Pion transition form factor in the Regge approach and incomplete vector-meson dominance

TL;DR

This paper explores the pion transition form factor using Regge models and incomplete vector-meson dominance, challenging traditional bounds and fitting experimental data with flexible theoretical models.

Contribution

It introduces a Regge-based approach to the pion form factor that accounts for violations of unitarity bounds and fits experimental data more accurately.

Findings

Incomplete vector-meson dominance explains data better than full dominance.

Regge models can satisfy or violate the Terazawa-West bound by parameter adjustment.

The photon momentum asymmetry significantly affects the analysis.

Abstract

The concept of incomplete vector-meson dominance and Regge models is applied to the transition form factor of the pion. First, we argue that variants of the chiral quark model fulfilling the chiral anomaly may violate the Terazawa-West unitarity bounds, as these bounds are based on unverified assumptions for the real parts of the amplitudes, precluding a possible presence of polynomial terms. A direct consequence is that the transition form factor need not necessarily vanish at large values of the photon virtuality. Moreover, in the range of the BaBar experiment, the Terazawa-West bound is an order of magnitude above the data, thus is of formal rather than practical interest. Then we demonstrate how the experimental data may be properly explained with incomplete vector-meson dominance in a simple model with one state, as well as in more sophisticated Regge models. Generalizations of the simple Regge model along the lines of Dominguez result in a proper description of the data, where one may adjust the parameters in such a way that the Terazawa-West bound is satisfied or violated. We also impose the experimental constraint from the Z -> pi0 gamma decay. Finally, we point out that the photon momentum asymmetry parameter may noticeably influence the precision analysis.