Two-pole structure of the $D_0^{\ast }(2400)$

Abstract

The so far only known charmed non-strange scalar meson is dubbed as $D_0^{\ast }(2400)$ in the Review of Particle Physics. We show, within the framework of unitarized chiral perturbation theory, that there are in fact two $(I=1/2,J^P=0^{+})$ poles in the region of the $D_0^{\ast }(2400)$ in the coupled-channel $D\pi$, $D\eta$ and $D_s\bar{K}$ scattering amplitudes. With all the parameters previously fixed, we predict the energy levels for the coupled-channel system in a finite volume, and find that they agree remarkably well with recent lattice QCD calculations. This successful description of the lattice data is regarded as a strong evidence for the two-pole structure of the $D_0^{\ast }(2400)$. With the physical quark masses, the poles are located at $\left(2105_{-8}^{+6}-i102_{-12}^{+10}\right)$~MeV and $\left(2451_{-26}^{+36}-i134_{-8}^{+7}\right)$~MeV, with the largest couplings to the $D\pi$ and $D_s\bar{K}$ channels, respectively. Since the higher pole is close to the $D_s\bar{K}$ threshold, we expect it to show up as a threshold enhancement in the $D_s\bar{K}$ invariant mass distribution. This could be checked by high-statistic data in future experiments. We also show that the lower pole belongs to the same SU(3) multiplet as the $D_{s0}^{\ast }(2317)$ state. Predictions for partners in the bottom sector are also given.

Comments: 6 pages, 5 figures