In this work, we propose a method for quantifying the difference between nuclear parton distribution functions in different nuclei and parton distribution functions in free nucleons using relative entropy (also known as the Kullback-Leibler divergence), a measure widely employed in quantum information theory. By introducing certain constraints and the ''minimum relative entropy'' hypothesis, we can determine the shape of the structure function in the intermediate-$\textit{x}$ region, which is closely connected to the renowned EMC effect. For quark structure functions, our results are consistent with the latest global fits to experimental data. This agreement suggests that the relative entropy-based methodology may provide novel insights into nucleon structure, particularly in cases where experimental data and theoretical QCD constraints are limited, such as those relevant to gluon nPDFs. Therefore, we apply this methodology to gluon nPDFs, analyzing the results from two commonly used global fitting groups, EPPS21 and nNNPDF3.0. Our analysis suggests that the central values of EPPS21 align more closely with the ''minimum relative entropy'' hypothesis. This finding underscores the utility of the proposed method and provides a valuable reference for future global fits of nPDFs.

China

Shu-Man Hu

Ao-Sheng Xiong

Ji Xu

Fu-Sheng Yu

Ji-Xin Yu

An analysis of nuclear parton distribution function based on relative entropy * Supported in part by the National Natural Science Foundation of China (12335003), the Fundamental Research Funds for the Central Universities (lzujbky-2023-stlt01, lzujbky-2024-oy02, and lzujbky-2025-eyt01), and the Scientific Research Innovation Capability Support Project for Young Faculty (ZYGXQNJSKYCXNLZCXM-P2). Ji Xu is supported in part by the National Natural Science Foundation of China (12475098, 12105247)

Motivated by the enigmatic vector charmonium-like states, we investigate the strong decay behaviors of four types of vector tetraquark states, which are possible candidates for the $Y(4660)$ , within the framework of three-point QCD sum rules based on rigorous quark-hadron duality. We take into account vacuum condensates up to dimension 5 on the QCD side and obtain the hadronic coupling constants and hence the partial decay widths of these states. The predicted total width, $61.5\pm7.3\,{\rm{MeV}}$ , is in excellent agreement with the experimental data for the $Y(4660)$ , supporting its interpretation as a $[sc][\bar{s}\bar{c}]$ tetraquark state with $J^{PC}=1^{--}$ .

Xiao-Song Yang

Zhi-Gang Wang

Analysis of the strong decays of the $\textit{Y}$ (4660) in tetraquark scenario via the QCD sum rules * Supported by the National Natural Science Foundation of China (12575083)

Hyperon-antihyperon pairs produced in high-energy electron-positron annihilation constitute a naturally spin-entangled system in the high-energy regime. Recently, a probabilistic amplification of entanglement, termed autodistillation, has been found in the daughter baryon-antibaryon pairs from hyperon decay and is constrained by an upper boundary. This work demonstrates that the quantum entanglement in this process may be accompanied by a decrease, constrained by a lower boundary, but it will not be completely lost. Thus, the entanglement of these systems undergoes redistribution within the phase space during the sequential decays of hyperons, highlighting the important role of hyperon polarization. By using the explicit spin density matrix of baryon pairs, it is also found that the quantumness of the system, characterized by quantum discord, always has the possibility to increase during decay processes, even when entanglement evaluated by concurrence and negativity does not increase.

Cong Li

Xu Cao

Ai-Qiang Guo

Chun-Xu Yu

Hong-Wei Zhang

Zhe Zhang

Entanglement redistribution of hyperon-antihyperon pair via sequential decay * Supported by the National Natural Science Foundation of China (12547111, 12447132, 12575089) and the National Key R&D Program of China (2023YFA1606703)

In this study, we discuss general critical properties of bound states with a one-boson-exchange potential. For simplicity, we first consider a system of two identical scalar particles as an example. The interaction between these two scalar particles is described by the exchange of another massive scalar meson under the instantaneous approximation, which yields the Yukawa potential. A highly accurate numerical method is used to determine the critical mass of the system. The resulting critical mass for the ground state is consistent with values reported in the literature, agreeing to about 35 significant figures. Highly accurate results for the $l=1$ case are also presented, which are significantly more precise than those previously reported in the literature. Furthermore, we extend the discussion to physical hadronic molecular states, for which form factors are introduced in the interaction to describe the structure of hadrons. Our numerical results show that although the binding energies of the hadronic molecular states depend on the cutoff in the form factors, the number of hadronic molecular states is almost independent of the cutoffs over a very wide physically relevant range. This indicates a strong and important property: for physically small couplings, the number of hadronic molecular states is almost solely determined by the coupling constants and the masses of the exchange particles. This highly accurate numerical method can also be straightforwardly applied to higher $\textit{l}$ cases or other systems.

