Chinese Physics C -

Investigating interacting dark energy models using fast radio burst observations

Hang Yan, Yu Pan, Jia-Xin Wang, Wen-Xiao Xu, Ze-Hui Peng

2025, 49(11): 115109. doi:10.1088/1674-1137/adf316

Abstract:
This study investigates the utility of Fast Radio Bursts (FRBs) as novel observational probes to constrain models of interacting dark energy (IDE). By leveraging FRBs' dispersion measures (DMs) and redshifts, we perform a comprehensive analysis of three IDE models— $ \gamma_{\mathrm{m}} $ IDE, $ \gamma_{\mathrm{x}} $ IDE, andξIDE—using Markov Chain Monte Carlo (MCMC) methods based on 86 localized FRBs and simulated datasets containing 2,500 to 10,000 mock events. By disentangling the contributions to the observed DMs from the Milky Way, host galaxies, and intergalactic medium (IGM), key cosmological parameters are constrained, including the Hubble constant ( $ H_{0} $ ), matter density ( $ \Omega_{\mathrm{m}} $ ), dark energy equation of state ( $ \omega_{\mathrm{x}} $ ), and interaction strengths ( $ \gamma_{\mathrm{m}} $ , $ \gamma_{\mathrm{x}} $ ,ξ). The best-fit values of the $ \gamma_{\mathrm{m}} $ IDE models indicate a potential alleviation of the cosmic coincidence problem. Subsequently, we utilize information criteria (IC) to conduct a comparative assessment of the three IDE models. When applied to the current sample of observed FRBs, theξIDE model yields slightly lower IC values than the $ \gamma_{\mathrm{m}} $ IDE and $ \gamma_{\mathrm{x}} $ IDE models across all three information criteria, although the differences are not statistically significant. Notably, our study emphasizes the significance of current FRB observations in exploring potential interactions within the dark sector. These results underscore the value of FRB measurements as valuable complementary probes that provide further constraints on alternative cosmological models.

Detecting cosmological phase transitions with Taiji: sensitivity analysis and parameter estimation

Fan Huang, Zu-Cheng Chen, Qing-Guo Huang

2025, 49(10): 105103. doi:10.1088/1674-1137/ade65f

Abstract:
We investigate the capability of the Taiji space-based gravitational wave observatory to detect stochastic gravitational wave backgrounds produced by first-order phase transitions in the early universe. Using a comprehensive simulation framework that incorporates realistic instrumental noise, galactic double white dwarf confusion noise, and extragalactic compact binary backgrounds, we systematically analyze Taiji's sensitivity across a range of signal parameters. Our Bayesian analysis demonstrates that Taiji can robustly detect and characterize phase transition signals with energy densities exceeding $\Omega_{\text{PT}} \gtrsim 1.4 \times 10^{-11}$ across most of its frequency band, with strong sensitivity at approximately $10^{-3}$ to $10^{-2}$ Hz. For signals with amplitudes above $\Omega_{\text{PT}} \gtrsim 1.1 \times 10^{-10}$ , Taiji can determine the peak frequency with relative precision better than 10%. These detection capabilities would enable Taiji to probe electroweak-scale phase transitions in various beyond-Standard-Model scenarios, potentially revealing new physics connected to baryogenesis and dark matter production. We quantify detection confidence using both Bayes factors and the Deviance Information Criterion, obtaining consistent results that validate our statistical methodology.

