Gluonic components of the pion and the transition form factor $\gamma^*\gamma^*\to\pi^0 $

TL;DR

This paper introduces a gluonic component in the neutral pion's structure, calculated via an effective Lagrangian and instanton liquid model, potentially explaining the anomalous behavior observed in the pion transition form factor at high photon virtuality.

Contribution

It presents a novel effective Lagrangian for pion-gluon coupling and quantifies its impact on the transition form factor using the instanton liquid model.

Findings

Gluonic contributions are significant in the pion transition form factor.

The model explains the BaBar anomaly at high photon virtuality.

Gluonic effects could be key to understanding pion structure at large energies.

Abstract

We propose an effective lagrangian for the coupling of the neutral pion with gluons whose strength is determined by a low energy theorem. We calculate the contribution of the gluonic components arising from this interaction to the pion transition form factor $\gamma^*\gamma^*\to\pi^0 $ using the instanton liquid model to describe the QCD vacuum. We find that this contribution is large and might explain the anomalous behavior of the form factor at large virtuality of one of the photons, a feature which was recently discovered by the BaBar Collaboration.