Chinese Physics C

Alpha-decay systematics and a new scaling law in heavy and superheavy nuclei

Hisham Anwer, A. R. Abdulghany

2026, 50(1): 014111. doi: 10.1088/1674-1137/ae0307

Abstract:
This paper presents a systematic investigation of α-decay properties in even-even isotopic chains of Po ($ Z=84 $), Cm ($ Z=96 $), Hs ($ Z=108 $), and Fl ($ Z=114 $) using a semi-classical approach. Ground-state properties, including binding energies and nucleon density distributions, are calculated by minimizing a Skyrme-based energy density functional augmented with microscopic corrections. The derived nuclear densities and $ Q_\alpha $-values are used to construct the α decay potential through the double-folding model (DFM). The α-decay dynamics are treated quantum mechanically based on the preformed cluster model (PCM) within the Wentzel-Kramers-Brillouin (WKB) approximation. The analysis reveals distinct signatures of spherical shell closures at $ N=126 $ and $ N=184 $, along with secondary anomalies near $ N = 148 $, $ 152 $, and $ 162 $, which are consistent with deformed sub-shell effects predicted by nuclear structure models. The signature of daughter nuclear stability is systematically observed through one or more of the following features: shortened α-decay half-lives, enhanced $ Q_\alpha $ values, increased penetrabilities, and/or reduced assault frequencies. A new universal scaling relation, relating the decay half-lives and a scaled combination of nuclear charge and decay energy, is established, showing strong correlation across a wide mass range. Systematic comparisons demonstrate particular predictive advantages for superheavy nuclei, with the proposed method accurately reproducing observed half-life variations across all isotopic chains. The results confirm the sensitivity of α-decay observables to both spherical and deformed shell effects and reinforce the role of α-decay systematics as powerful tools for probing nuclear structure and guiding predictions in unexplored regions of the nuclear chart.

0νββ decay nuclear matrix elements under Left-Right symmetric model from the spherical quasi-particle random phase approximation method with realistic force

Ri-Guang Huang, You-Cai Chen, Dong-Liang Fang

2026, 50(1): 014113. doi: 10.1088/1674-1137/ae1196

Abstract:
We perform the calculation of nuclear matrix elements for the neutrinoless double beta decays under a Left-Right symmetric model mediated by light neutrinos, and we adopt the spherical quasi-particle random-phase approximation (QRPA) approach with a realistic force. For eight nuclei: ⁷⁶Ge, ⁸²Se, ⁹⁶Zr, ¹⁰⁰Mo, ¹¹⁶Cd, ¹²⁸Te, ¹³⁰Te, and ¹³⁶Xe, related nuclear matrix elements are given. We analyze each term, and the details of contributions from different parts are also provided. For the q term, we find that the weak-magnetism components of the nucleon current contribute equally to other components such as the axial-vector. We also discuss the influence of short-range correlations on these NMEs. It is found that the R term is more sensitive to short-range correlations than other terms due to the large portion of the contribution from high exchange momenta.

³H and ³He nuclei production in a combined thermal and coalescence framework for heavy-ion collisions in the few-GeV energy regime

2026, 50(1): 014104. doi: 10.1088/1674-1137/ae099a

Abstract:
A thermal model describing hadron production in heavy-ion collisions in the few-GeV energy regime is combined with the concept of nucleon coalescence to make predictions for the production of ³H and ³He nuclei. A realistic parametrization of the freeze-out conditions is employed, which accurately reproduces the spectra of protons and pions. It also correctly predicts the deuteron yield, which agrees with experimental observations. However, the predicted yields of ³H and ³He are lower than the experimental results by approximately a factor of two. The model predictions for the spectra can be compared with future experimental data.

Nuclear temperature of spectator source extracted by neutron spectra in ¹²⁴Sn,¹⁰⁷Sn + ¹²⁰Sn collisions at 600 MeV/nucleon

Huixiao Duan, Fan Zhang, Kailei Wang, Jun Su

2026, 50(1): 014110. doi: 10.1088/1674-1137/ae0f85

Abstract:
The properties of neutrons from spectator sources produced in ^107,124Sn + ¹²⁰Sn collisions at 600 MeV/nucleon are studied. The isospin-dependent quantum molecular dynamics (IQMD) model is used to describe the dynamical process of fragmentation, and the statistical model GEMINI is applied to simulate the secondary decay of the pre-fragments. The differential cross section and multiplicity of the neutrons emitted from the spectator source are used to prove the model's feasibility. The temperatures of the spectator source are extracted by two-source-fitting the transverse momentum distributions of the neutrons using the classical Maxwellian functions. The temperatures of the spectator sources extracted from calculations are consistent with the experimental data, those from the SMM model, and the isotopic temperature $ T_{\text{HeLi}} $. However, the participant source exhibits anomalously high temperatures. Our work suggests the possible model-errors of the IQMD+GEMINI model when describing the neutron emission from the participant source, which is reference for the further development of the model.

