It is demonstrated that Gounaris-Sakurai model of the pion electromagnetic form factor is based on the P-wave iso-vector $\pi\pi$ scattering phase-shift given by a generalized effective-range formula of the Chew-Mandelstam type, valid exclusively only at the elastic region up to 1 GeV$^2$. Therefore the Gounaris-Sakurai model is justified to be used in a determination of the $\rho(770)$ meson parameters from existing data, however, in no case in a determination of the inelastic $\rho(1450)$ and $\rho(1700)$ resonance parameters.
We propose the pion electromagnetic form factor model found on the analyticity in the complex energy plane in which all three resonances $\rho(770)$, $\rho(1450)$, $\rho(1700)$ are defined on equal level as poles on unphysical sheets of the corresponding Riemann surface. The $\rho(770)$ meson parameters obtained in a such way coincide with the parameters obtained in the framework of the GKPY Roy-like equations analysis.
Volume 314 -
The European Physical Society Conference on High Energy Physics (EPS-HEP2017) -
QCD and Hadronic Physics (Poster Session). Scientific Secretary: Luciano Canton.
Generalized Gounaris-Sakurai formula and $\rho^0(770)$, $\rho^0(1450)$ and $\rho^0(1700)$ masses and widths
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Pre-published on:
January 18, 2018
Published on:
March 20, 2018
Abstract
DOI: https://doi.org/10.22323/1.314.0730
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Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.