Model independent bounds on the modulus of the pion form factor on the unitarity cut below the $\omega \pi$ threshold

Abstract

We calculate upper and lower bounds on the modulus of the pion electro magnetic form factor on the unitarity cut below the $\omega \pi$ inelastic threshold, using as input the phase in the elastic region known via the Fermi-Watson theorem from the $\pi \pi$ $P$-wave phase shift, and a suitably weighted integral of the modulus squared above the inelastic threshold. The normalization at $t=0$, the pion charge radius and experimental values at spacelike momenta are used as additional input information. The bounds are model independent, in the sense that they do not rely on specific parametrizations and do not require assumptions on the phase of the form factor above the inelastic threshold. The results provide nontrivial consistencychecks on the recent experimental data on the modulus available below the $\omega \pi$ threshold from $e^{+}{e}^{-}$ annihilation and $\tau$-decay experiments. In particular, at low energies the calculated bounds offer a more precise description of the modulus than the experimental data.

arXiv comment12 pages, 23 figures, prepared using EPJ style files; v2 corresponds to proofs version to appear in European Physical Journal C; extended discussion compared to v1

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Cited by in corpus (8)

• The branching ratio $\omega \to {\pi }^{+}{\pi }^{-}$ revisited
• Precise determination of the low-energy hadronic contribution to the muon $g-2$ from analyticity and unitarity: An improved analysis
• Pion electromagnetic form factor in the Covariant Spectator Theory
• Two-pion low-energy contribution to the muon $g-2$ with improved precision from analyticity and unitarity
• Constraints on the $\omega \pi$ form factor from analyticity and unitarity
• Dispersion relations for the hadronic VVA correlator
• Parametrization-free determination of the shape parameters for the pion electromagnetic form factor
• Test of analyticity and unitarity for the pion form-factor data around the $\rho$ resonance