Confirmation of the existence of an exotic state in the $\pi D$ system

Abstract

In recent years many candidates for states beyond the most simple realization of the quark model were found in various experiments around the world. However, so far no consensus exists on their structure, although there is strong evidence that at least some of those are dynamically generated from meson-meson interactions. In this Letter we provide an important missing piece from the theoretical side to prove that the lightest open charm strange and non-strange scalars $D_{s0}^*(2317)$ and $D_0^*$ as well as their axial-vector partner states can all be understood as emerging from the interactions between Goldstone bosons stemming from the spontaneous breaking of chiral symmetry and the ground state charmed mesons. For that purpose we exploit the flavor multiplet structure of the lightest open-charm positive-parity scalar states in an SU(3) symmetric lattice QCD simulation at large pion masses to establish that there exists a bound state in the flavor-sextet representation, which cannot emerge for quark-antiquark states but appears naturally for four-quark configurations. Moreover, we find repulsion in the $[15]$ representation and thus no single-particle state in this representation exists, falsifying the expectation for tetraquark models. The findings establish the pattern predicted for the interactions of Goldstone bosons with $D$ mesons from chiral symmetry and the paradigm of the lowest-lying positive-parity charmed mesons as dynamically generated states.