Correlation between Zero-Sound modes and nuclear equation of state stiffness detected by light vector boson

Jing Ye, Wei-Zhou Jiang

2026, 50(1): 014101. doi: 10.1088/1674-1137/adfa81

Abstract:
We investigate zero-sound modes in nuclear matter and neutron star matter using the relativistic random phase approximation (RRPA), focusing on the role of a light vector U boson in stiffening the nuclear equation of state (EOS). The occurrence of zero sound is closely linked to the stiffness of the nuclear EOS. The additional vector repulsive potential induced by the U boson results in the occurrence of zero sound at high densities in models with a soft high-density EOS, and the density range for zero sound extends to higher densities with larger coupling strength of the U boson. This confirms the unambiguous role of stiffening the high-density EOS in resulting in the appearance of zero sound.

Probing the cluster structure of ⁶Li with the ⁶Li + ¹²C nuclear reaction at 68 MeV

2026, 50(1): 014102. doi: 10.1088/1674-1137/ae072b

Abstract:
This study presents a combined experimental and theoretical investigation of the ⁶Li + ¹²C nuclear reaction at a laboratory energy of 68 MeV. The reaction products are identified via the standard $ \Delta E $–E technique. Angular distributions are constructed for the elastic, inelastic, and deuteron transfer channels by detecting emitted particles – ⁶Li and α. Elastic and inelastic scattering of ⁶Li off ¹²C are analyzed using the optical model and coupled channels approaches, with the interaction described by a double-folding potential. This potential is calculated based on the three-body wave function of ⁶Li. Pronounced coupled-channel effects that modify the potential and allow accurate reproduction of the experimental cross sections are observed. The resulting polarized potentials provide a more precise description of the initial-state interaction for further reaction modeling. The deuteron transfer channel, ¹²C(⁶Li, α)¹⁴N, is studied using the coupled reaction channels method. The coupling between the transfer and elastic channels is implemented using the three-body wave function of ⁶Li. As an alternative, a regular wave function constructed with a phenomenological Woods–Saxon potential is also employed. Comparison between the calculated differential cross sections and experimental data reveals a more complex and nuanced reaction mechanism, which supports the cluster structure of ⁶Li.

Breakup of ⁷Li in the field of ^118,120Sn nuclei and its effect on the elastic scattering channel

N. Amangeldi, N. Burtebayev, G. Yergaliuly, Maulen Nassurlla, B. Balabekov, Abylay Tangirbergen, Awad A. Ibraheem, Mohamed A. Dewidar, Sh. Hamada

2026, 50(2): 024101. doi: 10.1088/1674-1137/ae0999

Abstract:
The breakup of weakly-bound projectiles has been shown to significantly influence scattering processes, including elastic scattering. In this context, we revisit the angular distributions (ADs) for the elastic scattering of ⁷Li from ¹¹⁸Sn and ¹²⁰Sn targets. The study analyzes ⁷Li + ¹¹⁸Sn ADs over the energy range of 18.15–48 MeV and ⁷Li + ¹²⁰Sn ADs from 20 to 44 MeV, utilizing various nuclear interaction models, including the São Paulo potential, CDM3Y6 potential (with and without the rearrangement term), and cluster folding model. The results indicate that the real component of the folded potentials must be scaled down by 40–65% to achieve an accurate fit to the experimental ADs, underscoring the prominent role of ⁷Li breakup effects. Interestingly, the conventional threshold anomaly observed in reactions involving tightly bound nuclei is not present. Further analysis using the continuum discretized coupled channels (CDCC) approach provides excellent agreement with the data, reinforcing these findings.

Extracting the kinetic freeze-out properties of high energy pp collisions at the LHC with event shape classifiers

Jialin He, Xinye Peng, Zhongbao Yin, Liang Zheng

2026, 50(1): 014108. doi: 10.1088/1674-1137/ae07ba

Abstract:
Event shape measurements are crucial for understanding the underlying event and multiple-parton interactions (MPIs) in high energy proton-proton (pp) collisions. In this study, the Tsallis blast-wave model with independent non-extensive parameters for mesons and baryons was applied to analyze the transverse momentum spectra of charged pions, kaons, and protons in pp collision events at $ \sqrt{s}=13 $ TeV classified by event shape estimators such as relative transverse event activity, unweighted transverse spherocity, and flattenicity. Our analysis reveals consistent trends in the kinetic freeze-out temperature and non-extensive parameter across different collision systems and event shape classes. The use of diverse event-shape observables in pp collisions has significantly expanded the accessible freeze-out parameter space, enabling a more comprehensive exploration of its boundaries. Among these event shape classifiers, flattenicity emerges as a unique observable for disentangling hard process contributions from additive MPI effects, which helps isolate collective motion effects encoded by the radial flow velocity. Through the analysis of the interplay between event-shape measurements and kinetic freeze-out properties, we gain deeper insights into mechanisms responsible for flow-like signatures in pp collisions.

