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Test of analyticity and unitarity for the pion form-factor data around the � resonance

Ananthanarayan, B and Caprini, I and Das, D (2020) Test of analyticity and unitarity for the pion form-factor data around the � resonance. In: Physical Review D, 102 (9).

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Official URL: https://dx.doi.org/10.1103/PhysRevD.102.096003


High-statistics data on the e+e-��+�- cross section and the pion vector form factor have been obtained recently by several collaborations. Unfortunately, there are some tensions between different data sets, 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 � resonance. The study reveals some inconsistencies, in particular, below the � peak, the BABAR data are slightly higher than the band of extrapolated values, while above the � peak, all the data are situated at the lower edge of the band. The implications of the results on the two-pion vacuum polarization contribution to the anomalous magnetic moment of the muon are briefly discussed. © 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.

Item Type: Journal Article
Publication: Physical Review D
Publisher: American Physical Society
Additional Information: The copyright of this article belongs to American Physical Society
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 15 Jan 2021 09:26
Last Modified: 15 Jan 2021 09:26
URI: http://eprints.iisc.ac.in/id/eprint/67312

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