Regular Article – Theoretical Physics
On the nature of near-threshold bound and virtual states
Forschungszentrum Jülich, Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, 52425, Jülich, Germany
2 Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115, Bonn, Germany
3 Institute for Theoretical and Experimental Physics NRC (Kurchatov Institute), 117218, Moscow, Russia
4 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Leninskiy Prospect 53, 119991, Moscow, Russia
5 CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China
6 School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
Accepted: 5 March 2021
Published online: 22 March 2021
Physical states are characterised uniquely by their pole positions and the corresponding residues. Accordingly, in those parameters also the nature of the states should be encoded. For bound states (poles on the real s-axis below the lowest threshold on the physical sheet) there is an established criterion formulated originally by Weinberg in the 1960s, which allows one to estimate the amount of compact and molecular components in a given state. We demonstrate in this paper that this criterion can be straightforwardly extended to shallow virtual states (poles on the real s-axis below the lowest threshold on the unphysical sheet) which should be classified as molecular. We argue that predominantly non-molecular or compact states exist either as bound states or as resonances (poles on the unphysical sheet off the real energy axis) but not as virtual states. We also discuss the limitations of the mentioned classification scheme.
© The Author(s) 2021
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