Exploring axion-like particle from observation of FSRQ Ton 599 by Fermi-LAT

Jun Li, Xiao-Jun Bi, Lin-Qing Gao, Peng-Fei Yin

2025, 49(10): 105107. doi:10.1088/1674-1137/ade6d2

Abstract:
High energy photons traveling through astrophysical magnetic fields have the potential to undergo oscillations with axion-like particles (ALPs), resulting in modifications to the observed photon spectrum. High energy $ \gamma $ -ray sources with significant magnetic field strengths provide an ideal environment to investigate this phenomenon. Ton 599, a flat spectrum radio quasar with a magnetic field strength on the order of Gauss in its emission region, presents a promising opportunity for studying ALP-photon oscillations. In this study, we analyze the effects of ALP-photon oscillations on theγ-ray spectrum of Ton 599, as observed by Fermi-LAT. Our investigation considers the potential influences of the broad-line region and dusty torus on the $ \gamma $ -ray spectrum of Ton 599. We set the constraints on the ALP parameters at a 95% confidence level and show that the constraints on $ g_{a\gamma} $ can reach approximately $ 2 \times 10^{-12}\; \text{GeV}^{-1} $ for $ m_a \sim 10^{-9}\; \text{eV} $ .

Gravitationally deformed polytropic models in extended teleparallel gravity and influence of decoupling parameters on constraining mass-radius relation

Sneha Pradhan, S. K. Maurya, A. Errehymy, G. Mustafa, P.K. Sahoo

2025, 49(10): 105101. doi:10.1088/1674-1137/ade4a1

Abstract:
In this study, we used the gravitational decoupling method (GD) via minimal geometric deformation (MGD) to analyze strange deformed stars (SS) within the modified $ f({\cal{T}}) $ gravity theory. By adopting the Buchdahl ansatz and the quadratic polytropic equation of state (EOS), we derived deformed SS models by assuming that the energy-momentum components of the deformed fluid satisfy $ \rho=\Theta_0^0 $ and $ p_r=\Theta_1^1 $ . This approach leads to different classes of exact solutions. The study of physical viability tests ensures that the proposed configurations adhere to realistic constraints. Furthermore, we analyzed the impact of relevant parameters in three scenarios: GR, $ f({\cal{T}}) $ , and $ f({\cal{T}})+MGD $ . In addition, observational constraints were used for comparison with GW190814 and neutron stars (NSTRs) PSR J1614-2230 and PSR J1903 + 327, with mass ranges of $ 2.5-2.67 M_\odot $ , $ 1.97 \pm 0.04 M_\odot $ , and $ 1.667 \pm 0.021 M_\odot $ , respectively. Remarkably, we observed from the $ M-R $ curves that NSTRs with masses ranging from $ 2.4 $ to $ 3.5M_{\odot} $ correspond to a range of radii from $ 9.80^{+0.02}_{-0.01} $ to $ 13.01^{+0.01}_{-0.01}\;{\rm km} $ for different values of the parametersα,β,γ, and $ \zeta_1 $ . Notably, for the $ \rho=\Theta_0^0 $ solution, higher values ofαproduce NSTRs with smaller masses and radii, while the $ p_r=\Theta_1^1 $ solution yields larger masses and radii. This evidences the existence of massive NSTRs within the modified gravity theory $ f({\cal{T}}) $ .

Rotating and non-linear magnetic-charged black hole with an anisotropic matter field

Qi-Quan Li, Yu Zhang, Hoernisa Iminniyaz

2025, 49(10): 105106. doi:10.1088/1674-1137/ade0a9

Abstract:
We present the solution for a non-linear magnetic-charged black hole with an anisotropic matter field and extend it to obtain the corresponding rotating black hole solution using the modified Newman-Janis algorithm. The event horizon and ergosphere of the rotating black hole are analyzed from a geometric perspective, revealing that the rotating black hole can have up to three horizons. The first law of thermodynamics and the squared-mass formula for the rotating black hole are derived from a thermodynamic perspective, based on which we obtain thermodynamic quantities and examine the thermodynamic stability of the rotating black hole. Additionally, we calculate the Penrose process for the rotating black hole, showing the influence of various black hole parameters on the maximum efficiency of the Penrose process.

