Low-Energy Theorems onKl3Decay Form Factors Based on Broken Chiral Symmetry

Abstract

A new and simpler technique is used to derive low-energy theorems on $K_{l3\mathrm{}}$ decay form factors $f_{+}\mathrm{}\left(0\right)\mathrm{}$ and $f_{-}\mathrm{}\left(0\right)\mathrm{}$ based on $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ symmetry breaking. We employ the $(3^{*},3)\oplus (3,3^{*})$ symmetry-breaking model for definiteness. Assumptions like field algebra, vector dominance, $c$-number Schwinger terms, or pole saturation are not used. The method yields the results of Callan and Treiman, Glashow and Weinberg, and Gerstein and Schnitzer in appropriate limits. The assumption under which our results agree with those of Dashen and Weinstein are also discussed. The sensitivity of the parameter $\xi \equiv \frac{f_{-}\mathrm{}\left(0\right)\mathrm{}}{f_{+}\mathrm{}\left(0\right)\mathrm{}}$ to assumptions of explicit symmetry breaking is demonstrated, and several conclusions are drawn.