Crossing conditions for the pion-pion amplitude
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In this article, a denumerable set of rigorous inequalities on π 0π0-π0π0 partial-wave amplitudes which guarantee that the amplitude is crossing symmetric are presented.Abstract:
We obtain a denumerable set of rigorous inequalities on the π0π0-π0π0 partial-wave amplitudes which guarantee that the amplitude is crossing symmetric. The numerical inequalities presented for the case of S and D waves indicate that one has very little freedom in the choice of the D-waves once the .S-waves are given.read more
Citations
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Journal ArticleDOI
Unambiguous ππS-Waves from general principles and the existence of the ρ-meson
TL;DR: In this article, the authors present a calculation of S-wave ππ amplitudes based upon known rigorous results due to analyticity, unitarity and crossing symmetry; inequalities and crossing sum rules.
Journal ArticleDOI
ππ S- and P-wave low-energy models from analyticity, unitarity and crossing symmetry
B. Bonnier,P. Gauron +1 more
TL;DR: In this article, the ππ S- and P-wave models were constructed using elastic unitarity, the known properties of the partial wave discontinuities across the left-hand cut at threshold, and the existence of the ϱ-meson.
Book ChapterDOI
Analyticity, unitarity, and crossing-symmetry constraints for pion--pion partial wave amplitudes.
Journal ArticleDOI
Rigorous results of axiomatic field theory applied to low energy ππ scattering
B. Bonnier,P. Gauron +1 more
TL;DR: In this article, a model for low energy S, P, and D-waves was constructed so as to be in agreement with the rigorous results deduced from analyticity, unitarity and crossing symmetry.
Journal ArticleDOI
Low-energy pion-pion scattering from current algebra: Unitarity corrections
David J. Morgan,Graham Shaw +1 more
TL;DR: In this article, unitarity corrections over the threshold regions can be included up to third order in the momenta in an essentially unique way, in an explicitly crossing symmetric manner using the variables Q s, Q t, Q u introduced by Iliopolous.
References
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Journal ArticleDOI
Theory of the low-energy pion-pion interaction
TL;DR: In this paper, the double-dispersion representation is applied to the problem of pion-pion scattering, and it is shown that, if inelastic effects are important only at very high energies and $S$-wave scattering dominates at low energy, a set of integral equations for the low-energy amplitudes can be derived.
Journal ArticleDOI
Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity-I
TL;DR: In this article, it was shown that the pion-pion scattering amplitude can be continued until the border-line of the double-spectral function, except for the case that the nearest singularities are induced by two-particle unitarity.
Journal ArticleDOI
A proof of the existence of functions that satisfy exactly both crossing and unitarity: I. Neutral pion-pion scattering. No subtractions.
TL;DR: In this paper, a fixed-point theorem is used to prove the existence of pion-pion scattering amplitudes that satisfy the Mandelstam representation with full crossing symmetry between the three channels, elastic unitarity between the elastic and inelastic thresholds, and the inequalities above the latter.
Journal ArticleDOI
Theory of low-energy scattering in field theory
TL;DR: In this article, an approximate representation for the scattering amplitude of processes with two final particles, expected to be valid below the threshold for anelastic production of new particles, is deduced from the Mandelstam double integral representation.
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Simultaneous "Partial-Wave" Expansion in the Mandelstam Variables: Crossing Symmetry for Partial Waves
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