Empirical parameterization of the $K^{\pm} \to \pi^{\pm}\pi^{0}\pi^{0}$ decay Dalitz plot

As first observed by the NA48/2 experiment at the CERN SPS, the $\pi^{0}\pi^{0}$ invariant mass ($M_{00}$) distribution from $K^{\pm} \rightarrow \pi^{\pm}\pi^{0}\pi^{0}$ decay shows a cusp-like anomaly at $M_{00}=2m_{+}$, where $m_{+}$ is the charged pion mass. An analysis to extract the $\pi\pi$ scattering lengths in the isospin $I=0$ and $I=2$ states, $a_{0}$ and $a_{2}$, respectively, has been recently reported. In the present work the Dalitz plot of this decay is fitted to a new empirical parameterization suitable for practical purposes, such as Monte Carlo simulations of $K^{\pm} \rightarrow \pi^{\pm}\pi^{0}\pi^{0}$ decays.