Lin-Qing Song

Hai-Qing Zhou

Critical properties of bound states with one-boson-exchange potential * Supported by the National Natural Science Foundation of China (NSFC) (12075058, 12150013), and supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX25_0420)

A dark photon is an Abelian gauge boson arising from a new $ U(1)_D $ gauge symmetry, coupled to the Standard Model through kinetic mixing. The mixing parameter $\textit{ϵ}$ induces an effective coupling to the electromagnetic current, while $ g_\chi $ couples the dark photon to a stable dark matter particle $\textit{χ}$. We study $ J/\psi $ two-body and four-body decays mediated by a light dark photon ( $ m_U \lt 3.0 $ GeV) within the non-relativistic QCD (NRQCD) framework, considering both visible decays of the dark photon into SM fermions and invisible decays into dark sector particles. We investigate the detection sensitivity of BESIII and STCF experiments to the dark photon mass $ m_U $ and kinetic mixing parameter $\textit{ϵ}$. Our results show that, for two-body final states with $ m_U \lt 2m_\chi $ , BESIII sets $\textit{ϵ}$ upper limits of $ 9.3\times10^{-4} $ and $ 7.6\times10^{-4} $ for lepton-pair and hadronic signals, respectively, while STCF yields $ 3.7\times10^{-4} $ and $ 3.1\times10^{-4} $ . For invisible decays ( $ m_U\ge 2m_\chi $ ), BESIII achieves an $\textit{ϵ}$ limit of $ 1.4\times10^{-3} $ in the mass range $ 0.3\sim0.8 $ GeV, and STCF reaches $ 2.3\times10^{-4} $ in $ 0.3\sim1.9 $ GeV; no signals are expected in other mass regions, and visible decays are severely suppressed throughout. For four-body decay channels, BESIII yields an $\textit{ϵ}$ upper limit of $ 7.6\times10^{-5} $ for $ m_U \lt 2.2 $ GeV, whereas STCF achieves $ 1.2\times10^{-5} $ over the full mass range. When $ m_U\ge 2m_\chi $ , visible modes are nearly excluded; BESIII and STCF set $\textit{ϵ}$ limits from invisible decays of $ 8.8\times10^{-5} $ for $ m_U \lt 2.4 $ GeV and $ 1.4\times10^{-5} $ for $ m_U \lt 2.8 $ GeV, respectively, with no detectable signals at higher masses. Except for the limit of $ 9.3\times10^{-4} $ , all the above $\textit{ϵ}$ bounds lie in regions that are not currently excluded by collider experiments. Compared with the constraints from two-body final state processes, the limits derived from four-body decay channels lie well below existing experimental bounds, providing supportive references for constraining this parameter in BESIII and STCF experiments. Numerical results for the decay ratios $ \Gamma/\Gamma_{J/\psi} $ , expected event numbers, significance $ S/\sqrt{B} $ , and $ p_T $ distributions are presented where applicable.

Xiao Liang

Chun-Yuan Li

Bin-Peng Shang

Zong-Guo Si

Hong-Xin Wang

Xing-Hua Yang

Dai-Xing Zhang

Searching for dark photons in $\textit{J/ψ}$ decays * Supported in part by the National Natural Science Foundation of China (12105162, 12305106, 12235008, 12321005), the Natural Science Foundation of Shandong Province (ZR2021QA058, ZR2021QA040), and the Youth Innovation Technology Project of Higher School in Shandong Province (2023KJ146)

A search for the decay $ B^+\to D_s^+ K^+K^- $ has been reported by the LHCb Collaboration using $ pp $ collision data corresponding to an integrated luminosity of $4.8\;{\rm{fb}}^{-1}$ , collected at center-of-mass energies of 7, 8, and 13 TeV, in which no amplitude analysis of the $ K^+K^- $ subsystem was performed. In this work, we study the resonant contributions to the decay $ B^+\to D_s^+ K^+K^- $ within the perturbative QCD (PQCD) factorization framework. Contributions from the $\textit{S}$-wave resonances $ f_0(980) $ , $ f_0(1370) $ , and $ f_0(1500) $ , the $\textit{P}$-wave resonance $ \phi(1020) $ , and the $\textit{D}$-wave resonances $ f_2(1270) $ and $ f_2(1525) $ are taken into account. By introducing the corresponding two-meson distribution amplitudes for the $ K^+K^- $ system, we perform a complete perturbative analysis of the quasi-two-body decays $ B^+\to D_s^+(R\to)K^+K^- $ , where $\textit{R}$ denotes an intermediate resonance, and present the first PQCD predictions for the associated branching fractions. Using the narrow-width approximation, we further extract the branching fractions of the corresponding two-body decays $ B^+\to D_s^+R $ . Our results are consistent with the available experimental measurements and previous theoretical studies. Finally, we find that direct CP asymmetries vanish for these quasi-two-body decays within the Standard Model, so that any experimentally observed nonzero CP asymmetry would constitute a clear signal of physics beyond the Standard Model.

