Test of analyticity and unitarity for the pion form-factor data around the $\rho$ resonance

Abstract

High-statistics data on the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross section and the pion vector form factor have been obtained recently by several collaborations. Unfortunately, there are some tensions between different datasets, especially the most precise ones, which have not been resolved so far. Additional independent constraints on the data are therefore of interest. We consider a parametrization-free method of analytic extrapolation proposed recently, which is based on a mixed phase and modulus extremal problem and combines rigorous upper and lower bounds with numerical simulations to account for the statistical distributions of the input and output values. Spacelike data on the form factor and measurements of the modulus in the region $(0.65-0.71)$ GeV are used as input. In previous works, the formalism was applied for extrapolating the form factor to low energies. In the present work, we use it as a stringent and model-independent test of consistency with analyticity and unitarity for the high-statistics data around the $\rho$ resonance. The study reveals some inconsistencies, in particular below the $\rho$ peak the BABAR data are slightly higher than the band of extrapolated values, while above the $\rho$ peak all the data are situated at the lower edge of the band. The implications of the results on the two-pion vacuuum polarization contribution to the anomalous magnetic moment of the muon are briefly discussed.

10 pages, 7 figures

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Cited by in corpus (9)

• Constraints on the two-pion contribution to hadronic vacuum polarization
• New $\tau$-based evaluation of the hadronic contribution to the vacuum polarization piece of the muon anomalous magnetic moment
• Elucidating the effect of intermediate resonances in the quark interaction kernel on the time-like electromagnetic pion form factor
• Pion and Kaon box contribution to $a_{\mu }^{\text{HLbL}}$
• Chiral extrapolation of hadronic vacuum polarization
• Dispersion relations for the hadronic VVA correlator
• Pion scalar, vector and tensor form factors from a contact interaction
• Study of pion vector form factor and its contribution to the muon $(g-2)$
• Elucidating the rho-meson's role as intermediate resonance in the time-like electromagnetic pion form factor