Determination of off-shell ambiguities in correlation functions: Strategies to minimize them

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 Λ , K Σ , and η N coupled channels, which are related to the N * ( 1535 ) resonance, and the K + K ¯ 0 channel related to the a 0 ( 980 ) resonance. We find that, by 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.