The pion form factor at timelike momentum transfers in a dispersion approach

TL;DR

This paper develops a dispersion-based model for the pion form factor at timelike momentum transfers, incorporating vector meson dominance and mixing effects, and analyzes experimental data to extract meson properties.

Contribution

It introduces a dispersion approach that accounts for momentum-dependent $ ho$-meson decay constants and mixing effects, providing a refined description of the pion form factor.

Findings

The effective $ ho$-meson decay constant depends on momentum transfer.

The model successfully fits experimental data from $e^+e^-$ and $ au$ decay.

Extracted meson masses and coupling constants agree with known values.

Abstract

We consider a model with $\rho\pi\pi$, $\rho KK$, and gauge-invariant $\rho\gamma$ couplings and obtain the pion form factor $F_\pi$ at timelike momentum transfers by resummation of pion and kaon loops. We use a dispersion representation for the loop diagrams and analyse ambiguities related to subtraction constants. The resulting representation for $F_\pi$ is shown to have the form of the conventional vector meson dominance formula with one important distinction - the effective $\rho$-meson decay constant $f^{\rm eff}_\rho$ turns out to depend on the momentum transfer. For the electromagnetic pion form factor we include in addition the $\rho-\omega$ mixing effects. We apply the representations obtained to the analysis of the data on the pion form factors from $e^+e^-$ annihilation and $\tau$ decay and extract the $\rho^-$, $\rho^0$ and $\omega$ masses and coupling constants.