Rho-omega Mixing and the Pion Electromagnetic Form-Factor

We compare the predictions of a range of existing models based on the Vector Meson Dominance hypothesis with data on e^+ e^- -> pi^+ pi^$ and e^+ e^- -> mu^+ mu^- cross-sections and the phase and near-threshold behavior of the timelike pion form factor, with the aim of determining which (if any) of these models is capable of providing an accurate representation of the full range of experimental data. We find that, of the models considered, only that proposed by Bando et al. i...

Motivated by the planned measurements of the time-like electromagnetic proton form factors an exploratory study of the time-like electromagnetic pion form factor is presented in a formalism which describes mesons as Poincar\'e-invariant bound states. In the respective quark interaction kernel, beyond the gluon-intermediated interactions for valence-type quarks, non-valence effects are included by allowing the pions to couple back in a self-consistent manner to the quarks. Con...

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 an...

Recent results by Benayoun et al. comparing the predictions of a range of existing models based on the Vector Meson Dominance hypothesis are summarized and discussed. These are compared with data on e+ e- -> pi+ pi- and e+ e- -> mu+ mu- cross-sections and the phase and near-threshold behavior of the timelike pion form factor, with the aim of determining which (if any) of these models is capable of providing an accurate representation of the full range of experimental data. We...

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 effecti...

In this paper, we address the universality problem in the mass-mixing representation of vector meson dominance. First we stress the importance of using physical (mass eigenstate) fields in order to get the correct $q^2$ dependence of the pion form factor. Then we show that, when a direct coupling of the (proto-)photon to the pions is included, it is not necessary to invoke universality. Our method is similar to the delocalization idea in some deconstrunction theories.

We update our analysis of rho-omega mixing effects in the pion form factor to incorporate the recently published BaBar e^+e^- --> pi^+\pi^- cross-sections. The implications for tau-decay-based Standard Model estimates of the leading order hadronic contribution [a_\mu]_{had}^{LO}, to the anomalous magnetic moment of the muon, and for the extraction of the off-diagonal vector meson self-energy matrix element, Pi_{\rho\omega}(m_\rho^2), are discussed.

We reexamine the $\omega \to \pi^{0} \pi^{0} \gamma $ decay, adding the effect of $\omega-\rho$ mixing to the amplitude calculated with the aid of chiral perturbation theory and vector meson dominance. We predict the neutral decay to occur with a width of $\Gamma($\omega \to \pi^{0} \pi^{0} \gamma $) =(390\pm96) {\rm eV}$ and also analyze the effect of the $\omega-\rho$ mixing on the $\Gamma($\omega \to \pi^{0} \pi^{0} \gamma $)/ \Gamma($\omega \to \pi^{+} \pi^{-} \gamma $)$ ...

It is shown that the relative sign between the $NN\omega$ and $\pi\rho\omega$ coupling constants can be determined most sensitively from $\omega$ production processes in $NN$ collisions. Recent data on these reactions clearly favor the sign of the $\pi\rho\omega$ coupling constant which is opposite to that inferred from studies of the photoproduction reaction in combination with the vector meson dominance assumption and used by many authors. Implication of this finding in the...

The electromagnetic pion form-factor is calculated in a Bethe-Salpeter approach which accounts for pion rescattering. In the scattering kernel the pion-pion contact interaction from lowest-order chiral perturbation theory is considered together with an optional vector meson in the s-channel. Correspondingly the virtual photon couples to a two-pion state and optionally to the vector meson. It is shown that for reasonable ranges of input parameters the experimentally observed p...