Bootstrap analysis of meromorphic observables in large-N QCD yields universal and SVZ-type bounds that constrain chiral Lagrangian parameters and link hadronic data to asymptotic freedom.
Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
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abstract
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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Multipositivity bounds derived from planar tree-level scattering amplitudes constrain Wilson coefficients of the chiral Lagrangian from below by the chiral anomaly.
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Bootstrapping Pion Form Factors at Large $N$
Bootstrap analysis of meromorphic observables in large-N QCD yields universal and SVZ-type bounds that constrain chiral Lagrangian parameters and link hadronic data to asymptotic freedom.
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Multipositivity Constrains the Chiral Lagrangian
Multipositivity bounds derived from planar tree-level scattering amplitudes constrain Wilson coefficients of the chiral Lagrangian from below by the chiral anomaly.