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Toward an understanding of discrete ambiguities in truncated partial-wave analyses

Aug 22, 2017

13 pages

Published in:

Phys.Rev.C 96 (2017) 6, 065202

Published: Dec 7, 2017

e-Print:

1708.06840 [nucl-th]

DOI:

10.1103/PhysRevC.96.065202

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Abstract: (APS)

It is well known that the observables in a single-channel scattering problem remain invariant once the amplitude is multiplied by an overall energy- and angle-dependent phase. This invariance is called the continuum ambiguity and acts on the infinite partial-wave set. It has also long been known that, in the case of a truncated partial wave set, another invariance exists, originating from the replacement of the roots of partial-wave amplitudes with their complex conjugate values. This discrete ambiguity is also known as the Omelaenko-Gersten-type ambiguity. In this paper, we show that for scalar particles, discrete ambiguities are just a subset of continuum ambiguities with a specific phase and thus mix partial waves, as the continuum ambiguity does. We present the main features of both continuum and discrete ambiguities and describe a numerical method which establishes the relevant phase connection.

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References(17)

Figures(7)

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