Perturbations of massless external fields on magnetically charged black holes in string-inspired Euler-Heisenberg theory

Xufen Zhang, De-Cheng Zou, Chao-Ming Zhang, Ming Zhang, Rui-Hong Yue

2025, 49(10): 105109. doi:10.1088/1674-1137/ade661

Abstract:
This study investigates the perturbations of massless scalar and electromagnetic fields on the magnetically charged black holes in string-inspired Euler-Heisenberg theory. We calculate the quasinormal frequencies (QNFs) and discuss the influence of black hole magnetic charge $ Q_m $ , coupling parameter $ \epsilon $ , and angular momentumlon QNFs, emphasizing the relationship between these parameters and the behavior of QNMs. Results obtained using the AIM method were in good agreement with those obtained using the WKB method. In addition, the WKM method was used to calculate the greybody factor to understand how it is affected by the black hole magnetic charge $ Q_m $ and coupling parameter $ \epsilon $ .

Testing the cosmic distance duality relation using Type Ia supernovae and radio quasars through model-independent methods

Fan Yang, Xiangyun Fu, Bing Xu, Kaituo Zhang, Yang Huang, Ying Yang

2025, 49(10): 105108. doi:10.1088/1674-1137/ade4a3

Abstract:
In this study, we perform a cosmological-model-independent test on the cosmic distance duality relation (CDDR) by comparing the angular diameter distance (ADD) obtained from the compact radio quasars (QSOs) with the luminosity distance (LD) obtained from the Pantheon+ Type Ia supernovae (SNIa) sample. The binning method and artificial neural network are employed to match ADD data with LD data at the same redshift, and three different parameterizations are adopted to quantify possible deviations from the CDDR. We initially investigate the effects of specific prior values for the absolute magnitude $ M_{\rm{B}} $ from SNIa and linear size scaling factorlfrom QSOs on the CDDR test. The results demonstrate that these prior values introduce significant biases in the CDDR test. To avoid the biases, we propose a method independent of $ M_{\rm{B}} $ andlto test the CDDR, which treats the fiducial value of a new variable $ \kappa\equiv 10^{M_{\rm{B}} \over 5}\,l $ as a nuisance parameter and then marginalize its impact with a flat prior in the statistical analysis. The results show that the CDDR is consistent with the observational data, and QSOs can serve as a powerful tool for testing the CDDR independent of cosmological models.

Black holes immersed in modified Chaplygin-like dark fluid and cloud of strings: geodesics, shadows, and images

Xiang-Qian Li, Yoonbai Kim, Bum-Hoon Lee, Hao-Peng Yan, Xiao-Jun Yue

2025, 49(10): 105104. doi:10.1088/1674-1137/add9fa

Abstract:
This study investigates a black hole surrounded by a cloud of strings and a cosmological dark fluid characterized by a modified Chaplygin-like equation of state (MCDF), $ p=A\rho-B/\rho^{\beta} $ . We analyze its geodesic structure, shadow, and optical appearance. An analysis of the effective potential and epicyclic frequencies reveals that the existence of innermost/outermost stable circular orbits (ISCOs/OSCOs) for timelike particles is controlled by the parameters of the MCDF and the cloud of strings. The behavior of orbital conserved quantities and the Keplerian frequency are also examined. By equating the influence of the MCDF on the spacetime metric at spatial infinity with that of a cosmological constant, we constrain the MCDF parameters using the observed shadow radii of Sgr A* and M87*. We investigate the effects of the cloud of strings and MCDF on the shadows and optical images of the black hole, assuming various thin disk accretion profiles. Using the method developed by Wald and collaborators, light trajectories are classified by their impact parameters into direct emission, the lensing ring, and the photon ring. The presence of OSCOs can lead to the existence of outer edges in the direct emission and lensing ring images. The observed brightness primarily originates from direct emission, with a minor contribution from the lensing ring, whereas the contribution of the photon ring is negligible owing to extreme demagnification. The influence of the cloud of strings and MCDF parameters on all results is analyzed throughout the study.

