Connection between angle-dependent phase ambiguities and the uniqueness of the partial-wave decomposition

Švarc, Alfred; Wunderlich, Y.; Osmanović, H.; Hadžimehmedović, M.; Omerović, R.; Stahov, J.; Kashevarov, V. L.; Nikonov, K.; Ostrick, M.; Tiator, L.; Workman, R. L.

doi:10.1103/physrevc.97.054611

Cited by 20 publications

(32 citation statements)

References 21 publications

(31 reference statements)

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“…New relationships were discovered [416,461]. Studies of the phase-ambiguity problem, associated with amplitude analyses, were conducted in collaboration with the Mainz, Bonn, and Zagreb groups [462,463]. These studies have more clearly defined the amplitude information that can be extracted from data with minimal input from reaction models.…”

Section: Recent Progress With the Juelich-bonn And Said Analysis Frameworkmentioning

confidence: 99%

Strong QCD from Hadron Structure Experiments

Brodsky

Burkert

Carman

et al. 2020

Int. J. Mod. Phys. E

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The topical workshop Strong QCD from Hadron Structure Experiments took place at Jefferson Lab from November 6–9, 2019. Impressive progress in relating hadron structure observables to the strong QCD mechanisms has been achieved from the ab initio QCD description of hadron structure in a diverse array of methods in order to expose emergent phenomena via quasi-particle formation. The wealth of experimental data and the advances in hadron structure theory make it possible to gain insight into strong interaction dynamics in the regime of large quark–gluon coupling (the strong QCD regime), which will address the most challenging problems of the Standard Model on the nature of the dominant part of hadron mass, quark–gluon confinement, and the emergence of the ground and excited state hadrons, as well as atomic nuclei, from QCD. This workshop aimed to develop plans and to facilitate the future synergistic efforts between experimentalists, phenomenologists, and theorists working on studies of hadron spectroscopy and structure with the goal to connect the properties of hadrons and atomic nuclei available from data to the strong QCD dynamics underlying their emergence from QCD. These results pave the way for a future breakthrough extension in the studies of QCD with an Electron–Ion Collider in the U.S.

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Section: Recent Progress With the Juelich-bonn And Said Analysis Frameworkmentioning

confidence: 99%

Strong QCD from Hadron Structure Experiments

Brodsky

Burkert

Carman

et al. 2020

Int. J. Mod. Phys. E

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“…From our earlier research [1] we know that the natural candidate for such an effect is the change of reaction amplitude phase. As the essential part of our AA/PWA model is the penalty factor P, and the possible change of phase is introduced via this factor, we shall put this factor under magnifying glass.…”

Section: B Analysis Of Phase Dependence Of Solmentioning

confidence: 99%

“…In ref. [1] it has been shown that without fixing the reaction-amplitude phase, many combinations of partial waves at neighbouring energies in single-energy single-channel partial wave analysis reproduce experimental data identically, but are discontinuous and disconnected. So, to obtain the continuous solution, the phase has to be fixed to some continuous value.…”

Section: Introductionmentioning

confidence: 99%

Is the pole content of each single-energy, single-channel partial wave analysis inherently model dependent?

Svarc

2021

Preprint

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Unfortunately, yes it is. In ref. [1] it has been shown that without fixing the reaction-amplitude phase, many combinations of partial waves at neighbouring energies in single-energy, single-channel partial wave analysis reproduce experimental data identically, but are discontinuous and disconnected. To obtain the continuous solution, the phase has to be fixed to some continuous value. In the same reference it has also been shown that the change of angular part of reaction-amplitude phase mixes partial waves, so the pole structure of any single-energy single-channel partial wave analysis depends on the chosen phase. As in any single-channel analysis the overall reaction-amplitude phase cannot be determined because of continuum ambiguity, it is in principle free and has to be taken from some coupled-channel model. Because of the difference in the angular part of the phase, choosing different phases results in the change of the pole content of the obtained solution. Therefore, single-energy single-channel partial wave analysis is inherently model dependent, and the number of poles it contains strongly depends on the choice of the phase. In that reference these facts have been illustrated on the pseudo-scalar meson production toy model. This truth is now for the measured observables demonstrated on the realistic model of ref.[2] which combines amplitude and partial wave analysis in one self-consistent scheme for the the world collection of η-photoproduction data, and fixes the phase to BG2014-2 solution [3]. We show that the pole structure of the solution whose phase is very close to the BG2014-2 theoretical ED phase is very similar to the pole structure of BG2014-2 solution, but the agreement with the data is not ideal. However, improving the agreement with the data requires the departure from BG2014-2 ED phase, and this spoils analytic structure of the obtained solution. This also demonstrated under which conditions the new method of ref. [2] is reliable for direct data analysis and generating single-channel, single-energy partial wave analysis with the minimal model dependence, and we offer a new solution which is a compromise between good fit and good analytic structure.

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“…It is a general knowledge that as a direct consequence of continuum ambiguity the unconstrained partial-wave amplitudes obtained at discrete energies even from fits to complete sets of eight independent observables [14] which are required to uniquely reconstruct reaction amplitudes do not vary smoothly with energy, and are in principle nonunique [15]. In [1] it has been shown that for a complete set of pseudo-data this problem can be easily solved by simple phase rotations.…”

Section: Introductionmentioning

confidence: 99%

From Experimental Data to Pole Parameters in a Model Independent Way (Fixed-t Single-Energy Partial Wave Analysis (SE PWA) and Laurent + Pietarinen Model (L+P) for Pole Extraction)

Švarc

2020

EPJ Web Conf.

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As it has been shown in the invited talk at the NSTAR-2017 conference [1] it is in principle possible to extract pole parameters directly from experiment with minimal model dependence, and in this contribution one way to achieve it in practice by fixed-t analyticity has been demonstrated. Namely, unconstrained partial- wave amplitudes obtained at discrete energies from fits even to complete sets of independent observables which are required to uniquely reconstruct reaction amplitudes do not vary smoothly with energy, and are in prin ciple non-unique. We have demonstrated that this behavior can be ascribed to the continuum ambiguity. We have applied continuum ambiguity invariance to pseudo-scalar meson photoproduction and showed that for a complete set of pseudo-data the non-uniqueness effect can be removed through a phase rotation generating “up-to-a-phase” unique set of single energy partial wave amplitudes. Now we show that for real data this method does not work, but another approach - fixed-t analyticity solves the problem. We present the final results for the η and π0 -photoproduction [2, 3]. Extracting pole positions from partial wave amplitudes is the next step, and we summarize the essence of the new, Laurent + Pietarinen expansion method applicable for continuous and discrete data. It is based on applying the Laurent decomposition of partial wave amplitude, and expanding the non-resonant background into a power series of a conformal-mapping-generated, quickly converging power series obtaining the simplest analytic function with well-defined partial wave analytic properties which fits the input. Unifying both methods in succession, one constructs a model independent procedure to extract pole parameters directly from experimental data without referring to any theoretical model.

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Connection between angle-dependent phase ambiguities and the uniqueness of the partial-wave decomposition

Cited by 20 publications

References 21 publications

Strong QCD from Hadron Structure Experiments

Strong QCD from Hadron Structure Experiments

Is the pole content of each single-energy, single-channel partial wave analysis inherently model dependent?

From Experimental Data to Pole Parameters in a Model Independent Way (Fixed-t Single-Energy Partial Wave Analysis (SE PWA) and Laurent + Pietarinen Model (L+P) for Pole Extraction)

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