Determination of the $K^+\bar{K}^0$ scattering length and effective range from the $D^+\to\bar{K}^0\pi^+\eta$ reaction

We study the scattering parameters of the \(K^+\bar{K}^0\) system through the analysis of the \(D^+\to\bar{K}^0\pi^+\eta\) reaction, aiming at determining the scattering length \(a\) and effective range \(r_0\) of the \(K^+\bar{K}^0\) interaction. These parameters are extracted by analyzing and fitting the mass distributions of the pairs in the final \(\bar{K}^0\pi^+\eta\) state. To ensure the reliability of the results, we apply resampling techniques to evaluate statistical uncertainties and improve the precision of the scattering parameters. The obtained results are compared with previous theoretical predictions and experimental data, providing new insights into the \(K^+\bar{K}^0\) interaction at low energies.