Theoretical Study ofKl4Decay

Abstract

$K_{l4\mathrm{}}$ decay is formulated in a way which allows the extraction of form factors and $\pi -\pi$ phase-shift differences from data with limited statistics. The only assumptions required are $T$ invariance and a restriction to $S$ and $P$ waves in the final state, no other dynamical assumptions being required. It is shown that the assumption of the $\Delta I=\frac{1}{2}$ rule is not necessary if all $K_{l4\mathrm{}}$ decays are taken into account. When the existing available data are analyzed in the simple extension of the Cabibbo-Maksymowicz approach in which all $P$-wave contributions are taken into account, there is a sign ambiguity in the $S$-wave $\pi -\pi$ phase shift. This ambiguity is fundamental to this approach and can be solved only by means of another angular distribution. Such a distribution could be obtained from the existing data.