Motivated by the observation of the doubly charmed tetraquark $ T_{cc}(3875)^+ $ , we present a systematic study of doubly heavy tetraquarks ( $ T_{QQ'\bar{q}\bar{q}'} $ ) using heavy antiquark-diquark symmetry (HADS) within a constituent quark model. By calibrating model parameters to known hadron spectra and incorporating the effective mass formula, we predict the masses for 38 ground-state tetraquarks with $ cc $ , $ bb $ , and $ bc $ heavy quark pairs, including the non-strange, single-strange, and double-strange configurations with quantum numbers $ J^P = 0^+, 1^+ $ and $ 2^+ $ . Notably, we identify several stable states below the relevant meson-meson thresholds, particularly in the $ bb\bar{q}\bar{q}' $ sector. The explicit connection between the doubly heavy tetraquark and the heavy baryon spectra through HADS reduces model dependence and reveals the fundamental systematics in the heavy-quark hadron landscape.

China

Liu-Yu Zhang

Tian-Wei Wu

Yong-Liang Ma

Bridging doubly heavy tetraquark mass spectrum with heavy baryons utilizing heavy antiquark-diquark symmetry * The work of Tian-Wei Wu is supported by the National Natural Science Foundation of China (12405108). Yong-Liang Ma is supported in part by the National Science Foundation of China (NSFC) (12347103) and Gusu Talent Innovation Program (ZXL2024363)

We present a comprehensive study of the axial-vector resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math> within the unitarized chiral perturbation theory, focusing on its two-pole structure and manifestation in femtoscopic observables. By considering the dominant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>K</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi></math> coupled channels, we reproduce the well-established double-pole structure and trace the chiral evolution of both poles as functions of the pion mass, using the vector-meson mass trajectories fitted to lattice-QCD data and experimental values. The lower pole, dominantly coupled to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mi>π</mi></math>, evolves from an above-threshold resonance to a virtual or bound state with increasing pion mass. In comparison, the higher pole, dominantly coupled to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>K</mi></math>, moves downward in energy, reflecting the strengthening of the chiral attraction. The influence of the finite vector-meson widths is systematically examined, showing that their inclusion smooths the pole trajectories without altering their qualitative behavior. Furthermore, femtoscopic correlation functions are calculated for all relevant vector-pseudoscalar channels in both charged sectors. The results exhibit distinct resonance and bound-state features consistent with the two-pole dynamics. The weak impact of higher channels, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mi>η</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, confirms that the simplified two-channel treatment captures the essential dynamics of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math> resonance. This study demonstrates that combining chiral extrapolation and femtoscopic correlation analyses provides a powerful and complementary framework for connecting lattice-QCD calculations, chiral effective theory, and experimental measurements, offering new insights into the molecular nature and chiral origin of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math> resonance.

Japan

Jia-Ming Xie

Zhi-Wei Liu

Jun-Xu Lu

Haozhao Liang

Spain

Raquel Molina

Li-Sheng Geng

Chiral evolution and femtoscopic signatures of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></mrow></math> resonance

A crossover involving three-fermion clusters is relevant to the hadron-quark crossover, which, if occurring in a neutron star, could naturally reproduce the dense-matter equation of state recently deduced from simultaneous observations of neutron-star masses and radii. To understand the crossover mechanism, we examine the role of tripling fluctuations induced by the formation of three-fermion clusters. The phase-shift representation of fluctuations manifests an interplay of bound and scattering states, leading to nonmonotonic momentum distributions of baryonlike clusters and peaked sound speed at finite densities. We demonstrate them by applying our approach to a nonrelativistic system of one-dimensional three-color fermions analogous to the hadron-quark matter.

Hiroyuki Tajima

Kei Iida

Toru Kojo

Tripling Fluctuations and Peaked Sound Speed in Fermionic Matter

We adapt the local density approximation to add the high-momentum tails (HMTs) to finite nuclei's Slater-determinant momentum distributions. The HMTs are extracted by the extended Brueckner-Hartree-Fock (EBHF) method or by the lowest order cluster approximation. With a correction factor being added to EBHF, it is sufficiently in agreement with the experimental benchmark, i.e., the high-momentum <math altimg='si1.svg'><mi>N</mi><mo stretchy='false'>/</mo><mi>Z</mi></math> ratios approximately equal to 1, and the low-momentum <math altimg='si1.svg'><mi>N</mi><mo stretchy='false'>/</mo><mi>Z</mi></math> ratios approximately equal to <math altimg='si1.svg'><mi>N</mi><mo stretchy='false'>/</mo><mi>Z</mi></math> of the systems. It is also found that the tensor force makes the nucleon-nucleon correlations appear more easily on the nuclear surface region and the percentage of high-momentum ( <math altimg='si2.svg'><mi>p</mi><mo linebreak='goodbreak' linebreakstyle='after'>&gt;</mo><mn>300</mn></math> MeV/c) nucleons, around 17%&#8211;18%, independent of isospin asymmetry.

