Revealing the $D_0^{\ast }(2300)$ two-pole structure from lattice data and the SU(3) limit

Abstract

We perform an analysis of LQCD light - charmed (pseudoscalar) meson scattering data with UChPT for pion masses ranging from $m_{\pi }\simeq 230$~MeV till the SU(3) limit, $m_{\pi }\simeq 700$~MeV. We find two poles in the non-strange isospin $I=1/2$ sector that can be related to the experimental $D_0(2300)$ resonance. At the physical pion mass, the poles are located at $\sqrt{s_0}=2094(7)(1)-i111(7)(13)$ MeV, and $2463(60)(30)-i108(14)(12)$~MeV. While the first pole, named here $D_0^{\ast }(2100)$, is always a resonance in $D\pi$ within the $1\sigma$ region, the second pole can be a resonance or virtual state close to the $D\eta ,D_s\bar{K}$ thresholds. For the first time, the pion mass dependence on different chiral trajectories including SU(3) LQCD data are investigated for these poles. We find that in the $m_s=m_{s,\mathrm{phy}}$ trajectory, the $D_0^{\ast }(2100)$ resonance pole behaves similarly as the $\sigma$ resonance in $\pi \pi$ scattering, splitting into two poles, connected to the $\bar{3}$ representation. Moreover, we found that the higher pole related to the experimental $D_0^{\ast }(2300)$ can be related to the $6$ representation. We highlight that since this pole couples strongly to channels with hidden strangeness, its mass is fairly constant in the $\mathrm{Tr}[M]=C$ trajectory, what can be tested in future LQCD simulations. The compositeness of the $D_0^{\ast }(2100)$ state at the SU(3) limit is evaluated. Finally, other sectors are also discussed.