Experimental Study of $K_{e 4}^{+}$ Decay

The rare

K_{e 4}^{+}

decay modes

π^{+} π^{-} e^{+} ν

π^{+} π^{+} e^{-} \bar{ν}

, and

π^{+} π^{+} μ^{-} \bar{ν}

were searched for in a sample of approximately 3×

10^{6}

K^{+}

decays. A total of 69 events of the mode

π^{+} π^{-} e^{+} ν

were observed. The other two modes are forbidden by the

Δ S = Δ Q

rule and no examples of them were found. This experiment gives an upper limit for the amplitude ratio

X = | \frac{[A (Δ S = - Δ Q)]}{[A (Δ S = Δ Q)]} |

, for the axial-vector current of 0.25, with the assumption of no final-state

π - π

interaction. The effects of final-state interactions in the

π - π

system modify the interpretation of this result and may be large. The rate for the

π^{+} π^{-} e^{+} ν

mode was determined to be (2.9±0.6)×

10^{3}

\sec^{- 1}

. The angular correlations between the planes formed by the lepton pair and the pion pair, and the angular distribution of

π^{+}

with respect to the dipion line of flight in the dipion rest system for the 69 events, were studied. The dipion mass spectrum is presented for the 69

π^{+} π^{-} e^{+} ν

events. The value of the ratio of the two form factors in

K_{e 4}

decay (

p

wave to

s

wave) was found to be

η = 0.8 \pm 0.30

from an analysis of these correlations. An estimate of the low-energy

π - π

phase shift was determined to be

" δ_{0} - δ_{1} " = 35 ° \pm 30 °

from the angular correlations. The difference "

δ_{0} - δ_{1}

" between the

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Experimental Study ofKe4+Decay