Implications of Current Algebra for η Decay— A Summary

Abstract

In calculations involving pions, the use of equal time commutation relations for the currents together with PCAC (Partial Conservation of Axial Vector Current) principle for the pion field operator has had some success over the last couple of years. Most spectacular among these is the calculation of Adler1 and Weissberger2 giving the weak axial vector renormalization g A in terms of the total crosssection in π-N scattering. Subsequently, the current algebra was found successful in relating various leptonic K-decay processes3 and in giving some details of nonleptonic decays.4 Hara and Nambu4 applied these techniques to successfully predict the energy spectrum of the unlike pion in the K → 3π decay. There is a lot of similarity between η → 3π and K → 3π decays, and it is natural to expect that similar mechanism explain both processes. However, the current algebra techniques that were so successful in K decays have not had a similar effect in η decays. We shall see that some of the difficulties will be traced to the ambiguity in the various extrapolations possible from the soft pion limit (where the current algebra makes definite predictions) to the physical pions. In this talk we shall review briefly the various approaches and then suggest an extrapolation procedure that we think best explains the π-decay process.