Study ofKe4Decays

A study of 13.3×${10}^6$ stopped $K^{+}$ in a heavy-liquid bubble chamber yielded 269 $K_{e4\mathrm{}}$ decays of the type $e^{+}{\pi }^{+}{\pi }^{-}\nu$, a total greater by a factor of 4 than the number found in a previous experiment. No examples of $e^{-}{\pi }^{+}{\pi }^{+}\overline{\nu }$ were found. With 95% confidence, the upper limit for the decay rate of $K_{e4\mathrm{}}\left(e^{-}\right)$ was found to be 56 ${\sec }^{-1\mathrm{}}$. The rate for $K_{e4\mathrm{}}\left(e^{+}\right)$ was found to be (2.60±0.30)×${10}^3$ ${\sec }^{-1\mathrm{}}$. The angular distributions and the dipion invariant-mass plot have been fitted by varying the form factors $f_s$, $f_p$, $g$, and $h$, and the difference between $s$- and $p$-wave $\pi -\pi$ phase shift. Two acceptable solutions have been found. Both agree that the vector form factor $h$ is significantly nonzero and that its sign is negative with respect to that of $f_g$. Also, it has been found necessary to include $f_p$ in order to obtain a good fit. Although both solutions give the magnitude of the phase difference to be 25±9 deg, the two estimates have opposite sign. No evidence of a $\sigma$ resonance is seen. The angular distributions are found to be consistent with time-reversal invariance, and with the locality of lepton production.