Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes

We test the positivity property of the chiral perturbation theory (ChPT) pion-pion scattering amplitudes within the Mandelstam triangle. In the one-loop approximation, ${\cal O}(p^4)$, the positivity constrains only the coefficients $b_3$ and $b_4$, namely one obtains that $b_4$ and the linear combi...

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Autor principal: Dita, P
Lenguaje:eng
Publicado: 1999
Materias:
Acceso en línea:https://dx.doi.org/10.1103/PhysRevD.59.094007
http://cds.cern.ch/record/366582
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author Dita, P
author_facet Dita, P
author_sort Dita, P
collection CERN
description We test the positivity property of the chiral perturbation theory (ChPT) pion-pion scattering amplitudes within the Mandelstam triangle. In the one-loop approximation, ${\cal O}(p^4)$, the positivity constrains only the coefficients $b_3$ and $b_4$, namely one obtains that $b_4$ and the linear combination $b_3+3 b_4$ are positive quantities. The two-loops approximation gives inequalities involving all the six arbitrary parameters entering ChPT amplitude, but the corrections to the one-loop approximation results are small. ChPT amplitudes pass unexpectedly well all the positivity tests giving strong support to the idea that ChPT is the good theory of the low energy pion-pion scattering.
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institution Organización Europea para la Investigación Nuclear
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spelling cern-3665822019-09-30T06:29:59Zdoi:10.1103/PhysRevD.59.094007http://cds.cern.ch/record/366582engDita, PPositivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering AmplitudesParticle Physics - PhenomenologyWe test the positivity property of the chiral perturbation theory (ChPT) pion-pion scattering amplitudes within the Mandelstam triangle. In the one-loop approximation, ${\cal O}(p^4)$, the positivity constrains only the coefficients $b_3$ and $b_4$, namely one obtains that $b_4$ and the linear combination $b_3+3 b_4$ are positive quantities. The two-loops approximation gives inequalities involving all the six arbitrary parameters entering ChPT amplitude, but the corrections to the one-loop approximation results are small. ChPT amplitudes pass unexpectedly well all the positivity tests giving strong support to the idea that ChPT is the good theory of the low energy pion-pion scattering.hep-ph/9809568oai:cds.cern.ch:3665821999
spellingShingle Particle Physics - Phenomenology
Dita, P
Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
title Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
title_full Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
title_fullStr Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
title_full_unstemmed Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
title_short Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
title_sort positivity constraints on chiral perturbation theory pion-pion scattering amplitudes
topic Particle Physics - Phenomenology
url https://dx.doi.org/10.1103/PhysRevD.59.094007
http://cds.cern.ch/record/366582
work_keys_str_mv AT ditap positivityconstraintsonchiralperturbationtheorypionpionscatteringamplitudes