A study of the resonances $K_{0}^{*}(800)$ and $K_{0}^{*}(1430)$

TL;DR

This paper investigates the scalar kaonic states $K_{0}^{*}(800)$ and $K_{0}^{*}(1430)$ using a relativistic quantum field theory approach, revealing two poles in the complex plane and suggesting $K_{0}^{*}(800)$ as a dynamically generated four-quark state.

Contribution

The study introduces a relativistic QFT model considering both derivative and non-derivative interactions, identifying a companion pole for $K_{0}^{*}(800)$ and analyzing its nature.

Findings

Two poles identified: one for $K_{0}^{*}(1430)$ and one for $K_{0}^{*}(800)$.

$K_{0}^{*}(800)$ emerges as a dynamically generated four-quark state.

Spectral function shows a peak near 1.4 GeV, but two poles are present.

Abstract

We study the scalar kaonic states $K_{0}^{\ast}(800)$ and $K_{0}^{\ast}(1430)$ by using a relativistic QFT Lagrangian in which only a single kaonic field corresponding to the well-established scalar state $K_{0}^{\ast}(1430)$ is considered and in which both derivative and non-derivative interaction terms are taken into account. Even if the scalar spectral function shows a unique peak close to $1.4$ GeV, we find two poles in the complex plane: $1.413\pm0.002-i(0.127\pm0.003)$ GeV, which is related to the seed quark-antiquark state $K_{0}^{\ast}(1430),$ and $0.746\pm0.019-i(262\pm0.014)$ GeV, which is an additional companion pole related to $K_{0}^{\ast}(800)$. As a further investigation for increasing $N_{c}$ confirms, $K_{0}^{\ast}(800)$ emerges as a dynamically generated four-quark object as a consequence of pion-kaon loops.