Scattering lengths of Nambu-Goldstone bosons off $D$ mesons and dynamically generated heavy-light mesons

TL;DR

This study uses unitary chiral perturbation theory to analyze lattice QCD data on scattering lengths involving D mesons, revealing the dynamic generation of the $D^*_{s0}(2317)$ and proposing a new renormalization scheme consistent with heavy-quark symmetry.

Contribution

The paper introduces a covariant formulation for scattering length analysis, demonstrates the dynamic generation of the $D^*_{s0}(2317)$, and proposes a new renormalization scheme aligned with chiral and heavy-quark symmetries.

Findings

Lattice QCD data are better described by covariant formulation.

The $D^*_{s0}(2317)$ is dynamically generated from $DK$ interactions.

A new renormalization scheme satisfying chiral power counting is proposed.

Abstract

Recent lattice QCD simulations of the scattering lengths of Nambu-Goldstone bosons off the $D$ mesons are studied using unitary chiral perturbation theory. We show that the Lattice QCD data are better described in the covariant formulation than in the heavy-meson formulation. The $D^*_{s0}(2317)$ can be dynamically generated from the coupled-channels $DK$ interaction without \textit{a priori} assumption of its existence. A new renormalization scheme is proposed which manifestly satisfies chiral power counting rules and has well-defined behavior in the infinite heavy-quark mass limit. Using this scheme we predict the heavy-quark spin and flavor symmetry counterparts of the $D^*_{s0}(2317)$.