What $\ddot{I}€-\ddot{I}€$ 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 ($\ddot{I}‡$PT) are relegated to higher orders. The new expansion represents a systematic and unambiguous generalization of the standard $\ddot{I}‡$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 $\ddot{I}‡$PT values. The importance of new, more accurate, experimental information on low-energy $\ddot{I}€-\ddot{I}€$ scattering is stressed.

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