No abstract

We analyze the most recent data for the pion vector form factor in the timelike region, employing a modelindependent approach based on dispersion theory. We confirm earlier observations about the inconsistency of different modern high-precision data sets. Excluding the BaBar data, we find an updated value for the isospin-violating branching ratio B(ω → π + π − ) = (1.46 ± 0.08) × 10 −2 . As a side result, we also extract an improved value for the pion vector or charge radius, r 2 V = 0.6603 (5)(4) fm, where the first uncertainty is statistical as derived from the fit, while the second estimates the possible size of nonuniversal radiative corrections. In addition, we demonstrate that modern high-quality data for the decay η → π + π − γ will allow for an even improved determination of the transition strength ω → π + π − .

We argue that high-quality data on the reaction $$e^+e^-\rightarrow \pi ^+\pi ^-\eta $$ e + e - → π + π - η will allow one to determine the doubly-virtual form factor $$\eta \rightarrow \gamma ^*\gamma ^*$$ η → γ ∗ γ ∗ in a model-independent way with controlled accuracy. This is an important step towards a reliable evaluation of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. When analyzing the existing data for $$e^+e^-\rightarrow \pi ^+\pi ^-\eta $$ e + e - → π + π - η for total energies squared $$k^2>1\,\text {GeV}^2$$ k 2 > 1 GeV 2 , we demonstrate that the effect of the $$a_2$$ a 2 meson provides a natural breaking mechanism for the commonly employed factorization ansatz in the doubly-virtual form factor $$F_{\eta \gamma ^*\gamma ^*}(q^2,k^2)$$ F η γ ∗ γ ∗ ( q 2 , k 2 ) . However, better data are needed to draw firm conclusions.