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.

31 pages, 13 figures, 14 tables

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• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Prediction of an $I(J^P)=0(1^{-})$ $\bar{b}\bar{b}ud$ Tetraquark Resonance Close to the $B^{\ast }{B}^{\ast }$ Threshold Using Lattice QCD Potentials
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• Coupled-channel scattering of $DD,D{D}^{\ast }$ and $D^{\ast }{D}^{\ast }$ in isospin-$1$ from lattice QCD
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$
• Low-energy $DD$ scattering in lattice QCD
• Exotic hadrons associated with $b$-quark