Pole structure and compositeness

J. A. Oller

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arXiv · 1711.10811

Pole structure and compositeness

J. A. Oller

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Abstract

We present in this talk a series of new results on the nature of a bound state or resonance based on the calculation of the expectation values of the number operators of the free particles in the state of interest. In this way, a new universal criterion for the elementariness of a bound state emerges. In the case of large particle wavelengths compared to the range of their interaction, a new closed formula for the compositeness of a bound state in a two-particle continuum is obtained. The extension of these results to resonances with respect to the open channels can be given by making use in addition of suitable phase-factor transformations as also reviewed here. We end with a discussion on the $X(3872)$ as possible double- or triple-pole virtual state, which would be the first case in particle phenomenology.

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J. A. Oller. 2017-11-29. Pole structure and compositeness. https://arxiv.org/abs/1711.10811

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