CALCULATION OF LOW-ENERGY S-WAVE PION-PION INTERACTION FROM KE4 DECAY USING CHARGE COMMUTATION RELATIONS

By making use of an appropriate charge commutation relation, we have computed the low-energy pion-pion scattering length directly from the rate of Ke4-decay. The main differences from previous approaches are as follows: (a) Instead of using the current commutation relations (which have been extensively used with the soft-pion technique), we stick to the better-known charge commutation relations. This enables us, as in the Adler-Weisberger calculation, to avoid taking the usual soft-pion limit kμ→0; instead we let only k2(=-mπ2)→0, which is certainly a smaller extrapolation. (b) In contrast with previous calculations of Ke4 decays, which utilized essentially the kaonic PCAC (mK→0), we use the pionic PCAC, which involves a much smaller extrapolation (mπ→0). From the presently available Ke4 decay rate, we have estimated the values of the I=0 and 2 S-wave pion-pion scattering length as a00.18 and a2-0.017. Although our numerical results for a0, a2, and the Ke4-decay form factors turn out to be not very different from those obtained by using the current commutation relations with soft-pion techniques, we emphasize the important difference between the two approaches mentioned in (a) with respect to the extrapolation procedures. © 1968 The American Physical Society.