# Implications of chiral symmetry on $S$-wave pionic resonances and the scalar charmed mesons

## TL;DR

This paper explores how chiral symmetry influences low-energy pionic resonances and scalar charmed mesons, revealing that traditional Breit-Wigner models overestimate their masses and proposing a two-state interpretation for the $D^*_0(2400)$.

## Contribution

It demonstrates that considering chiral symmetry and final-state interactions explains B-meson decay data and suggests the $D^*_0(2400)$ is better described as two separate states.

## Key findings

- Breit-Wigner parameterization overestimates resonance masses.
- Experimental decay data are consistent with chiral effective field theory.
- The scalar charmed meson $D^*_0(2400)$ likely consists of two states.

## Abstract

The chiral symmetry of QCD requires energy-dependent pionic strong interactions at low energies. This constraint, however, is not fulfilled by the usual Breit--Wigner parameterization of pionic resonances, leading to masses larger than the real ones. We derive relations between nonleptonic three-body decays of the $B$-meson into a $D$-meson and a pair of light pseudoscalar mesons based on SU(3) chiral symmetry. Employing effective field theory methods, we demonstrate that taking into account the final-state interactions, the experimental data of the decays $B^-\to D^+\pi^-\pi^-$, $B_s^0\to \bar{D}^0K^-\pi^+$, $B^0\to\bar{D}^0\pi^-\pi^+$, $B^-\to D^+\pi^-K^-$ and $B^0\to\bar{D}^0\pi^-K^+$ can all be described by the nonperturbative $\pi/\eta/K$-$D/D_s$ scattering amplitudes previously obtained from a combination of chiral effective field theory and lattice QCD calculations. The results provide a strong support of the scenario that the broad scalar charmed meson $D^\ast_0(2400)$ should be replaced by two states, the lower one of which has a mass of around 2.1 GeV, much smaller than that extracted from experimental data using a Breit--Wigner parameterization.