Principles and problems of phase-shift analysis

Abstract

Phase-shift analysis is the extraction of the scattering amplitude from the scattering cross section and other experimentally observable quantities such as polarizations. When only elastic scattering is energetically allowed, unitarity determines the unobservable angle-dependent complex phase of the scattering amplitude with, at most, only a few discrete alternative solutions. Above the inelastic threshold the unitarity constraint on a scattering amplitude is only an inequality and a continuum of different amplitudes will correspond to exactly the same observables. In practical cases these differences can be important. Extra theoretical input of a dynamical nature can, in principle, remove the continuum ambiguity but, because numerical analytic continuation is always involved, data of absurd accuracy are required. Thus unique answers can, in practice, only be found by introducing further model-dependent assumptions ; it is important to recognize this and ensure that these assumptions are as dynamically plausible as possible. Recent results using the structure of the amplitude in both kinematic variables suggest that fixed-t dispersion relations might form a sound basis for an inelastic phase-shift analysis.

πN→ηNData Require the Existence of theN(1710)PCeci1, Švarc2, Zauner3 2006Phys. Rev. Lett.402540View full textAdd to dashboardCite

“…This finding contradicts the smooth energy behavior of the offered VPI/GWU FA02 (SP06) solution, but is not in controversy with the collection of single energy solutions (SES) of the same group. We believe that reported enlargement of error bars of VPI/GWU SES in the critical energy range is not only of experimental, but primarily of theoretical nature, and we offer the explanation that a N(1710) P 11 resonance is "hidden" within the continuum ambiguity [4,5] in the 1700 MeV range. The way how the πN → ηN data have been used in the VPI/GWU analysis is also not being of much help for eliminating the 1700 MeV continuum ambiguity: all data above T lab = 800 MeV, important to see the N(1710) P 11 resonance, have unfortunately not been included in this analysis.…”

“…On the other hand, the error bars of single energy solutions (SES) accompanying it on the web page [3] do show disproportionable increase in that energy domain. As this analysis heavily relies on the elastic channel, the immanent continuum ambiguity problem [4,5] is handled by iteratively stabilizing the solution during the minimization procedure through applying the fixed t dispersion relations. Yet, the suspicious error bars increase in SES has not been understood and the N(1710) P 11 pole has not been established.…”

Amplitude Analysis

“…It is actually possible to see effects of such phases via multiple scattering [1,2] and to (in principle) measure some of them using the Hanbury-Brown−Twiss method [10]. In practice, however, some theoretical input is necessary to fix this phase.…”

Determining dominant partial waves in photoproduction

“…The infinite partial wave series reads A(W, θ ) = ∑ ∞ =0 (2 + 1)A P (cos θ ). In case this series is truncated at some maximal angular momentum quantum number max and then inserted into the cross section, one obtains the expansion (see reference [2])…”