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Title: Improved Pion Pion Scattering Amplitude from Dispersion Relation Formalism

Abstract

Pion-pion scattering amplitude is obtained from Chiral Perturbation Theory at one- and two-loop approximations. Dispersion relation formalism provides a more economic method, which was proved to reproduce the analytical structure of that amplitude at both approximation levels. This work extends the use of the formalism in order to compute further unitarity corrections to partial waves, including the D-wave amplitude.

Authors:
 [1];  [2];  [3]
  1. Universidade Federal de Mato Grosso do Sul (Brazil)
  2. Universidade Federal do Rio de Janeiro (Brazil)
  3. Universidade do Estado do Rio de Janeiro (Brazil)
Publication Date:
OSTI Identifier:
20798162
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 814; Journal Issue: 1; Conference: 11. international conference on hadron spectroscopy, Rio de Janeiro (Brazil), 21-26 Aug 2005; Other Information: DOI: 10.1063/1.2176570; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; APPROXIMATIONS; CHIRAL SYMMETRY; CHIRALITY; CORRECTIONS; D WAVES; DISPERSION RELATIONS; PERTURBATION THEORY; PION-PION INTERACTIONS; UNITARITY

Citation Formats

Cavalcante, I. P., Coutinho, Y. A., and Borges, J. sa. Improved Pion Pion Scattering Amplitude from Dispersion Relation Formalism. United States: N. p., 2006. Web. doi:10.1063/1.2176570.
Cavalcante, I. P., Coutinho, Y. A., & Borges, J. sa. Improved Pion Pion Scattering Amplitude from Dispersion Relation Formalism. United States. doi:10.1063/1.2176570.
Cavalcante, I. P., Coutinho, Y. A., and Borges, J. sa. Sat . "Improved Pion Pion Scattering Amplitude from Dispersion Relation Formalism". United States. doi:10.1063/1.2176570.
@article{osti_20798162,
title = {Improved Pion Pion Scattering Amplitude from Dispersion Relation Formalism},
author = {Cavalcante, I. P. and Coutinho, Y. A. and Borges, J. sa},
abstractNote = {Pion-pion scattering amplitude is obtained from Chiral Perturbation Theory at one- and two-loop approximations. Dispersion relation formalism provides a more economic method, which was proved to reproduce the analytical structure of that amplitude at both approximation levels. This work extends the use of the formalism in order to compute further unitarity corrections to partial waves, including the D-wave amplitude.},
doi = {10.1063/1.2176570},
journal = {AIP Conference Proceedings},
number = 1,
volume = 814,
place = {United States},
year = {Sat Feb 11 00:00:00 EST 2006},
month = {Sat Feb 11 00:00:00 EST 2006}
}
  • ABS>A method is proposed for using relativistic dispersion relations, together with unitarity. to determine the pion nucleon scattering amplitude. The usual dispersion relations by themselves are not sufficient, and a representation is assumed which exhibits the analytic properties of the scattering amplitude as a function of the energy snd the momentum transfer. Unitarity conditions for the two reactions pi + N yields pi + N and N + N bar yields 2 pi will be required, and they will be approximated by neglecting states with more than two particles. The method makes use of an iteration procedure analogous to thatmore » used by Chew and Low for the corresponding problem in ihe static theory. One has to introduce two coupling constants; the pion-pion coupling constant can be found by fitting the sum of the threshold scattering lengths with experiment. It is hoped that this method avoids some of the formal difficulties of the TammDancoff and Bethe-Salpeter methods and. in particular. the existence of ghost states. The assumptions introduced are justified in perturbation theory. As an incidental result, we find the precise limits of the region for which the absorptive part of the scattering amplitude is an analytic function of the momentum transfer, and hence the boundaries of the region in which the partial-wave expansion is valid. (auth)« less
  • We complete and improve the fits to experimental {pi}{pi} scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations belowKK threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and changemore » very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by 1.5{sigma}. These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables. In particular, we find a{sub 0}{sup (0)}=0.223{+-}0.009M{sub {pi}}{sup -1}, a{sub 0}{sup (2)}=-0.0444{+-}0.0045M{sub {pi}}{sup -1}, and {delta}{sub 0}{sup (0)}(m{sub K}{sup 2})-{delta}{sub 0}{sup (2)}(m{sub K}{sup 2})=50.9{+-}1.2{sup o}.« less
  • No abstract prepared.