DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States.

For the first time, we implement the deep-neural-network-based variational Monte Carlo approach for the multiquark bound states, whose complexity surpasses that of electron or nucleon systems due to strong SU(3) color interactions. We design a novel and high-efficiency architecture, DeepQuark, to address the unique challenges in multiquark systems such as stronger correlations, extra discrete quantum numbers, and intractable confinement interaction. Our method demonstrates competitive performance with state-of-the-art approaches, including diffusion Monte Carlo and Gaussian expansion method, in the nucleon, doubly heavy tetraquark, and fully heavy tetraquark systems. Notably, it outperforms existing calculations for pentaquarks, exemplified by the triply heavy pentaquark. For the nucleon, we successfully incorporate three-body flux-tube confinement interactions without additional computational costs. In tetraquark systems, we consistently describe hadronic molecule T_{cc} and compact tetraquark T_{bb} with an unbiased form of wave function ansatz. In the pentaquark sector, we obtain weakly bound D[over ¯]^{*}Ξ_{cc}^{*} molecule P_{ccc[over ¯]}(5715) with S=5/2 and its bottom partner P_{bbb[over ¯]}(15569). They can be viewed as the analogs of the molecular T_{cc}. We recommend experimental search of P_{ccc[over ¯]}(5715) in the D-wave J/ψΛ_{c} channel. DeepQuark holds great promise for extension to larger multiquark systems, overcoming the computational barriers in conventional methods. It also serves as a powerful framework for exploring confining mechanism beyond two-body interactions in multiquark states, which may offer valuable insights into nonperturbative QCD and general many-body physics.