Correlation function for the $a_0(980)$

Abstract

We have conducted a model independent analysis of the $K^+ \bar{K}^0$ pair correlation function obtained from ultra high energy $pp$ collisions, with the aim of extracting the information encoded in it related to the $K\bar{K}$ interaction and the coupled channel $\pi^+ \eta$. With the present large errors at small relative $K^+\bar{K}^0$ momenta, we find that the information obtained about the scattering matrix suffers from large uncertainties. Even then, we are able to show that the data imply the existence of the $a_0$ resonance, $a_0(980)$, showing as a strong cusp close to the $K\bar{K}$ threshold. We also mention that the measurement of the $\pi^+ \eta$ correlation function will be essential in order to constrain more the information on $K\bar{K}$ dynamics that can be obtained from correlation functions.