Dynamical generation of hadronic resonances

TL;DR

This paper investigates the dynamical generation of hadronic resonances through loop contributions, analyzing scalar resonances with models that reveal conditions for stable states and the emergence of specific resonances.

Contribution

It presents a detailed analysis of pole structures in scalar resonances using simple quantum field theory and the extended Linear Sigma Model, clarifying conditions for resonance emergence.

Findings

A second pole below the pion-pion threshold can emerge for $f_{0}(500)$, indicating a stable state.

No additional pole for $a_{0}(1450)$ was found, suggesting $a_{0}(980)$ is not dynamically generated.

Next-to-leading-order contributions are generally small and negligible despite large coupling constants.

Abstract

One type of dynamical generation consists in the formation of multiple hadronic resonances from single seed states by incorporating hadronic loop contributions on the level of $s$-wave propagators. Along this line, we study the propagator poles within two models of scalar resonances and report on the status of our work: (i) Using a simple quantum field theory describing the decay of $f_{0}(500)$ into two pions, we may obtain a second, additional pole on the first Riemann sheet below the pion-pion threshold (i.e., a stable state can emerge). (ii) We perform a numerical study of the pole(s) of $a_{0}(1450)$ by using as an input the results obtained in the extended Linear Sigma Model (eLSM). Here, we do not find any additional pole besides the original one, thus we cannot obtain $a_{0}(980)$ as an emerging state. (iii) We finally demonstrate that, although the coupling constants in typical effective models might be large, the next-to-leading-order contribution to the decay amplitude is usually small and can be neglected.