# Study of open-charm $0^+$ states in unitarized chiral effective theory with one-loop potentials

## TL;DR

This paper derives and unitarizes chiral potentials for Goldstone boson and pseudoscalar charmed meson interactions, validating simplified models and exploring open-charm $0^+$ states as dynamically generated poles.

## Contribution

It introduces a covariant chiral effective theory with explicit vector charmed mesons and demonstrates the validity of $D^*$-less potentials for scattering length calculations.

## Key findings

- Negligible difference between models with and without explicit vector mesons for S-wave scattering.
- Successfully unitarized one-loop potentials to fit lattice QCD data.
- Identified poles corresponding to open-charm $0^+$ states and analyzed their trajectories.

## Abstract

Chiral potentials are derived for the interactions between Goldstone bosons and pseudoscalar charmed mesons up to next-to-next-to-leading order in a covariant chiral effective field theory with explicit vector charmed-meson degrees of freedom. Using the extended-on-mass-shell scheme, we demonstrate that the ultraviolet divergences and the so-called power counting breaking terms can be properly absorbed by the low-energy constants of the chiral Lagrangians. We calculate the scattering lengths by unitarizing the one-loop potentials and fit them to the data extracted from lattice QCD. The obtained results are compared to the ones without an explicit contribution of vector charmed mesons given previously. It is found that the difference is negligible for $S$-wave scattering in the threshold region. This validates the use of $D^\ast$-less one-loop potentials in the study of the pertinent scattering lengths. We search for dynamically generated open-charm states with $J^P=0^+$ as poles of the $S$-matrix on various Riemann sheets. The trajectories of those poles for varying pion masses are presented as well.