A MASTER FORMULA FOR CHIRAL SYMMETRY BREAKING

Abstract

We derive a master formula for chiral $SU(2)\times SU(2)$ breaking, based on the Veltman-Bell equations and the Peierls-Dyson relation. Our approach does not rely on the use of the soft pion limit or an expansion around the chiral limit, and yields exact results for on-shell pions. Threshold theorems for $\pi N\to \pi N$, $\gamma N\to \pi N$, $\pi N\to \pi \pi N$, $\gamma N\to \gamma \pi N$, $\gamma N\to \pi \pi N$ and $\pi N\to \pi \gamma N$ are recovered, and corrections to them are given. The reactions $\pi \to e\nu \gamma$, $\pi \to e\nu e^{+}{e}^{-}$, $\gamma \pi \to \gamma \pi$ and $\gamma \gamma \to \pi \pi$ are also discussed. A general formula for $\pi \pi$ scattering and a new one loop effective action are obtained. The new effective action reproduces the KSFR relation, and yields specific estimates for the pion polarisabilities. A detailed comparison with baryon-free chiral perturbation theory to one loop is made. An extension of our effective action to two loops is outlined.

119 pages + 7 Figures available from (I.Zahed)

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