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

TL;DR

This lattice QCD study investigates the structure of the $D_{s0}^*(2317)$ meson, finding it to be predominantly a quark-antiquark state with little tetraquark component, and accurately determining its mass relative to the $D K$ threshold.

Contribution

The paper provides the first lattice QCD evidence that the $D_{s0}^*(2317)$ meson is mainly a quark-antiquark state, not a tetraquark, and accurately computes its mass using scattering analysis.

Findings

Identified a state 60 MeV below the $D K$ threshold.

Found weak coupling of the state to tetraquark interpolating fields.

Mass determined to be 51 MeV below the $D K$ threshold, consistent with experimental data.

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 $m_\pi \approx 0.296 \, \textrm{GeV}$ 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 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 $51 \, \textrm{MeV}$ below the $D K$ threshold, rather close to both our finite volume result and the experimentally observed value.