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

TL;DR

This study precisely determines the $K^{+}ar{K}^{0}$ scattering length and effective range from $ ext{chi}_{c1}$ decay data, revealing the first measurement of the effective range and improving understanding of meson interactions.

Contribution

It introduces a novel, precise determination of the $K^{+}ar{K}^{0}$ effective range, using high-quality experimental data and advanced statistical methods, enhancing meson scattering knowledge.

Findings

Effective range determined for the first time.

Scattering length and effective range uncertainties below 20%.

Data well reproduced by chiral unitary approach.

Abstract

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 $20\%$. The effective range is determined for the first time with this analysis.