Measurement of the quadratic slope parameter in theKL→3π0decay Dalitz plot

We report a value of -[3.3±1.1 (stat)±0.7(sys)]×${10}^{\mathrm{-}3}$ for the quadratic slope parameter h in the Dalitz plot of the ${\mathit{K}}_{\mathit{L}}$→3${\mathrm{\pi }}^0$ decay. This result is obtained from a sample of 5.1×${10}^6$ decays. The validity of the ΔI=1/2 rule in the quadratic term is investigated using this result. This is the first measurement of the 3${\mathrm{\pi }}^0$ slope parameter, and also the most sensitive measurement of any of the quadratic slope parameters for the charged or neutral kaons.