Dispersive analysis with ρ-ω mixing produces a two-parameter fit describing BESIII data on the J/ψ→π⁰γ* form factor from 0 to 2.8 GeV and extracts a (62 ± 21)° relative phase between strong and electromagnetic modes.
Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region
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abstract
The recently evaluated two-pion contribution to the muon g-2 and the phase of the pion electromagnetic form factor in the elastic region, known from \pi\pi scattering by Fermi-Watson theorem, are exploited by analytic techniques for finding correlations between the coefficients of the Taylor expansion at t=0 and the values of the form factor at several points in the spacelike region. We do not use specific parametrizations and the results are fully independent of the unknown phase in the inelastic region. Using for instance, from recent determinations, <r^2_\pi> = (0.435 \pm 0.005) fm^2 and F(-1.6 GeV^2)=0.243^{+0.022}_{-0.014}, we obtain the allowed ranges 3.75 GeV^{-4}\lesssim c \lesssim 3.98 GeV^{-4} and 9.91 GeV^{-6}\lesssim d \lesssim 10.46 GeV^{-6} for the curvature and the next Taylor coefficient, with a strong correlation between them. We also predict a large region in the complex plane where the form factor can not have zeros.
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Pedagogical review explaining how causality implies analyticity and its use in scattering amplitudes, form factors, and resonance extraction in hadronic physics.
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Dispersive analysis of the $J/\psi\to\pi^0 \gamma^\ast$ transition form factor with $\rho$-$\omega$ mixing effects
Dispersive analysis with ρ-ω mixing produces a two-parameter fit describing BESIII data on the J/ψ→π⁰γ* form factor from 0 to 2.8 GeV and extracts a (62 ± 21)° relative phase between strong and electromagnetic modes.
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Pedagogical review explaining how causality implies analyticity and its use in scattering amplitudes, form factors, and resonance extraction in hadronic physics.