Higher-order inner photon rings of a horizonless ultracompact object with an antiphoton sphere and their interferometric pattern

Yuan-Xing Gao

2025, 49(10): 105102. doi:10.1088/1674-1137/addc52

Abstract:
A horizonless ultracompact object can have a stable antiphoton sphere, which causes the photons inside the unstable photon sphere to strongly deflect, thereby leading to the formation of distinctive inner photon rings. In this study, we present analytical descriptions for the shape, thickness, and interference pattern of higher-order inner photon rings. By taking the static spherically symmetric Schwarzschild star with a photon sphere as an example, we find that its inner photon rings can be more non-circular and thicker than the outer ones and show that the inclusion of the inner photon rings can result in new features in the interferometric pattern. Further, our formulae can be applied to other ultracompact objects, providing a convenient approach for studying the observational properties of their higher-order photon rings.

Imprints of an early matter-dominated era arising from dark matter dilution mechanism on cosmic string dynamics and gravitational wave signatures

Shi-Qi Ling, Zhao-Huan Yu

2025, 49(10): 105105. doi:10.1088/1674-1137/addcd6

Abstract:
We investigate the influence of an early matter-dominated era in cosmic history on the dynamics of cosmic strings and the resulting stochastic gravitational waves. Specifically, we examine the case where this era originates from the dark matter dilution mechanism within the framework of the minimal left-right symmetric model. By numerically solving the Boltzmann equations governing the energy densities of the relevant components, we meticulously analyze the modifications to the cosmological scale factor, the number density of cosmic string loops, and the gravitational wave spectrum. Our results reveal that the early matter-dominated era causes a characteristic suppression in the high-frequency regime of the gravitational wave spectrum, providing distinct and testable signatures for future ground-based interferometer experiments.

Circular motion and acceleration of charged particles around magnetized rotating black holes in scalar-tensor-vector gravity

Saeed Ullah Khan, Javlon Rayimbaev, Zhi-Min Chen, Zdeněk Stuchlík

2025, 49(9): 095102. doi:10.1088/1674-1137/add8fc

Abstract:
One of the most critical issues in relativistic astrophysics is explaining the origin mechanisms of (ultra)high-energy charged particle components of cosmic rays. Black holes (BHs), which are vast reservoirs of (gravitational) energy, are candidates for such energetic cosmic ray sources. The main idea of this study is to investigate the effects of scalar-tensor-vector gravity (STVG) and so-called modified gravity (MOG) on charged particle acceleration by examining their dynamics and acceleration through the magnetic Penrose process (MPP) near magnetized Kerr BHs in MOG (Kerr-MOG BHs). First, we briefly study the horizon structure of the Kerr-MOG BH. Then, we derive the effective potential for the circular motion of charged particles by considering electromagnetic and MOG field interactions on the particles to gain insight into the stability of circular orbits. Our results show that the magnetic field can extend the region of stable circular orbits, whereas the STVG parameter reduces the instability of the circular orbit. Thus, from the examination of particle trajectories, we observe that, at fixed values of other parameters, the Schwarzschild BH captures the test particle; in the case of the Kerr BH, the test particle escapes to infinity or is captured by the BH, while in the Kerr-MOG BH, the test particle is trapped in some region around the BH and starts orbiting it at a smaller value of the MOG field parameter. By investigating the MPP, we found that, in stronger magnetic fields, the behavior of orbits becomes more chaotic. As a result, the particle escapes to infinity with high energies.

