Shi-Lin Zhu

We present the first systematic calculations of ϕ -, η c -, and J / ψ -nucleus ground states up to mass number A = 12 based on the HAL QCD meson-nucleon potentials at near-physical point. The ( A + 1 )-body Schrödinger equation is solved with a neural-network variational Monte Carlo framework, generalized to incorporate mesonic degrees of freedom. Benchmarking on light nuclei from H 2 to C 12 yields ground-state energies consistent with the experiment. Meson-nucleus bound states emerge at A ≥ 2 for ϕ , A ≥ 4 for J / ψ , and A ≥ 6 for η c . The ϕ -nucleus systems exhibit the strongest binding, with binding energies reaching tens of MeV. The J / ψ -nucleus and η c -nucleus systems are weakly bound at the few-MeV and sub-MeV scale, respectively. The binding energy per nucleon deepens nearly linearly with A for charmonium systems, whereas the ϕ -nucleus system exhibits a nonmonotonic behavior peaking at He 4 —a distinctive hallmark of the short-range and strongly attractive ϕ N interaction. The meson compresses the nucleon distribution relative to the parent nucleus, and evolves from a halo configuration to one embedded inside the nucleus with increasing A . Our results provide predictions for future experimental searches, and establish a quantitative bridge between lattice QCD meson-nucleon interactions and the emergent many-body phenomena in meson-nucleus bound states.

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,200 new measurements from 903 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Most of the 118 reviews are updated, including many that are heavily revised. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 96 review articles. Volume 2 consists of the Particle Listings and contains also 22 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group ( pdg.lbl.gov ) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app. The PDG API (Application Programming Interface) provides access to the data published in the Review in machine-readable format.

We investigate the electromagnetic polarizabilities of singly heavy mesons and doubly heavy baryons within the framework of heavy hadron chiral perturbation theory up to O ( p 3 ) . We estimate the low-energy constants using the nonrelativistic constituent quark model. A striking prediction of our study is the giant electric polarizabilities of the D * mesons: α E ( D ¯ * 0 ) ≈ 294 × 10 − 4 fm 3 and α E ( D * − ) ≈ 1.42 – 64.5 i × 10 − 4 fm 3 . These anomalously large values arise from the near-degenerate mass between D * and D π , which are orders of magnitude larger than those of their bottom counterparts. This kinematic coincidence induces a pronounced cusp structure in the chiral loops, reflecting the long-range dynamics of a pion cloud. For doubly heavy baryons, polarizabilities depend strongly on heavy-flavor composition: the b c q system differs markedly from c c q and b b q due to mixing with scalar heavy-diquark states. Using heavy diquark–antiquark symmetry (HDAS), we unify the chiral dynamics of singly heavy mesons and doubly heavy baryons in the heavy-quark limit. The pion-loop contributions dominate the electromagnetic structure of heavy hadrons and provide essential benchmarks for future lattice QCD simulations.

In this work, we perform a systematic investigation of the hidden-charm tetraquark states with I G ( J P C ) = 1 + ( 1 + − ) within the hadronic molecular picture, placing particular emphasis on systems composed of an S -wave ( D , D * ) meson and a P -wave [ D 0 * ( 2300 ) , D 1 ( 2430 ) , D 1 ( 2420 ) , D 2 * ( 2460 ) ] meson. Adopting the one-boson exchange potential, we solve the Schrödinger equation in momentum space via the complex scaling method. A crucial feature of our approach is the rigorous treatment of the unstable nature of the P -wave constituents by incorporating three-body decay effects arising from self-energy corrections and the static limit approximation. Our results demonstrate that these three-body dynamics play a crucial role in determining the pole positions, specifically in reproducing the large decay widths observed experimentally. We identify several broad resonances in the D * D ¯ 1 ( 2420 ) and D * D ¯ 2 * ( 2460 ) systems as candidates for the Z c ( 4430 ) , while the significantly broader resonances in the D D ¯ 0 * ( 2300 ) and D D ¯ 1 ( 2430 ) sectors are suggested as candidates for the Z c ( 4200 ) . Focusing on the D * D ¯ 2 * ( 2460 ) assignment as a specific case study, we further analyze the line shape of the Z c ( 4430 ) candidate using a Flatté-like parametrization with energy-dependent self-energy terms, providing predictions for its open-charm decay modes to guide future experimental searches.

We systematically investigate the S-wave singly heavy tetraquark systems containing two or three strange quarks, Q s s ¯ s ¯ , Q n s ¯ s ¯ , and Q s s ¯ n ¯ ( Q = c , b , n = u , d ) , within the constituent quark potential model. We solve the four-body Schrödinger equation using the Gaussian expansion method and identify resonances via the complex scaling method. There are no bound states below the lowest two-meson thresholds. We obtain several compact resonances with J P = 0 + , 2 + in Q s s ¯ s ¯ , and J P = 2 + in Q n s ¯ s ¯ and Q s s ¯ n ¯ . The pole positions are mainly distributed around 7.0–7.2 GeV (bottom) and 3.7–3.9 GeV (charm), with widths from a few to several tens of MeV. These resonances decay into D s η ′ , D ( s ) * ϕ , D s * K * , and D s * K ¯ * (and their bottom counterparts), providing targets for future experimental searches.

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 c c and compact tetraquark T b b with an unbiased form of wave function ansatz. In the pentaquark sector, we obtain weakly bound D ¯ * Ξ c c * molecule P c c c ¯ ( 5715 ) with S = 5 2 and its bottom partner P b b b ¯ ( 15569 ) . They can be viewed as the analogs of the molecular T c c . We recommend experimental search of P c c c ¯ ( 5715 ) in the D-wave J / ψ Λ 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.