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

Sasa Prelovsek ^1,2,*, Emmanuel Ortiz-Pacheco ^1,3,†, Sara Collins ^4,‡, Luka Leskovec ^1,2,§, M. Padmanath ^5,6,∥, and Ivan Vujmilovic ^1,2,¶

¹Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
²Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia
³Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
⁴Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
⁵The Institute of Mathematical Sciences, CIT Campus, Chennai, 600113, India
⁶Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India

^*Contact author: sasa.prelovsek@ijs.si
^†Contact author: ortizpac@msu.edu
^‡Contact author: sara.collins@ur.de
^§Contact author: luka.leskovec@ijs.si
^∥Contact author: padmanath@imsc.res.in
^¶Contact author: ivan.vujmilovic@ijs.si

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Phys. Rev. D 112, 014507 – Published 8 July, 2025

DOI: https://doi.org/10.1103/rlgp-c9tb

Abstract

Lattice studies of the doubly charm tetraquark $T_{c c} = c c \bar{u} \bar{d}$ require the determination of the $D D^{*}$ 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 $D D^{*}$ scattering amplitude based on the meson-meson as well as diquark antidiquark interpolators. The effect of the additional operators renders slightly smaller values of $p$ $\cot δ_{0}$ and a $T_{c c}$ 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 $T_{c c}$ is found to be a subthreshold resonance with a pole at $m_{T_{c c}} - m_{D} - m_{D^{*}} = - {5.2}_{- 0.8}^{+ 0.7} - i \cdot {6.3}_{- 4.8}^{+ 2.4} MeV$ , employing coordinated lattice simulations (CLS) ensembles with $m_{π} ≃ 280 MeV$ and the distillation method. A more significant effect of diquark-antidiquark operators on eigen-energies is found for larger heavy quark masses relevant for $T_{b b}$ . We find that deeply bound $T_{b b}$ 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.

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Phys. Rev. D 112, 014507– Published 8 July, 2025

Vol. 112, Iss. 1 — 1 July 2025

Received 11 April 2025
Accepted 17 June 2025

DOI: https://doi.org/10.1103/rlgp-c9tb

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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

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