Propagator poles and an emergent stable state below threshold: general discussion and the E(38) state
Abstract
In the framework of a simple quantum field theory describing the decay of a scalar state into two (pseudo)scalar ones we study the pole(s) motion(s) of its propagator: besides the expected pole on the second Riemann sheet, we find -- for a large enough coupling constant -- a second, additional pole on the first Riemann sheet below threshold, which corresponds to a stable state. We then perform a numerical study for a hadronic system in which a scalar particle couples to pions. We investigate under which conditions a stable state below the two-pion threshold can emerge. In particular, we study the case in which this stable state has a mass of 38 MeV, which corresponds to the recently claimed novel scalar state E(38). Moreover, we also show that the resonance and the stable state E(38) could be two different manifestation of the same `object'. Finally, we also estimate the order of magnitude of its coupling to photons.
Keywords
Cite
@article{arxiv.1209.2332,
title = {Propagator poles and an emergent stable state below threshold: general discussion and the E(38) state},
author = {Francesco Giacosa and Thomas Wolkanowski},
journal= {arXiv preprint arXiv:1209.2332},
year = {2013}
}
Comments
9 pages, 4 figures