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

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}$$andspatialvolumeofextent$2.90 , $\text{fm}$$. 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 L"uscher’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.