Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes

Details Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes

1998-09-28

arxiv.org/abs/hep-ph/9809568v1

Phys.Rev. D59 (1999) 094007

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages, Latex

Scientific paper

10.1103/PhysRevD.59.094007

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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