elastic form factor within a continuum framework, linking nonperturbative and perturbative QCD.

Findings

Agreement with experimental data from CELLO, CLEO, and Belle.

Connection between pion PDA and perturbative QCD predictions.

Highlighting the importance of dynamical chiral symmetry breaking scale.

Abstract

The $\gamma^\ast \gamma \to \pi^0$ transition form factor, $G(Q^2)$, is computed on the entire domain of spacelike momenta using a continuum approach to the two valence-body bound-state problem in relativistic quantum field theory: the result agrees with data obtained by the CELLO, CLEO and Belle Collaborations. The analysis unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA) and elastic electromagnetic form factor, and demonstrates, too, that a fully self-consistent treatment can readily connect a pion PDA that is a broad, concave function at the hadronic scale with the perturbative QCD prediction for the transition form factor in the hard photon limit. The normalisation of that limit is set by the scale of dynamical chiral symmetry breaking, which is a crucial feature of the Standard Model. Understanding of the latter will thus remain incomplete until definitive transition form factor data is available on $Q^2>10\,$GeV$^2$.