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

TL;DR

This paper investigates off-shell ambiguities in correlation functions within meson-baryon interactions, demonstrating that realistic chiral dynamics reduce uncertainties and proposing strategies to minimize these ambiguities in analysis.

Contribution

The study provides a systematic approach to reduce off-shell uncertainties in correlation functions, especially in meson-baryon interactions involving the $K\Lambda$, $K\\Sigma$, and $\\eta N$ channels.

Findings

Uncertainties are about 2-3% with chiral dynamics.

Other methods can lead to larger uncertainties.

Recommendations are provided to minimize ambiguities.

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.