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

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 $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$, $B_s^0\to {\bar{D}}^0{K}^{-}{\pi }^{+}$, $B^0\to {\bar{D}}^0{\pi }^{-}{\pi }^{+}$, $B^{-}\to D^{+}{\pi }^{-}{K}^{-}$ 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 $D_0^{\ast }(2400)$ 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.

Comments: 26 pages, 9 figueres