What $\pi -\pi$ Scattering Tells Us About Chiral Perturbation Theory

Abstract

We describe a rearrangement of the standard expansion of the symmetry breaking part of the QCD effective Lagrangian that includes into each order additional terms which in the standard chiral perturbation theory ($\chi$PT) are relegated to higher orders. The new expansion represents a systematic and unambiguous generalization of the standard $\chi$PT, and is more likely to converge rapidly. It provides a consistent framework for a measurement of the importance of additional ``higher order'' terms whose smallness is usually assumed but has never been checked. A method of measuring, among other quantities, the QCD parameters $\hat{m}⟨\bar{q}q⟩$ and the quark mass ratio $m_s/\hat{m}$ is elaborated in detail. The method is illustrated using various sets of available data. Both of these parameters might be considerably smaller than their respective leading order standard $\chi$PT values. The importance of new, more accurate, experimental information on low-energy $\pi -\pi$ scattering is stressed.

arXiv commentRevTeX 62 pages (6 figures not added, request from any author), IPNO/TH 92-106, PURD-TH-93-01

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