Investigating the shadows of new regular black holes with a Minkowski core: effects of spherical accretion and core type differences

Yi Xiong, Jin Pu, Yi Ling, Guo-Ping Li, Gao-Ming Deng

2025, 49(9): 095101. doi:10.1088/1674-1137/addfce

Abstract:
We investigated the shadows and optical appearances of a new type of regular black holes (BHs) with a Minkowski core under various spherical accretion scenarios. These BHs are constructed by modifying the Newtonian potential based on the minimum observable length in the Generalized Uncertainty Principle (GUP). They correspond one-to-one with traditional regular BHs featuring a de-Sitter (dS) core (such as Bardeen/Hayward BHs), characterized by a quantum gravity effect parameter ( $ \alpha_0 $ ) and spacetime deformation factor (n). We found that the characteristic parameters give rise to some novel observable features. For these new BHs, both the shadow and photon sphere radii decrease with the increase in $ \alpha_0 $ , while the observed specific intensity increases. Conversely, asnincreases, the shadow and photon sphere radii increase, while the observed specific intensity decreases. Under different spherical accretion scenarios, the shadows and photon sphere radii remain identical; however, the observed specific intensity is greater under static spherical accretion than under infalling spherical accretion. Additionally, we found that these regular BHs with different cores exhibit variations in shadows and optical appearances, particularly under static spherical accretion. Compared with Bardeen BH, the new BHs exhibit a lower observed specific intensity, a dimmer photon ring, and smaller shadow and photon sphere radii. Larger values of $ \alpha_0 $ lead to more significant differences, and a similar trend was also observed when comparing with Hayward BH. Under infalling spherical accretion, the regular BHs with different cores exhibit only slight differences in observed specific intensity, which become more evident when $ \alpha_0 $ is relatively large. This suggests that the unique spacetime features of these regular BHs with different cores can be distinguished through astronomical observation.

Analytical solutions of CPT-odd Maxwell equations in Schwarzschild spacetime

Hao Wang, Zhi Xiao, Bing Sun

2025, 49(9): 095103. doi:10.1088/1674-1137/ade541

Abstract:
In this paper, we present the CPT-violating (CPTV) Maxwell equations in curved spacetime using the Newman-Penrose (NP) formalism. We obtain a semi-analytical solution to the Maxwell equations in Schwarzschild spacetime under the assumption that the CPT-odd $ \left(k_{AF}\right)^\mu $ term exhibits spherical symmetry in the Schwarzschild background. By retaining only terms up to the linear order in the $ \left(k_{AF}\right)^\mu $ coefficient, we obtain perturbative solutions by treating the solutions of the Lorentz-invariant Maxwell equations as the zeroth-order approximation and incorporating the $ \left(k_{AF}\right)^\mu $ terms jointly as an additional source term alongside the external charge current. Each resulting NP scalar field can be factorized into two components: the radial component, expressed in terms of hypergeometric functions, and the angular component, described by spin-weighted spherical harmonics.

Nuclear mass predictions with a Bayesian neural network

Shuang Qu, Jin-Yan Zhang, Man Bao

2025, 49(10): 104106. doi:10.1088/1674-1137/ade958

Abstract:
The Bayesian neural network (BNN) has been widely used to study nuclear physics in recent years. In this study, a BNN was applied to optimize seven theoretical nuclear mass models, namely, six global models and one local model. The accuracy of these models in describing and predicting masses of nuclei with both the proton number and the neutron number greater than or equal to eight was improved effectively for two types of numerical experiments, particularly for the liquid drop model and the relativistic mean-field theory, whose root mean square deviations (RMSDs) for describing (predicting) nuclear masses were reduced by 81.5%−90.6% (66.9%−84.2%). Additionally, the relatively stable RMSDs as nuclei move away from theβ-stability line and the good agreement with experimental single-neutron separation energies further confirm the reliability of the BNN.

