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 $m_pi approx 0.296 , textrm{GeV}$ and spatial volume of extent $2.90 , textrm{fm}$. We find in addition to the expected spectrum of two-meson scattering states another state around $60 , textrm{MeV}$ below the $D K$ 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 $D K$ 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 Luschers method and the effective range approximation to determine the $D_{s0}^ast(2317)$ mass for infinite spatial volume. We find this mass $51 , textrm{MeV}$ below the $D K$ threshold, rather close to both our finite volume result and the experimentally observed value.