A combined study of the pion's static properties and form factors

TL;DR

This study uses a light-front model to analyze the pion's static properties and form factors, achieving good agreement with most data but highlighting challenges with BaBar results and the implications for QCD models.

Contribution

It provides a consistent framework for calculating pion observables and transition form factors, exploring the impact of model parameters on experimental data compatibility.

Findings

Results agree with Belle data on c*c transition form factor

BaBar data can be partially accommodated with relaxed constraints

Pion charge radius is smaller than experimental value

Abstract

We study consistently the pion's static observables and the elastic and \gamma*\gamma -> \pi^0 transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the \gamma*\gamma -> \pi^0 form factor at large q^2, yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40% smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data.