Charged-current quasielastic neutrino scattering off nuclei with nucleon-nucleon short-range correlations

Jian Liu, Qiang Su, Qinglin Niu, Lei Wang, Zhongzhou Ren

2025, 49(10): 104102. doi:10.1088/1674-1137/ade126

Abstract:
In recent years, neutrino-nucleus scattering has been extensively researched to investigate nuclear structures and interactions between neutrinos and nucleons. In this study, a charged-current quasielastic (CCQE) neutrino-nucleus scattering model is developed to explore the nuclear mean-field dynamics and short-range correlation effects. In this model, the effect of the nuclear structure is depicted using the scaling function $ f(\psi) $ , whereas the neutrino-nucleon interaction is represented by the elementary weak cross section $ \sigma_0 $ . The results indicate that the double-differential cross section of the scattered muon is influenced by the energy $ E $ and momentum $ {\bf{p}} $ of the nucleon in the nuclei, and the total cross section depends primarily on the incident neutrino energy $ E_\nu $ . Furthermore, incorporating short-range correlations results in the flux-integrated differential cross sections in the high- $ T_\mu $ region producing larger values, a longer tail, and achieving better experimental consistency. It eventually elucidates the physical relationship between the neutrino-nucleus scattering cross section and variation in the incident neutrino energy. This paper shares insights for the research on nucleon dynamics and presents detailed investigations of the neutrino-nucleus scattering mechanism.

Universal momentum distributions for the spin-singletNNchannels

O. A. Rubtsova, V. N. Pomerantsev, L. D. Blokhintsev

2025, 49(10): 104104. doi:10.1088/1674-1137/addaaf

Abstract:
The formalism for a quantitative treatment of high-momentum components of $ NN $ momentum distributions for the spin-singlet channels is presented. This approach suggests that the use of a distribution for a virtual state in momentum representation for the $ NN $ channel in question is a universal one, which can be further employed within contact formalisms for nuclei. It is shown how such distributions can be calculated from low-energy scattering wave functions in the same channels. As a result, a new characteristic (a constant) for the high-momentum part of the momentum distribution in a spin-singlet channel is introduced. To test the approach, we calculate the $ pp $ nuclear contacts for the $ ^3 {\rm{He}}$ , nucleus which appear to be nearly the same for four realistic $ NN $ interactions with essentially different high-momentum properties. The results should be useful for researchers studying the problem of short-range correlations in nuclei. In particular, the approach gives a generalization for the formalisms based on nuclear contacts.

Synthesis of unknown^287−290Og isotopes infusion-evaporation reactions

Rui Zhu, Gen Zhang, Xiao-Ye Zhang, Zi-Long Wang, Yue-Long Zhang, Jia-Le Cao, Feng-Shou Zhang

2025, 49(10): 104107. doi:10.1088/1674-1137/adec4d

Abstract:
Based on the dinuclear system model, the effects of capture, fusion, and survival stages on fusion-evaporation reactions were analyzed. The calculated evaporation residue cross sections were in good agreement with current experimental data. These outcomes indicate that Ar + Fm reactions are promising for synthesizing Oganesson isotopes, mainly due to the lower internal fusion barriers, which lead to higher fusion probabilities. New Og isotopes, such as $ ^{287-290}\text{Og}$ , could be synthesized through the reactions $ ^{254}\text{Fm}(^{36}\text{Ar}, 3{{n}})^{287}\text{Og}$ , $ ^{255}\text{Fm}(^{36}\text{Ar}, 3{{n}})^{288}\text{Og}$ , $ ^{254}\text{Fm}(^{38}\text{Ar}, 3{{n}})^{289}\text{Og}$ , and $ ^{257}\text{Fm}(^{36}\text{Ar}, 3{{n}})^{290}\text{Og}$ ; these reactions have maximum evaporation residue cross sections of 16.4 pb, 65.1 pb, 12.4 pb, and 111.1 pb, respectively.