The role of fission in mass sensitivity study of the r-process

Yi Wei Hao, Yi Fei Niu, Zhong Ming Niu

2026, 50(1): 014106. doi: 10.1088/1674-1137/adfe55

Abstract:
A sensitivity study was performed to investigate the impact of individual nuclear masses on r-process rare-earth peak abundances in different astrophysical scenarios. The most impactful nuclei are primarily distributed in two regions on the nuclear chart: one located 20-30 neutrons away from stability (defined as region I) and another 7-15 neutrons away from stability (defined as region II), as previously reported in Phys. Lett. B 844, 138092 (2023). In this study, we extend our analysis by focusing on the role of fission in the mass sensitivity study. The results show that, in astrophysical scenarios involving fission, the sensitivity of nuclei in region I is diminished owing to the deposition of a large number of fission fragments in the rare-earth mass region. However, nuclei in region II retain high sensitivity because the contribution of fission decreases in the later stages of nucleosynthesis. This study highlights the impact of fission on the sensitivity of r-process abundances to nuclear masses and enhances the understanding of the rare-earth peak formation mechanism.

Examination of proton radioactivity in exotic nuclei with a deformed Gamow-like model

Zhe Wang, Quan Liu, Jian-You Guo

2026, 50(1): 014109. doi: 10.1088/1674-1137/ae042f

Abstract:
We modified the deformed Gamow-like model (DGLM) by incorporating the effect of daughter nucleus deformation on Coulomb interaction between the daughter nucleus and emitted proton. Using this modified DGLM, we systematically calculated the half-lives of both single- and two-proton radioactivities within a unified framework. Computational results demonstrate remarkable consistency with the experimentally observed radioactivity half-lives. In addition, our study explores how deformation affects penetration probabilities and establishes a universal curve relating penetration probability to experimental half-lives, validating the efficacy of the DGLM. Further, we made unified predictions for the half-lives of potential single-proton and two-proton radioactive nuclei, which align well with other models, thereby underscoring the reliability of the DGLM in predicting proton radioactivity.

Study of yrast and yrare low-lying excited states using machine learning approaches

Zhi Long Li, Bing Feng Lv, Yong Jia Wang, C. M. Petrache

2026, 50(1): 014107. doi: 10.1088/1674-1137/adfe54

Abstract:
The low-lying excitation energies of the $2_1^+, 4_1^+,2_2^+, 0_2^+,3_1^-, 0_3^+$ states in even-even nuclei are studied using two modern machine learning algorithms: the Light Gradient Boosting Machine (LightGBM) and Sparse Variational Gaussian Process (SVGP). The obtained results demonstrate that both LightGBM and SVGP perform well on the training and validation datasets when informed by a physics-based feature space. A detailed comparison of the results obtained for $2_1^+$ and $2_2^+$ states using the Hartree-Fock-Bogoliubov theory extended by the generator coordinate method and mapped onto a five-dimensional collective quadrupole Hamiltonian shows that both ML algorithms outperform this model in terms of accuracy. The extrapolation capabilities of these algorithms were further validated using newly measured 12 data points of $2_1^+$ and $2_2^+$ states, which were not included in the training set. In addition, the partial dependence plot method and the Shapley additive explanations method are used as interpretability tools to analyze the relationship between the input features and model predictions. These tools provide in-depth insights into how the input features influence the prediction of low-lying excitation energies and help identify the most important features that drive the prediction, which are valuable for understanding the low-lying excitation energies.

Dynamic shadow of a black hole with a self-interacting massive complex scalar hair

