New insights into the $D^{*}_{s0}(2317)$ and other charm scalar mesons

TL;DR

This paper uses unitarized chiral effective field theory to analyze charm scalar mesons, especially the $D^{*}_{s0}(2317)$, exploring their pole structures, quark mass, and $N_C$ dependencies, revealing insights into their nature.

Contribution

It provides a detailed analysis of charm scalar mesons' pole structures and their dependence on quark mass and $N_C$, offering new understanding of their underlying dynamics.

Findings

The $D^{*}_{s0}(2317)$ pole shows similar pion mass trajectories to the $f_0(500)$.

Bound and virtual states in the $(S,I)=(1,0)$ channel approach the $DK$ threshold at $N_C=6$.

Neither the $D^{*}_{s0}(2317)$ nor the $(S,I)=(0,1/2)$ poles behave like standard quark-antiquark mesons at large $N_C$.

Abstract

Through the scattering of light-pseudoscalar mesons ($\pi,K,\eta,\eta'$) off charmed mesons ($D, D_s$), we study the $D^{*}_{s0}(2317)$ state and other relevant charm scalar mesons in a unitarized chiral effective field theory approach. We investigate the charm scalar meson poles with different strangeness ($S$) and isospin ($I$) quantum numbers as well as their corresponding residues, which provide the coupling strengths of the charm scalar mesons. Both the light-quark mass and $N_C$ dependences of the pole positions of the $D^{*}_{s0}(2317)$ and the poles with $(S,I)=(0,1/2)$ are analyzed in detail in this work. Interestingly we observe quite similar pion mass trajectories for the resonance pole at around 2.1 GeV with $(S,I)=(0,1/2)$ to those of the $f_0(500)$ given in the literature. When increasing the values of $N_C$ we find that a bound state and a virtual state in the $(S,I)=(1,0)$ channel asymmetrically approach the $D K$ threshold for $N_C<6$, and they meet at this threshold at $N_C=6$. When $N_C>6$, the bound and virtual states move into the complex plane on the second Riemann sheet and become a symmetric pair of resonance poles. For large enough values of $N_C$, neither the $D^{*}_{s0}(2317)$ pole nor the poles with $(S,I)=(0,1/2)$ tend to fall down to the real axis, indicating that they do not behave like a standard quark-antiquark meson at large $N_C$.