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 $K^{\pm}\rightarrow \pi^{\pm} \pi^{0} \pi^{0}$ decays using $35$ GeV/$c$ hadron beams at the IHEP (Protvino) accelerator. For the first time dependences of parameters and fit quality on the $\pi^0\pi^0$ mass cut were investigated. It is shown that the above mentioned expansion does not fit the experimental data near the $\pi^+\pi^-$ mass threshold and addition of the cubic terms only slightly improves the fit quality. This result points to the important role of nonanalytical terms in the matrix element that are connected with the pion rescattering. The comparison of our data with previous measurements is presented.