Mingzhi Wang, Cheng-Yong Zhang, Songbai Chen, Jiliang Jing

2026, 50(2): 025102. doi: 10.1088/1674-1137/ae1442

Abstract:
We investigate the dynamic shadows of a black hole with a self-interacting massive complex scalar hair. The complex scalar field $\psi$ evolves with time t, and its magnitude on the apparent horizon $|\psi_{\rm h}|$ starts from zero, undergoes a sharp rise followed by rapid oscillations, and eventually converges to a constant value. The variation in the photon sphere radius $r_{\rm ps}$ is similar to that of the magnitude $|\psi_{\rm h}|$. Owing to the emergence of the complex scalar hair $\psi$, the apparent horizon radius $r_{\rm h}$ starts increasing sharply and then smoothly approaches a stable value eventually. The shadow radius $R_{\rm sh}$ of the black hole with an accretion disk increases with time $t_{\rm o}$ at the observer's position. In the absence of an accretion disk, the shadow radius $R_{\rm sh}$ is larger and also increases as $t_{\rm o}$ increases. Furthermore, we slice the dynamical spacetime into spacelike hypersurfaces for all time points $t$. For the case with an accretion disk, the variation in $R_{\rm sh}$ is similar to that in the apparent horizon $r_{\rm h}$, because the inner edge of the accretion disk extends to the apparent horizon. In the absence of an accretion disk, the variation in $R_{\rm sh}$ is similar to that in the photon sphere radius $r_{\rm ps}$, because the black hole shadow boundary is determined by the photon sphere. As the variation in $r_{\rm ps}$ is induced by $\psi$, it can be stated that the variation in the size of the shadow is similarly caused by the change in $\psi$. Regardless of the presence or absence of the accretion disk, the emergence of the complex scalar hair $\psi$ causes the radius $R_{\rm sh}$ of the shadow to start changing. Moreover, we investigate the time delay $\Delta t$ of light propagating from light sources to the observer. These findings not only enrich the theoretical models of dynamic black hole shadows but also provide a foundation for testing black hole spacetime dynamics.

Prospects for probing dark matter particles and primordial black holes with the Square Kilometre Array using the 21 cm power spectrum at cosmic dawn

Meng-Lin Zhao, Yue Shao, Sai Wang, Xin Zhang

2026, 50(2): 025101. doi: 10.1088/1674-1137/ae1375

Abstract:
Probing the nature of dark matter (DM) remains an outstanding problem in modern cosmology. The 21 cm signal, a sensitive tracer of neutral hydrogen during the cosmic dawn, provides a unique means to investigate DM nature during this critical epoch. The annihilation and decay of DM particles, as well as Hawking radiation of primordial black holes (PBHs), can modify the thermal and ionization histories of the early universe, leaving distinctive imprints on the 21 cm power spectrum. Therefore, the redshifted 21 cm power spectrum serves as an effective tool for investigating such DM processes. In this work, we systematically assess the potential of the upcoming Square Kilometre Array (SKA) to constrain DM and PBH parameters using the 21 cm power spectrum. Assuming 10,000 h of integration time, the SKA is projected to reach sensitivities of $ \langle\sigma v\rangle \leq 10^{-28}\,{{\rm{cm}}}^{3}\,{{\rm{s}}}^{-1} $ and $ \tau\ge10^{28}\, \rm{s} $ for $ 10\; {{\rm{GeV}}} $ DM particles. It can also probe PBHs with masses of $ 10^{16}\,{{\rm{g}}} $ and abundances of $ f_{{{\rm{PBH}}}} \leq 10^{-6} $. These results indicate that the SKA can place constraints on DM annihilation, decay, and PBH Hawking radiation that are up to two to three orders of magnitude stronger than current limits. Furthermore, the SKA is expected to exceed existing bounds on sub-GeV DM and probe Hawking radiation from PBHs with masses above $ 10^{17}\,{{\rm{g}}} $, which are otherwise inaccessible using conventional cosmological probes. Overall, the SKA holds significant promise for advancing our understanding of both DM particles and PBHs, potentially offering new insights into the fundamental nature of DM.

Stellar configurations in f(R, L_m, T) gravity: probing anisotropy and stability via minimal geometric deformation

M. Zubair, Hira Sohail, Saira Waheed, Amara Ilyas, Irfan Mahmood

2026, 50(2): 025103. doi: 10.1088/1674-1137/ae1202

Abstract:
This study uses a minimal geometric deformation scheme within the $ f({\cal{R}},{\cal{L}}_m,T) $ gravity paradigm to model anisotropic compact stars using class-1 embedding spacetime. We introduce the deformation of the radial component of the metric tensor, which decouples the Einstein field equations and introduces an additional gravitational source. The relevant constants are evaluated using observational data from seven realistic star candidates by matching the inner region with the outer Schwarzschild line element. A comprehensive graphical analysis of three compact stars is performed to examine the impact of the coupling parameter β and deformation parameter n, revealing positive, well-behaved energy densities and pressures that satisfy the energy conditions. The study found that negative values of the coupling parameter β allow greater mass accumulation while preserving key physical characteristics, such as stability under Herrera's cracking condition and the extended Tolman-Oppenheimer-Volkoff equation. This study highlights the significance of gravitational decoupling for determining mass, redshift, and compactness and provides important insights into the internal structure of stellar bodies within this new generalized gravity framework.

