Large-$N_{c}$ pole trajectories of the vector kaon $K^{\ast}(892) $ and of the scalar kaons $K_{0}^{\ast}(800)$ and $K_{0}^{\ast}(1430)$

TL;DR

This study investigates how the spectral functions and pole trajectories of vector and scalar kaons evolve with increasing N_c using relativistic quantum field theory, revealing a single pole for the vector kaon and two poles for scalar kaons, including a dynamically generated one.

Contribution

It introduces a detailed analysis of N_c dependence of kaon spectral functions and pole structures, highlighting the dynamical generation of the scalar K0*(800) pole.

Findings

Vector kaon has a single pole and spectral peak.

Scalar sector contains two poles: one for K0*(1430) and a dynamically generated K0*(800).

K0*(800) does not produce a spectral peak, only a low-energy enhancement.

Abstract

We study the spectral functions, the poles and their trajectories for increasing $N_{c}$ of the vector kaon state $K^{\ast}(892),$ characterized by $I(J^{P})=\frac{1}{2}(1^{-})$, and of the scalar kaons $K_{0}^{\ast}(800)$ and $K_{0}^{\ast}(1430),$ characterized by $I(J^{P})=\frac{1}{2}(0^{+})$. To this end, we use relativistic QFT's Lagrangians with both derivative and non-derivative terms. In the vector kaonic sector the spectral function is well approximated by a Breit-Wigner function: there is one single peak and, correspondingly, a single pole in the complex plane. On the contrary, in the scalar sector, although the Lagrangian contains only one scalar kaonic field, we find two poles, one corresponding to a standard quark-antiquark ,,seed\textquotedblright\ state $K_{0}^{\ast}(1430),$ and one to a \textquotedblleft companion\textquotedblright\ dynamically generate pole $K_{0}^{\ast}(800)$. The latter does not correspond to any peak in the scalar kaonic spectral function, but only to an enhancement in the low-energy regime.