Off-shell ambiguities in correlation functions: strategies to minimize them

Abstract: We face here the problem of uncertainties in correlation functions due to the freedom in the off-shell dependence of the wave functions, or equivalently, off-shell ambiguities in the scattering matrices. We make the study for the case of meson baryon interaction, choosing the $K\Lambda$, $K \Sigma$, $\eta N$ coupled channels, which are related to the $N^*(1535)$ resonance. We find that using realistic interactions based on chiral dynamics the uncertainties are small, of the order of $2-3$~\%, but could be much bigger if other methods are used. However, our study shows the way to optimally overcome these uncertainties in the analysis of correlation functions, and we provide a series of recommendations for any general analysis.