Potential dangers when phase shifts are used as a link between experiment and QCD

TL;DR

This paper discusses the complexities and potential pitfalls of using phase shifts and eigenphases in multi-channel QCD scattering problems, emphasizing careful resonance extraction and the importance of multi-channel analysis.

Contribution

It highlights the dangers of applying single-channel phase shift criteria to multi-channel baryon resonance sectors and proposes using trace functions for more reliable analysis.

Findings

Eigenphases replace phase shifts in multi-channel scenarios.

Resonance criteria need to be carefully applied to eigenphases.

Trace functions can improve stability of resonance extraction.

Abstract

Luscher has shown that in single channel problem (elastic region below first inelastic threshold) there exists a direct link between the discrete value of the energy in a finite QCD volume and the scattering phase shift at the same energy. However, when the extension of the theorem is made to the baryon resonance sector (multi-channel situation in the inelastic region above first inelastic threshold), eigenphases (diagonal multi-channel quantities) replace phase shifts (single channel quantities). It is necessary to stress that the renowned pi/2 resonance criterion is formulated for eigenphases and not for phase shifts, so the resonance extracting procedure has to be applied with utmost care. The potential instability of extracting eigenphases from experimental data which occurs if insufficient number of channels is used can be reduced if a trace function which explicitly takes multi-channel aspect of the problem into account is used instead of single-channel phase shifts.