Hawking tunneling radiation with thermodynamic pressure

Cheng Hu, Xiao-Xiong Zeng

2026, 50(1): 015103. doi: 10.1088/1674-1137/ae07b4

Abstract:
Hawking radiation elucidates black holes as quantum thermodynamic systems, thereby establishing a conceptual bridge between general relativity and quantum mechanics through particle emission phenomena. While conventional theoretical frameworks predominantly focus on classical spacetime configurations, recent advancements in extended phase space thermodynamics have redefined cosmological parameters (such as the Λ-term) as dynamic variables. Notably, the thermodynamics of anti-de Sitter (AdS) black holes has been successfully extended to incorporate thermodynamic pressure P. Within this extended phase space framework, although numerous intriguing physical phenomena have been identified, the tunneling mechanism of particles incorporating pressure and volume remains unexplored. This study investigates Hawking radiation through particle tunneling in Schwarzschild AdS black holes within the extended phase space, where the thermodynamic pressure P is introduced via a dynamic cosmological constant Λ. By employing semi-classical tunneling calculations with self-gravitation corrections, we demonstrate that emission probabilities exhibit a direct correlation with variations in Bekenstein-Hawking entropy. Significantly, the radiation spectrum deviates from pure thermality, aligning with unitary quantum evolution while maintaining consistency with standard phase space results. Moreover, through thermodynamic analysis, we verified that the emission rate of particles is related to the difference in Bekenstein-Hawking entropy of the emitted particles before and after they tunnel through the potential barrier. These findings establish particle tunneling as a unified probe of quantum gravitational effects in black hole thermodynamics.

Prospects for searching for sterile neutrinos in dynamical dark energy cosmologies using joint observations of gravitational waves and γ-ray bursts

Lu Feng, Tao Han, Jing-Fei Zhang, Xin Zhang

2026, 50(1): 015105. doi: 10.1088/1674-1137/ae0b43

Abstract:
In the era of third-generation (3G) gravitational-wave (GW) detectors, GW standard siren observations from binary neutron star mergers provide a powerful tool for probing the expansion history of the universe. Because sterile neutrinos can influence cosmic evolution by modifying the radiation content and suppressing structure formation, GW standard sirens offer promising prospects for constraining sterile neutrino properties within a cosmological framework. Building on this, we investigate the prospects of detecting sterile neutrinos in dynamical dark energy (DE) models using joint observations from 3G GW detectors and a future short gamma-ray burst detector, such as a THESEUS-like telescope. We consider the wCDM, holographic DE (HDE), and Chevallier–Polarski–Linder (CPL) models. Our results show that the properties of DE can influence the constraints on sterile neutrino parameters. Moreover, the inclusion of GW data significantly improves constraints on both sterile neutrino parameters and other cosmological parameters across all three models compared to the current limits derived from CMB+BAO+SN (CBS) observations. When GW data are included in the CBS dataset, a preference for $ \Delta N_{\rm{eff}} > 0 $ emerges at approximately the $ 1\sigma $ level in the wCDM and CPL models, while it reaches approximately $ 3\sigma $ in the HDE model. Moreover, the upper limits on $ m_{\nu,{\rm{sterile}}}^{\rm{eff}} $ are reduced by approximately 13%, 75%, and 3% in the wCDM, HDE, and CPL models, respectively.

Null test of cosmic curvature using deep learning method

Li Tang, Liang Liu, Ying Wu

2026, 50(1): 015107. doi: 10.1088/1674-1137/ae0b42

Abstract:
Determining the spatial curvature of the Universe, a fundamental parameter defining the global geometry of spacetime, remains crucial yet contentious due to existing observational tensions. Although Planck satellite measurements have provided precise constraints on spatial curvature, discrepancies persist regarding whether the Universe is flat or closed. Here, we introduce a model-independent approach leveraging deep learning techniques, specifically residual neural networks (ResNet), to reconstruct the dimensionless Hubble parameter E(z) and the normalized comoving distance D(z) from H(z) data and multiple SNe Ia compilations. Our dual-block ResNet architecture, which integrates a model-driven block informed by $ \Lambda $CDM and a purely data-driven block, yields smooth and robust reconstructions and enables the derivation of D'(z). By combining these reconstructed quantities, we assess the curvature diagnostic function $ {\cal{O}}_k(z) $. Analyses of the Pantheon+ sample support spatial flatness at the 1$ \sigma $ level over 0 < z < 2.5, with a mild tendency toward negative curvature at high redshift. Reconstructions based on Union3 and DESY5, however, show stronger departures toward negative curvature at intermediate and high redshifts. These results highlight the need for expanded and refined observational datasets to conclusively resolve these tensions and comprehensively investigate cosmic geometry.

Revised classification of the CHIME fast radio bursts with machine learning

Liang Liu, Hai-Nan Lin, Li Tang

2026, 50(1): 015102. doi: 10.1088/1674-1137/ae0725

Abstract:
Fast radio bursts (FRBs) are short-duration and energetic radio transients of unknown origin. Observationally, they are commonly categorized into repeaters and non-repeaters. However, this binary classification may be influenced by observational limitations such as sensitivity and time coverage of telescopes. In this study, we employ unsupervised machine learning techniques to re-examine the CHIME/FRB catalog, with the goal of identifying intrinsic groupings in the FRB population without relying on preassigned labels. Using t-distributed stochastic neighbor embedding (t-SNE) for dimensionality reduction and hierarchical density-based spatial clustering of applications with noise (HDBSCAN) for clustering, we find that the FRB sample naturally separates into two major clusters. One cluster contains nearly all known repeaters but is contaminated by some apparently non-repeaters, while the other cluster is dominated by non-repeaters. This suggests that certain FRBs previously labeled as non-repeaters may share intrinsic similarities with repeaters. Mutual information analysis reveals that rest-frame frequency width and peak frequency are the most informative features governing the clustering structure. Even when reducing the input space to just these two features, the classification remains robust.

