Tetraquark interpolating fields in a lattice QCD investigation of the $D_{s0}^{\ast }(2317)$ meson

Abstract

We investigate the $D_{s0}^{\ast }(2317)$ meson using lattice QCD and considering correlation functions of several $\bar{c}s$ two-quark and $\bar{c}s(\bar{u}u+\bar{d}d)$ four-quark interpolating fields. These interpolating fields generate different structures in color, spin and position space including quark-antiquark pairs, tetraquarks and two-meson scattering states. For our computation we use an ensemble simulated with pion mass $m_{\pi }\approx 0.296\text{GeV}$ and spatial volume of extent $2.90\text{fm}$. We find in addition to the expected spectrum of two-meson scattering states another state around $60\text{MeV}$ below the $DK$ threshold, which we interpret as the $D_{s0}^{\ast }(2317)$ meson. This state couples predominantly to a quark-antiquark interpolating field and only weakly to a $DK$ two-meson interpolating field. The coupling to the tetraquark interpolating fields is essentially zero, rendering a tetraquark interpretation of the $D_{s0}^{\ast }(2317)$ meson rather unlikely. Moreover, we perform a scattering analysis using Lüscher's method and the effective range approximation to determine the $D_{s0}^{\ast }(2317)$ mass for infinite spatial volume. We find this mass $51\text{MeV}$ below the $DK$ threshold, rather close to both our finite volume result and the experimentally observed value.

arXiv comment13 pages, 6 figures; version accepted for publication in PRD

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