Determination of the $K^{+}{\bar{K}}^0$ scattering length and effective range and its relation to the $a_0^{+}(980)$ from the ${\chi }_{c1}\to {\pi }^{+}{\pi }^{-}\eta$ reaction

We analyze the clean cusp, seen in the $\eta \pi$ mass distribution with high precision of the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ reaction in the BESIII experiment, with the aim of making a precise determination of the scattering length $a$ and effective range $r_0$ of $K^{+}{\bar{K}}^0$. For that, we follow a previous theoretical work that gave a good reproduction of these data using the chiral unitary approach for the meson-meson interaction, and allow some flexibility in the input to carry a better fit to the data. The important task of determining the uncertainties in the scattering parameters is done using the resampling method and an accuracy in $a$ and $r_0$ is obtained better than $20\mathrm{\%}$. The effective range is determined for the first time with this analysis.