Propagator poles and an emergent stable state below threshold: general discussion and the E(38) state

TL;DR

This paper explores how a simple quantum field theory predicts the emergence of a stable scalar state below threshold, potentially explaining the E(38) particle and its relation to known resonances.

Contribution

It demonstrates the conditions under which a stable state below threshold appears and suggests the E(38) could be related to the $f_0(500)$ resonance.

Findings

A second pole on the first Riemann sheet indicates a stable state.

The stable state can have a mass around 38 MeV, matching E(38).

The stable state and $f_0(500)$ may be different manifestations of the same object.

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 $f_{0}(500)$ 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.