PION-PION SCATTERING LENGTHS FROM VENEZIANO FORMULA AND ETA-]3PI, K-]3PI DECAYS

The η→ 3 π decay amplitude is factorized into (a) the transition matrix element from η to π0 and (b) Lovelace's expression of the Veneziano type for the pion-pion scattering amplitude. (a) is related with the electromagnetic mass splitting between K+ and K0. The absolute value of (b) is then obtained by fitting the η decay width. The pion-pion scattering lengths from (b) are reasonable. Since the analogous treatment of K→ 3 π decay together with a soft-pion determination of the K→π transition matrix element yield very small scattering lengths we suggest that the K→2 π transition matrix element depends strongly on the pion masses. © 1969 Springer-Verlag.