Dynamical generation of hadronic resonances in effective models with derivative interactions

Abstract

Light scalar mesons can be understood as dynamically generated resonances. They arise as 'companion poles' in the propagators of quark-antiquark seed states when accounting for hadronic loop contributions to the self-energies of the latter. Such a mechanism may explain the overpopulation in the scalar sector - there exist more resonances with total spin $J=0$ than can be described within a quark model. Along this line, we study an effective Lagrangian approach where the isovector state $a_{0}(1450)$ couples via both non-derivative and derivative interactions to pseudoscalar mesons. It is demonstrated that the propagator has two poles: a companion pole corresponding to $a_{0}(980)$ and a pole of the seed state $a_{0}(1450)$. The positions of these poles are in quantitative agreement with experimental data. Besides that, we investigate similar models for the isodoublet state $K_{0}^{\ast}(1430)$ by performing a fit to $\pi K$ phase shift data in the $I=1/2,$ $J=0$ channel. We show that, in order to fit the data accurately, a companion pole for the $K_{0}^{\ast}(800)$, that is, the light $\kappa$, is required. A large-$N_{c}$ study confirms that both resonances below $1$ GeV are predominantly four-quark states, while the heavy states are quarkonia.