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

Abstract

Isospin-1/2 charmed axial-vector $D^{\ast }\pi -D^{\ast }\eta -D_s^{\ast }\bar{K}$ 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 $D^{\ast }\pi$ threshold, that is strongly coupled to $D^{\ast }\pi$ in a relative $S$-wave and influences a wide energy region up to the $D^{\ast }\eta$ threshold. An axial-vector $D_1^{\prime }$ resonance is observed in the elastic $D^{\ast }\pi$ energy-region, which is coupled more strongly to $D$-wave $D^{\ast }\pi$. A single narrow tensor state is seen in $J^P=2^{+}$ coupled to both $D\pi$ and $D^{\ast }\pi$. In the region where $D^{\ast }\eta$ and $D_s^{\ast }\bar{K}$ 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 $D^{\ast }\pi -D^{\ast }\eta -D_s^{\ast }\bar{K}$ amplitudes around the upper energy limit of this analysis.

Comments: 52 pages, 14 figures