Dark matter subhalo evaporation by Coulomb-like interaction with galactic gas

Yugen Lin, Yu Gao

2026, 50(1): 015104. doi: 10.1088/1674-1137/ae07be

Abstract:
Coulomb-like interactions typically have a cross-section that scales with relative particle velocity according to $ \sigma=\sigma_0 v^{-4} $. The momentum transfer rate between slightly charged dark matter (DM) and ionized particles increases significantly at low velocity, producing prominent evaporation effects on small-sized DM overdensities, which is a non-negligible influence for the evolution of DM subhalos. We calculate the subhalo evaporation rate in the ionized galactic region and show that, below the limits from current cosmic microwave background and baryon acoustic oscillation data, galactic ionized particles can effectively evaporate subhalos with masses below $ 10^{7.5} \;M_\odot $ at a kilo-parsec distance from the galactic center, which can potentially affect the subhalo distribution in the inner galaxy. We also show the evaporation limits in terms of the electron-recoil direct detection cross-section and show that the evaporation effects can readily extend to the sub-MeV range, which is unconstrained in direct detection experiments.

Testing Einstein-Maxwell Power-Yang-Mills hair via black hole photon rings

2026, 50(1): 015101. doi: 10.1088/1674-1137/ae039c

Abstract:
In this paper, the optical appearance of static and spherically symmetric hairy black holes is studied under the standard Einstein-Maxwell theory considering the p-power Yang-Mills term. During the research process, the specific case of $ p=1/2 $ was primarily selected for discussion. To understand the impact of the hairy parameter on black holes, we have studied the event horizon radius $ r_{\rm h} $, photon sphere radius $ r_{\rm ph} $, and radius of the innermost stable circular orbit $ r_{\rm isco} $ of this hairy black hole. Subsequently, we utilize the backward ray-tracing method to analyze the geodesics of photons around this black hole and discuss the influence of the hairy parameter on the photon geodesics. In addition, we calculate the distinctive shadow and photon ring structures of the black hole illuminated by a static thin accretion disk using three toy-model emission functions, and we briefly compare the optical appearance of the black hole in this nonlinear case ($ p=1/2 $) with that in the standard Yang-Mills case ($ p=1 $). The research results show that as the hairy parameter gradually increases, $ r_{\rm h} $, $ r_{\rm ph} $, $ r_{\rm isco} $, and the critical impact parameter $ b_{\rm ph} $ of the black hole all exhibit a decreasing trend. Meanwhile, it also causes the area of the black hole shadow and the photon ring to decrease accordingly. Compared with the standard case ($ p=1 $), the nonlinear Einstein-Maxwell Yang-Mills black hole exhibits a larger shadow radius and brighter ring radius but with an overall dimmer brightness relative to the standard scenario, demonstrating observable differences. Consequently, for the static and spherically symmetric Einstein-Maxwell power-Yang-Mills hairy black hole, no degeneracy occurs in the photon ring and shadow. Theoretically, it can reflect different black hole solutions and thus verify the Yang-Mills hair.

Valence quark distributions of pions: insights from Tsallis entropy

Jingxuan Chen, Xiaopeng Wang, Yanbing Cai, Xurong Chen, Qian Wang

2026, 50(1): 013103. doi: 10.1088/1674-1137/ae0998

Abstract:
We investigate the valence quark distributions of pions at a low initial scale ($Q^2_0$) using Tsallis entropy, a non-extensive measure that effectively captures long-range correlations among internal constituents. Utilizing the maximum entropy approach, we adopt two distinct functional forms and fit experimental data using the elegant GLR-MQ-ZRS evolution equation to derive the model parameters. Our findings indicate that the resulting valence quark distributions provide an optimal fit to the experimental data, with q values deviating from unity. This deviation indicates that correlations among valence quarks play a significant role in shaping understanding of the internal structures of pions. Additionally, our computations of the first three moments of the pion quark distributions at $ Q^2 = 4$ GeV² display consistency with other theoretical models, thereby reinforcing the importance of incorporating valence quark correlations within this analytical framework.

