Doubly heavy tetraquarks from lattice QCD: incorporating diquark-antidiquark operators and the left-hand cut

Lattice studies of the doubly-charm tetraquark $T_{cc}=cc\bar{u}\bar{d}$ require the determination of the $D{D}^{\ast }$ scattering amplitude, which most often incorporate only meson-meson interpolators. We additionally incorporate diquark-antidiquark operators and find that these have some impact on certain eigenenergies. This study presents the first extraction of the $D{D}^{\ast }$ scattering amplitude based on the meson-meson as well as diquark antidiquark interpolators. The effect of the additional operators renders slightly smaller values of $p\cot {\delta }_0$ and a $T_{cc}$ pole slightly closer to the threshold. The scattering amplitude is extracted from eigenenergies by adopting plane-wave and effective-field-theoretic methods, which also incorporate the left-hand cut and address the partial wave mixing. The $T_{cc}$ is found to be a subthreshold resonance with a pole at $m_{T_{cc}}-m_D-m_{D^{\ast }}=-5.2_{-0.8}^{+0.7}-i\cdot 6.3_{-4.8}^{+2.4}$MeV, employing CLS ensembles with $m_{\pi }\simeq 280$MeV and the distillation method. A more significant effect of diquark-antidiquark operators on eigen-energies is found for larger heavy quark masses relevant for $T_{bb}$. We find that deeply bound $T_{bb}$ does not emerge when employing only meson-meson operators, where each meson is separately momentum projected, while the deeply bound state emerges after adding local diquark antidiquark operators.