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arXiv · 1211.2829

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

B. El-Bennich·J. P. B. C. de Melo·T. Frederico
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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.

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B. El-Bennich, J. P. B. C. de Melo, T. Frederico. 2012-11-12. A combined study of the pion's static properties and form factors. https://doi.org/10.1007/s00601-013-0682-5

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