Soft pattern of gravitational Rutherford scattering from heavy target mass expansion

Yu Jia, Jichen Pan, Jia-Yue Zhang

2026, 50(1): 013102. doi: 10.1088/1674-1137/ad62d6

Abstract:
We investigate the soft behavior of the tree-level Rutherford scattering processes mediated via t-channel one-graviton exchange. We consider two types of Rutherford scattering processes: a low-energy massless structureless projectile (up to spin-1) hits a static massive composite particle carrying various spins (up to spin-2), and slowly moving light projectile hits a heavy static composite target. The unpolarized cross sections in the first type exhibit universal forms at the first two orders in $ 1/M $ expansion, yet differ at the next-to-next-to-leading order, though some terms at this order still remain universal or depend on the target spin in a definite manner. The unpolarized cross sections in the second type are universal at the lowest order in projectile velocity expansion and through all orders in $ 1/M $, independent on the spins of both projectile and target. The universality partially breaks down at relative order-$ v^2/M^2 $, albeit some terms at this order still depend on the target spin in a specific manner.

Search for the lepton number violating process ${{\boldsymbol J}/{\boldsymbol\psi }{\bf\to}{\boldsymbol K}^{\bf +}{\boldsymbol K}^{\bf +}{\boldsymbol e}^{\bf -}{\boldsymbol e}^{\bf -}{\bf +}{\boldsymbol {c.c.}}}$

M. Ablikim, M. N. Achasov, P. Adlarson, X. C. Ai, R. Aliberti, A. Amoroso, Q. An, Y. Bai, O. Bakina, Y. Ban, H.-R. Bao, V. Batozskaya, K. Begzsuren, N. Berger, M. Berlowski, M. B. Bertani, D. Bettoni, F. Bianchi, E. Bianco, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, H. Cai, M. H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, X. Y. Chai, J. F. Chang, T. T. Chang, G. R. Che, Y. Z. Che, C. H. Chen, Chao Chen, G. Chen, H. S. Chen, H. Y. Chen, M. L. Chen, S. J. Chen, S. L. Chen, S. M. Chen, T. Chen, X. R. Chen, X. T. Chen, X. Y. Chen, Y. B. Chen, Y. Q. Chen, Z. Chen, Z. K. Chen, J. C. Cheng, L. N. Cheng, S. K. Choi, X. Chu, G. Cibinetto, F. Cossio, J. Cottee-Meldrum, H. L. Dai, J. P. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, C. Q. Deng, Z. Y. Deng, A. Denig, I. Denisenko, M. Destefanis, F. De Mori, B. Ding, X. X. Ding, Y. Ding, Y. X. Ding, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, M. C. Du, S. X. Du, X. L. Du, Y. Y. Duan, Z. H. Duan, P. Egorov, G. F. Fan, J. J. Fan, Y. H. Fan, J. Fang, S.

2026, 50(1): 013107. doi: 10.1088/1674-1137/ae0f86

Abstract:
Based on $ (10087\pm 44)\times10^{6} $ $ J/\psi $ events collected with the BESIII detector, we search for the lepton number violating decay $ J/\psi \to K^+K^+e^-e^- + c.c. $ for the first time. The upper limit on the branching fraction of this decay is set to $ 2.1 \times 10^{-9} $ at the 90% confidence level with a frequentist method. This is the first search for $ J/\psi $ decays with a lepton number change by two, offering valuable insights into the underlying physical processes.

Charmed meson structure across crossover from SU(4) Polyakov quark meson model with isospin asymmetry

Abdel Magied DIAB

2026, 50(1): 013101. doi: 10.1088/1674-1137/ae042d

Abstract:
The Polyakov Quark Meson (PQM) model is extended to SU(4) flavor symmetry by incorporating the charm quark and introducing a finite isospin asymmetry. This model incorporates the light, strange, and charm chiral condensates, along with the Polyakov-loop variables, to describe the confinement–deconfinement phase transition in a thermal and dense QCD medium. The inclusion of the charm quark condensate enhances the capability of the SU(4) PQM model to explore the spatial and thermal resolution of the chiral phase structure, particularly in the crossover and high-temperature regimes. We construct the QCD phase diagram ($ T/T_\chi-\mu_I/m_\pi $) plane, indicating a decrease in the pseudo-critical temperature as the isospin chemical potential increases, and explore thermodynamic quantities related to the QCD equation of state at very high temperatures. Fluctuations of quark flavors, conserved charges, and baryon-charm correlations are studied across a wide temperature range. The SU(4) PQM model exhibits good qualitative agreement with lattice QCD calculations. Additionally, we calculate the meson mass spectrum at zero and finite temperature, showing that the charm sector remains thermally stable over a wide temperature range. Overall, this study highlights the capability of the SU(4) PQM model to describe key features of the QCD matter at high temperatures and its relevance to heavy-ion collisions and astrophysical studies.

