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

Abstract

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.

13 pages and two appendices, 16 figures, version to be published in PRD, minor changes: novelty aspects of this work more clearly emphasized