Zhi-Tian Zou

Jun-Peng Wang

Rui Zhou

Ying Li

Quasi-two-body decays $ {B^+\to D_s^+ (R\to) K^+K^-} $ in the perturbative QCD approach * Supported in part by the National Science Foundation of China (12375089, 12435004, 12075086), and the Natural Science Foundation of Shandong province (ZR2022ZD26, ZR2022MA035)

Motivated by the recent near-threshold enhancement in top-quark pair production reported by CMS and ATLAS, we study the $\textit{S}$-wave spectral structure of heavy-light systems containing a single top quark, namely $ t\bar{q} $ , $ t\bar{c} $ , and $ t\bar{b} $ , within the instantaneous Bethe-Salpeter formalism. Because the top quark decays on a timescale much shorter than the typical hadronization time, the discrete eigenvalues we obtain should be interpreted as model-dependent reference positions of possible quasi-bound heavy-light configurations, rather than as predictions for fully formed conventional hadrons. The numerical results indicate that the masses of these configurations lie close to the top-quark mass. For the $ t\bar{b} $ system, the masses of the first four $\textit{S}$-wave $ 0^{-} $ radial states are about $ 5.1 $ , $ 5.4 $ , $ 5.6 $ , and $ 5.7 $ GeV above the top-quark mass, respectively. For the $ t\bar{c} $ system, the corresponding values are about $ 1.9 $ , $ 2.2 $ , $ 2.5 $ , and $ 2.6 $ GeV. We also briefly discuss possible production and decay patterns at a qualitative level, which may serve as a reference for future dedicated phenomenological studies or for experimental constraints.

Jun-Hao Zhang

Shuo Yang

Bing-Dong Wan

The $\textit{S}$-wave topped meson * Supported in part by the National Natural Science Foundation of China (12575106, 12147214), and the Specific Fund of Fundamental Scientific Research Operating Expenses for Undergraduate Universities in Liaoning Province (LJ212410165019)

We propose a novel realization of the linear seesaw model with a non-invertible selection rule, assisted by $\mathbb{Z}_3$ symmetry. In our framework, Dirac mass matrices are generated at the one-loop level, breaking the non-invertible symmetry, while the symmetry remains intact at tree level. In addition to active neutrino masses, the model exhibits rich and testable phenomenology, including non-unitarity constraints, lepton flavor violation, lepton anomalous magnetic moments, and a dark matter candidate. After describing our model, we carry out a numerical analysis and present results for our physical parameters.

Hiroshi Okada

Slovenia

India

Yutaro Shoji

A novel realization of linear seesaw model in a non-invertible selection rule with the assistance of ${\mathbb{Z}_3}$ symmetry * Hiroshi Okada is supported by Zhongyuan Talent (Talent Recruitment Series) Foreign Experts Project. Yutaro Shoji is supported by the Slovenian Research Agency under the research grant J1-4389

We investigate the frame dependence of distribution functions within the framework of generalized chiral kinetic theory. Based on the derived transformation rules governing the choice of frame, we analytically obtain the global equilibrium solutions in the presence of vorticity and electromagnetic fields. Our results show that, under the assumption of varying electromagnetic fields, these equilibrium solutions can be uniquely determined.

Shu-Xiang Ma

Jian-Hua Gao

Frame dependence in generalized chiral kinetic theory * Supported in part by the National Natural Science Foundation of China (12575147, 12321005, 12175123)

Austria

H. Abele

Germany

G. Angloher

B. Arnold

Italy

M. Atzori Corona

Portugal

A. Bento

France

E. Bossio

F. Buchsteiner

J. Burkhart

F. Cappella

M. Cappelli

N. Casali

R. Cerulli

A. Cruciani

G. Del Castello

M. del Gallo Roccagiovine

S. Dorer

A. Erhart

M. Friedl

S. Fichtinger

V. Ghete

M. Giammei

C. Goupy

J. Hakenmüller

D. Hauff

F. Jeanneau

E. Jericha

M. Kaznacheeva

H. Kluck

A. Langenkämper

T. Lasserre

D. Lhuillier

M. Mancuso

R. Martin

B. Mauri

A. Mazzolari

L. McCallin

H. Neyrial

C. Nones

L. Oberauer

L. Peters

F. Petricca

W. Potzel

F. Pröbst

F. Pucci

F. Reindl

M. Romagnoni

J. Rothe

N. Schermer

J. Schieck

S. Schönert

C. Schwertner

L. Scola

G. Soum-Sidikov

L. Stodolsky

A. Schröder

R. Strauss

R. Thalmeier

C. Tomei

L. Valla

M. Vignati

M. Vivier

A. Wallach

P. Wasser

A. Wex

L. Wienke

Publisher Correction: Characterization of the low energy excess using a NUCLEUS $$\text {Al}_{2}\text {O}_{3}$$ detector