Xiao-Hua Fan

Zu-Xing Yang

United States

Peng Yin

Peng-Hui Chen

Jian-Min Dong

Zhi-Pan Li

A local-density-approximation description of high-momentum tails in isospin asymmetric nuclei

We investigate theoretically a nonrelativistic trace anomaly and its impact on the low-temperature equation of state in spatially one-dimensional three-component fermionic systems with a three-body interaction, which exhibit a nontrivial three-body crossover from a bound trimer gas to dense fermionic matter with increasing density. By applying the <math><mi>G</mi></math>-matrix approach to the three-body interaction, we obtain the analytical expression for the ground-state equation of state relevant to the high-density degenerate regime and thereby address how the three-body contact or, equivalently, the trace anomaly emerges. The analytical results are compared with the recent quantum Monte Carlo data. Our study of the trace anomaly and the sound speed could have some relevance to the physics of hadron-quark crossover in compact stars.

Nonrelativistic trace anomaly and equation of state in dense fermionic matter

The extractions of nuclear charge radii from muonic atom spectroscopy for $^{40}$Ca and $^{208}$Pb are revisited to analyze the model dependencies induced by employing a Fermi-type charge distribution. For that, the charge densities, together with the corresponding muonic transition energies, calculated by the covariant density functional theory are used as a benchmark. The root-mean-square deviation of transition energies is calculated to quantitatively investigate the sensitivities of transition energies to the details of the two-parameter Fermi distribution. It is found that the second and fourth moments of the charge distribution can be extracted accurately from the muonic atom spectroscopy without much model dependencies, whereas the obtained two-parameter Fermi distributions cannot reproduce the details of the benchmarking charge densities and, in particular, its surface-diffuseness parameter cannot be determined accurately with the present experimental uncertainties on the muonic transition energies.

Hui Hui Xie

Tomoya Naito

Jian Li

Revisiting the extraction of charge radii of Ca and Pb with muonic atom spectroscopy

A Kohn-Sham scheme based multi-task neural network is elaborated for the supervised learning of nuclear shell evolution. The training set is composed of the single-particle wave functions and occupation probabilities of 320 nuclei, calculated by the Skyrme density functional theory. It is found that the deduced density distributions, momentum distributions, and charge radii are in good agreements with the benchmarking results for the untrained nuclei. In particular, accomplishing shell evolution leads to a remarkable improvement in the extrapolation of nuclear density. After a further charge-radius-based calibration, the network evolves a stronger predictive capability. This opens the possibility to infer correlations among observables by combining experimental data for nuclear complex systems.

A Kohn-Sham scheme based neural network for nuclear systems

The spin symmetry in the Dirac sea has been investigated with relativistic Brueckner–Hartree–Fock theory using the bare nucleon–nucleon interaction. Taking the nucleus 16O as an example and comparing the theoretical results with the data, the definition of the single-particle potential in the Dirac sea is studied in detail. It is found that if the single-particle states in the Dirac sea are treated as occupied states, the ground state properties are in better agreement with experimental data. Moreover, in this case, the spin symmetry in the Dirac sea is better conserved and it is more consistent with the findings using phenomenological relativistic density functionals.

Hong Kong

Shihang Shen

South Africa

Jie Meng

Germany

Peter Ring

Shuangquan Zhang

Spin symmetry in the Dirac sea derived from the bare nucleon–nucleon interaction

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn–Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

Romania

Yifei Niu

Tetsuo Hatsuda

Functional renormalization group and Kohn–Sham scheme in density functional theory

A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin–orbit splittings in neutron drops. This result is obtained from relativistic Brueckner–Hartree–Fock theory using the bare nucleon–nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.

Effects of tensor forces in nuclear spin–orbit splittings from ab initio calculations