Models of Isospin Breaking in the Pion Form Factor: Consequences for the Determination of Pi_{\rho\omega}(m_rho^2) and (g-2)_mu/2

TL;DR

This paper analyzes recent high-precision measurements of the pion form factor to improve the understanding of rho-omega mixing and isospin-breaking effects, which are crucial for precise calculations of the muon's anomalous magnetic moment.

Contribution

It introduces a comprehensive analysis of model dependence in rho-omega mixing corrections and separates mixing effects from direct omega decay contributions.

Findings

Model dependence of rho-omega mixing correction exceeds experimental uncertainties.

Recent data enables separation of rho-omega mixing from direct omega decay effects.

Extracted Pi_{rho omega}(m_rho^2) is useful for meson exchange models in nuclear physics.

Abstract

We study the implications of several recent high-precision measurements of the pion form factor in the region of the rho-omega interference "shoulder" for (i) the extraction of the rho-omega mixing matrix element, Pi_{\rho\omega}(m_rho^2), and (ii) the evaluation of the isospin-breaking (IB) correction needed to incorporate hadronic tau decay data into the determination of the Standard Model expectation for the leading order hadronic contribution, [a_mu]_{had}^{LO}, to the anomalous magnetic moment of the muon, focussing, in the latter case, on the model-dependence of the rho-omega mixing component of the IB correction. We consider a range of different models for the broad rho contribution to the e^+e^- --> \pi\pi amplitude, applying these models to each experimental data set, and find that the model dependence of the rho-omega mixing correction is significantly larger than the uncertainty induced by experimental errors for any individual model. We also find that, for each such model, the recent data allows one to separate rho-omega mixing and direct omega --> \pi\pi coupling contributions to the amplitude, and hence to obtain a reasonably precise extraction of Pi_{\rho\omega}(m_rho^2), uncontaminated by direct omega --> \pi\pi coupling effects, for use in meson exchange model calculations of charge symmetry breaking in NN scattering.