Measurements of the Dalitz Plot Parameters for $K^{\pm}\to\pi^{\pm}\pi^0\pi^0$ Decays

The $g$, $h$, and $k$ Dalitz plot parameters, which are coefficients in a series expansion of the squared module of the matrix element $|M(u,v)|^{2} \propto 1 + gu + hu^{2} + kv^{2}$ ($u$, $v$ are invariant variables), have been measured for $K^{\pm}\to \pi^{\pm} \pi^{0} \pi^{0}$ decays using $35 GeV/c$ hadron beams at the IHEP (Protvino) accelerator. Dependences of parameters and fit quality on the $\pi^0\pi^0$ mass cut were investigated. The results point to the important role of $\pi^+\pi^- \to \pi^0\pi^0$ charge exchange scattering near the $\pi^0\pi^0$ mass threshold. The comparison of our data with previous measurements is presented.