$D_1$ and $D_2$ resonances in coupled-channel scattering amplitudes from lattice QCD

TL;DR

This lattice QCD study investigates isospin-1/2 charmed meson scattering amplitudes, revealing bound states and resonances such as a $D_1$ bound state, a $D_1^ extprime$ resonance, and a tensor state, with implications for coupled-channel dynamics.

Contribution

First lattice QCD calculation of coupled-channel $D^* o D extpi$, $D o D exteta$, and $D_sar{K}$ scattering amplitudes revealing new charmed meson states.

Findings

Identified a $D_1$ bound state just below $D^* extpi$ threshold.

Observed an $D_1^ extprime$ resonance in the elastic $D^* extpi$ channel.

Detected a narrow tensor state in $J^P=2^+$ channel.

Abstract

Isospin-1/2 charmed axial-vector $D^*\pi-D^*\eta-D^*_s\bar{K}$ scattering amplitudes are computed, along with interactions in several other $I=1/2$ $J^P$ channels. Using lattice QCD, we work at a light-quark mass corresponding to $m_\pi\approx 391$ MeV, where the lowest three-hadron threshold ($D\pi\pi$) lies high enough to enable a rigorous treatment of this system considering only two-hadron scattering channels. At this light-quark mass, an axial-vector $D_1$ bound state is observed just below $D^*\pi$ threshold, that is strongly coupled to $D^*\pi$ in a relative $S$-wave and influences a wide energy region up to the $D^*\eta$ threshold. An axial-vector $D_1^\prime$ resonance is observed in the elastic $D^*\pi$ energy-region, which is coupled more strongly to $D$-wave $D^*\pi$. A single narrow tensor state is seen in $J^P=2^+$ coupled to both $D\pi$ and $D^*\pi$. In the region where $D^*\eta$ and $D^*_s\bar{K}$ are kinematically open, the available energy levels indicate significant $S$-wave interactions. Upon searching this region for poles, several possibilities exist with large uncertainties. One additional state consistently arises, predominantly coupled to the $S$-wave $D^*\pi-D^*\eta-D^*_s\bar{K}$ amplitudes around the upper energy limit of this analysis.