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Precision of chiral-dispersive calculations of π π scattering

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Peláez Sagredo, José Ramón and Ynduráin, F. J. (2003) Precision of chiral-dispersive calculations of π π scattering. Physical review D, 68 (7). ISSN 0556-2821

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Official URL: http://dx.doi.org/10.1103/PhysRevD.68.074005


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Abstract

We calculate the combination 2a⁰_(0)-5a₀(^2) (the Olsson sum rule) and the scattering lengths and effective ranges a₁,a₂^(2) and b₁,b₂^(I) dispersively (with the Froissart-Gribov representation) using, at low energy, the phase shifts for π π scattering obtained by Colangelo, Gasser, and Leutwyler (CGL) from the Roy equations and chiral perturbation theory, plus experiment and Regge behavior at high energy, or directly, using the CGL parameters for a's and b's. We find mismatch, both among the CGL phases themselves and with the results obtained from the pion form factor. This reaches the level of several (2 to 5) standard deviations, and is essentially independent of the detai᾿ls of the intermediate energy region (0.82 ≤ E ≤ 1.42 GeV) and, in some cases, of the high energy behavior assumed. We discuss possible reasons for this mismatch, in particular in connection with an alternate set of phase shifts.


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©2003 The American Physical Society.
One of us (F.J.Y.) is grateful to G. Colangelo, J. Gasser, and H. Leutwyler for very interesting discussions that triggered his interest in this subject. Both of us thank again Professor Leutwyler for a very useful critical reading of a preliminary draft, which, in particular, allowed us to correct a few inconsistencies. J.R.P. acknowledges support from the Spanish CICYT projects PB98-0782 and BFM2000 1326, as well as from the Marie Curie Fellowship, grant No. MCFI- 2001-01155.

Uncontrolled Keywords:Phase-shift analysis; Cross sections; Gev-c; Construction; Parameters; Unitarity; Amplitude; Existence; Equation; π&π
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:35528
Deposited On:05 Feb 2016 16:38
Last Modified:10 Dec 2018 15:09

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