Contribution of constituent quark model $c\bar{s}$ states to the dynamics of the $D^\ast_{s0}(2317)$ and $D_{s1}(2460)$ resonances

TL;DR

This paper investigates the structure of the $D^ ext{*}_{s0}(2317)$ and $D_{s1}(2460)$ resonances, demonstrating they are predominantly hadronic-molecular states influenced by $D^{( ext{*})}K$ interactions, challenging simple quark model descriptions.

Contribution

The study introduces an effective field theory framework incorporating both $D^{( ext{*})}K$ meson-meson interactions and bare $car s$ states, fitting lattice data and estimating the molecular components of the resonances.

Findings

Resonances are mainly hadronic-molecular in nature.

The model successfully describes lattice QCD energy levels.

The $D^{( ext{*})}K$ components dominate the structure of these states.

Abstract

The masses of the $D^\ast_{s0}(2317)$ and $D_{s1}(2460)$ resonances lie below the $DK$ and $D^\ast K$ thresholds respectively, which contradicts the predictions of naive quark models and points out to non-negligible effects of the $D^{(\ast)}K$ loops in the dynamics of the even-parity scalar ($J^\pi=0^+$) and axial-vector ($J^\pi=1^+$) $c\bar s$ systems. Recent lattice QCD studies, incorporating the effects of the $D^{(\ast)}K$ channels, analyzed these spin-parity sectors and correctly described the $D^\ast_{s0}(2317)-D_{s1}(2460)$ mass splitting. Motivated by such works, we study the structure of the $D_{s0}^\ast(2317)$ and $D_{s1}(2460)$ resonances in the framework of an effective field theory consistent with heavy quark spin symmetry, and that incorporates the interplay between $D^{(\ast)}K$ meson-meson degrees of freedom and bare P-wave $c\bar s$ states predicted by constituent quark models. We extend the scheme to finite volumes and fit the strength of the coupling between both types of degrees of freedom to the available lattice levels, which we successfully describe. We finally estimate the size of the $D^{(\ast)}K$ two-meson components in the $D^\ast_{s0}(2317)$ and $D_{s1}(2460)$ resonances, and we conclude that these states have a predominantly hadronic-molecular structure, and that it should not be tried to accommodate these mesons within $c\bar{s}$ constituent quark model patterns.