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

TL;DR

This study uses lattice QCD to analyze coupled $DD^*$-$D^*D^*$ scattering, revealing a virtual bound state and a resonance pole, and predicts observable effects relevant for ongoing experiments.

Contribution

First lattice QCD determination of doubly-charmed coupled-channel scattering amplitudes, identifying poles and couplings relevant for experimental detection.

Findings

Identification of a virtual bound state $T_{cc}$ below $DD^*$ threshold.

Discovery of a resonance pole $T_{cc}^ ext{'}$ coupled to $D^*D^*$ channel.

Observation of a cusp in the $DD^*$ amplitude at the $D^*D^*$ threshold.

Abstract

The first determination of doubly-charmed isospin-0 coupled-channel $DD^\ast-D^\ast D^\ast$ 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 L\"{u}scher quantization condition. By analytically continuing the scattering amplitudes to complex energies, a $T_{cc}$ pole corresponding to a virtual bound state is found below $DD^\ast$ 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.