## 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

##### Date

##### Authors

Wolfe, C. E.

Maltman, K.

##### Journal Title

##### Journal ISSN

##### Volume Title

##### Publisher

##### Abstract

##### Description

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.

Comment: 25 pages, 4 figures. Final published version. Main change is inclusion of a detailed discussion of the source of differences between the present work and M. Davier et al. (arXiv:0906.5443v3)

Comment: 25 pages, 4 figures. Final published version. Main change is inclusion of a detailed discussion of the source of differences between the present work and M. Davier et al. (arXiv:0906.5443v3)

##### Keywords

High Energy Physics - Phenomenology