Near-threshold states in coupled $D{D}^{\ast }-D^{\ast }{D}^{\ast }$ scattering from lattice QCD

Abstract

The first determination of doubly-charmed isospin-0 coupled-channel $D{D}^{\ast }-D^{\ast }{D}^{\ast }$ scattering amplitudes from lattice QCD is presented. The finite-volume spectrum is computed for three lattice volumes with a light-quark mass corresponding to $m_{\pi }\approx 391$ MeV and is used to extract the scattering amplitudes in $J^P=1^{+}$ via the Lüscher quantization condition. By analytically continuing the scattering amplitudes to complex energies, a $T_{cc}$ pole corresponding to a virtual bound state is found below $D{D}^{\ast }$ threshold. We also find a second pole, $T_{cc}^{\prime }$, corresponding to a resonance pole below the kinematically closed $D^{\ast }{D}^{\ast }$ channel, to which it has a strong coupling. A non-zero coupling is robustly found between the $S$-wave $D{D}^{\ast }$ and $D^{\ast }{D}^{\ast }$ channels producing a clear cusp in the $D{D}^{\ast }$ amplitude at the $D^{\ast }{D}^{\ast }$ threshold energy. This suggests that the experimental $T_{cc}^{\prime }$ should be observable in $D{D}^{\ast }$ and $D^{\ast }{D}^{\ast }$ final states at ongoing experiments.

Comments: 31 pages, 13 figures, 14 tables