$ {\boldsymbol\rho\bf\to \boldsymbol\pi\boldsymbol\pi }$ hadronic decay in the Nambu-Jona-Lasinio model: Mass-Width interplay and Beyond-RPA corrections

Qing-Wu Wang, Xiao-Fu Łü, Hua-Zhong Guo

2026, 50(1): 013105. doi: 10.1088/1674-1137/ae07b3

Abstract:
This paper presents novel framework for analyzing unstable composite particles using Green's functions and dispersion relations. As an illustrative example, we explore the ρ vector meson decay process $\rho\to\pi\pi$ within the Nambu–Jona-Lasinio (NJL) model. This approach addresses a key limitation of the four-quark interaction description, which adequately describes two-quark bound states but fails to describe decay processes. The Bethe-Salpeter (BS) wave function of the ρ meson exhibits time evolution that leads to the physical mass M incorporating a correction $\Delta M $. This correction depends on the decay width $\Gamma(M)$. This work provides crucial insights into the dynamical relationship between resonance masses and their decay properties, addressing a long-standing challenge in hadron physics. The calculated mass and width are in good agreement with the experimental values, demonstrating the effectiveness of this approach for studying unstable hadronic systems beyond conventional bound-state approximations.

Towards a detection of reactor ${\overline {\boldsymbol v}_{\boldsymbol e} \boldsymbol\to \overline {\boldsymbol v}_{\boldsymbol\mu} }$ and ${\overline {\boldsymbol v}_{\boldsymbol e} \boldsymbol\to \overline {\boldsymbol v}_{\boldsymbol\tau} }$ oscillations with possible CP violation

Yifang Wang, Zhi-zhong Xing, Shun Zhou

2026, 50(1): 011001. doi: 10.1088/1674-1137/ae0996

Abstract:
We propose a novel method to detect reactor $ \overline{\nu}^{}_e \to \overline{\nu}^{}_\mu $ and $ \overline{\nu}^{}_e \to \overline{\nu}^{}_\tau $ oscillations by using elastic antineutrino-electron scattering processes $ \overline{\nu}^{}_\alpha + e^- \to \overline{\nu}^{}_\alpha + e^- $ (for $ \alpha = e, \mu, \tau $), among which the $ \overline{\nu}^{}_e $ events can be singled out by accurately measuring the $ \overline{\nu}^{}_e $ flux via the inverse beta decay $ \overline{\nu}^{}_e + p \to e^+ + n $. A proof-of-concept study shows that such measurements will not only be able to test the conservation of probability for reactor antineutrino oscillations, but also offer a new possibility to probe leptonic CP violation at the one-loop level.

Systematic study of α decay half-life within cluster-formation model

Wen-Chao Dai, Jie-Dong Jiang, Yin Fan, Xiao Liu, Peng-Cheng Chu, Xi-Jun Wu, Xiao-Hua Li

2026, 50(1): 014103. doi: 10.1088/1674-1137/ae042c

Abstract:
In this study, based on the Wentzel-Kramers-Brillouin (WKB) theory, by parameterizing the assault frequency $ \nu $ as a function of the $ \alpha $ decay energy and charge radius of parent nucleus, with the $ \alpha $ decay preformation factor $ P_\alpha $ being calculated through the cluster-formation model (CFM), we systematically investigate the $ \alpha $ decay half-lives of 559 nuclei from the ground state, including 177 even-even, 277 odd-A, and 105 odd-odd nuclei. The calculated results indicate that our model can effectively reproduce the experimental data, with a corresponding standard deviation of 0.408. In addition, we use this model to predict the $ \alpha $ decay half-lives of 70 even-even, odd-A, and odd-odd nuclei with Z = 119 and 120. For comparison, we also use the universal decay law (UDL) proposed by Qi et al. [Phys. Rev. Lett 103, 072501 (2009)] and the unitary Royer formula (DZR) proposed by Deng et al. [Phys. Rev. C 101, 034307 (2020)]. The calculated results are in good agreement.

Anisotropic quark propagation and Zeeman effect in an external magnetic field

Minghui Ding, Fei Gao, Sebastian M. Schmidt

2026, 50(1): 013104. doi: 10.1088/1674-1137/ae07b9

Abstract:
We investigated the impact of a constant external magnetic field on the dressed propagators of up-, down-, and strange quarks. In the weak field limit, we derive a general momentum-space representation for the propagator and numerically solve the corresponding gap equation. Our analysis reveals that the vector term of the propagator can be decomposed into components parallel and perpendicular to the magnetic field, resulting in anisotropic effective masses, with the transverse mass consistently exceeding the longitudinal mass. This mass disparity exhibits a power law dependence on the magnetic field strength and is less pronounced for the strange quark compared to up and down quarks. Additionally, the magnetic field induces axial-vector and tensor terms, highlighting the Zeeman effect, resulting from quark interactions with the magnetic field. These findings have important implications for (inverse) magnetic catalysis and phenomena such as vector meson and pion condensations.

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