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Examining potential shortcomings in using phase shifts as a link between experiment and QCD

Luscher [M. Luscher, Commun. Math. Phys. 105, 153 (1986) ; Nucl. Phys. B 354, 531 (1991)] has shown that in the single-channel problem (where the elastic region is below the 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 theorem is extended to the baryon resonance sector (multichannel situation in the inelastic region above first inelastic threshold), eigenphases (diagonal multichannel quantities) replace phase shifts (single-channel quantities). It is necessary to stress that the renowned π/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 that occurs if an insufficient number of channels is used can be reduced if a trace function that explicitly takes the multichannel aspect of the problem into account is used instead of single-channel phase shifts.

Luscher's theorem; multichannel scattering; QCD; phase shifts

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