Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
نویسنده
چکیده
We test the positivity property of the chiral perturbation theory (ChPT) pion-pion scattering amplitudes within the Mandelstam triangle. In the one-loop approximation, O(p4), the positivity constrains only the coefficients b3 and b4, namely one obtains that b4 and the linear combination b3 + 3b4 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. PACS: 13.75.Lb, 12.39.Fe, 11.55.Fv, 11.30.Rd Key-words: Pion-Pion Scattering, Chiral Perturbation Theory, Positivity Constraints
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تاریخ انتشار 1998