Analyticity, Crossing Symmetry and the Limits of Chiral Perturbation Theory

Details Analyticity, Crossing Symmetry and the Limits of Chiral Perturbation Theory Analyticity, Crossing Symmetry and the Limits of Chiral Perturbation Theory

1992-06-15

arxiv.org/abs/hep-ph/9206222v2

Phys.Rev. D47 (1993) 2930-2939

Physics

High Energy Physics

High Energy Physics - Phenomenology

harvmac, 18 pages (3 figures), HUTP-92/A025, BUHEP-92-18, new version fixes a TeX problem in little mode

Scientific paper

10.1103/PhysRevD.47.2930

The chiral Lagrangian for Goldstone boson scattering is a power series expansion in numbers of derivatives. Each successive term is suppressed by powers of a scale, $\Lambda_\chi$, which must be less than of order $4\pi f/\sqrt{N}$ where $f$ is the Goldstone boson decay constant and $N$ is the number of flavors. The chiral expansion therefore breaks down at or below $4 \pi f/\sqrt{N}$. We argue that the breakdown of the chiral expansion is associated with the appearance of physical states other than Goldstone bosons. Because of crossing symmetry, some ``isospin'' channels will deviate from their low energy behavior well before they approach the scale at which their low energy amplitudes would violate unitarity. We argue that the estimates of ``oblique'' corrections from technicolor obtained by scaling from QCD are untrustworthy.

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