Signature splitting in three-quasineutron rotational band 3/2[521]_ν $\otimes $ 1/2[660]_ν $\otimes $ 1/2[660]_νof¹⁵⁵Dy

Manpreet Kaur, Sushil Kumar, Sukhjeet Singh, A. K. Jain

2025, 49(10): 104103. doi:10.1088/1674-1137/ade95e

Abstract:
The signature splitting observed in the 3/2[521]_ν↑ $\otimes $ 1/2[660]_ν↑ $\otimes $ 1/2[660]_ν↑ three-quasineutron rotational band of¹⁵⁵Dy is examined within the framework of axially symmetric three-quasiparticle plus axially symmetric rotor model. The experimental level energies and magnitudes of observed splitting are well-reproduced with RMS deviations of 68.13 keV and 0.58 keV, respectively. The major contributing bands in the observed splitting areK^π=7/2^–:5/2[512]_ν↑ $\otimes $ 3/2[651]_ν↑ $\otimes $ 1/2[660]_ν↓,K^π=5/2^–: 5/2[512]_ν↑ $\otimes $ 3/2[651]_ν↑ $\otimes $ 3/2[651]_ν↓,K^π=1/2^–:3/2[521]_ν↑ $\otimes $ 1/2[660]_ν↑ $\otimes $ 3/2[651]_ν↓,K^π=1/2^–: 3/2[521]_ν↓ $\otimes $ 1/2[660]_ν↑ $\otimes $ 3/2[651]_ν↑,K^π=5/2^–:3/2[521]_ν↑ $\otimes $ 3/2[651]_ν↑ $\otimes $ 1/2[660]_ν↓, andK^π=3/2^–: 3/2[521]_ν↑ $\otimes $ 3/2[651]_ν↑ $\otimes $ 3/2[651]_ν↓, which mix through rotor-particle (ΔK=1) and particle-particle (ΔK=0) couplings among the bands comprising the given basis space. The observed signature splitting is also well-reproduced by the superposition of calculated energy staggering of the strongly interacting bands, which further strengthens the validity of present particle rotor model calculations. Based on the present calculations, we assign the bandhead spin K^π= 3/2^–to the band under discussion. Additionally, the locations of 13 low-lying band members in the spin range I^π=3/2^–to 23/2^–and at 27/2^–and 31/2^–are predicted, which will be useful for future experimental investigations.

Impact of particle production mechanisms on pseudorapidity distribution and directed flow in Au+Au and Cu+Cu collisions at ${ \sqrt{{\boldsymbol s}_{\boldsymbol{ NN}}}}$ = 19.6 GeV using AMPT model

Muhammad Farhan Taseer, Subhash Singha

2025, 49(10): 104101. doi:10.1088/1674-1137/ade660

Abstract:
The STAR experiment at the top RHIC energy has observed that the directed flow ( $ v_1 $ ) of inclusive light hadrons is independent of the collision system size at a given centrality [ 1 ]. However, recent STAR measurements indicate a system-size dependence in the $ v_1(y) $ -slope ( $ {\rm d}v_{1}/{\rm d}y $ ) of protons, antiprotons, and their differences ( $ \Delta {\rm d}v_{1}/{\rm d}y $ ) at a given centrality, suggesting a potential influence of baryon production and transport mechanisms [ 2 ]. In this study, we analyzed pseudorapidity ( $ {\rm d}N/{\rm d}y $ ) distributions and directed flow ( $ v_1 $ and $ {\rm d}v_{1}/{\rm d}y $ ) for pions, kaons, and protons in Au+Au and Cu+Cu collisions at $ \sqrt{s_{NN}} = 19.6 $ GeV using A Multi-Phase Transport (AMPT) model. Specifically, we investigated the influence of string junction parameters in the AMPT model via the PYTHIA/JETSET routines, focusing on the popcorn mechanism and string-splitting parameters, on $ {\rm d}N/{\rm d}y $ , $ {\rm d}v_{1}/{\rm d}y $ , and their charge-dependent splittings ( $ \Delta {\rm d}N/{\rm d}y $ and $ \Delta {\rm d}v_{1}/{\rm d}y $ ). We observed that string junction parameters can affect $ {\rm d}N/{\rm d}y $ , $ {\rm d}v_{1}/{\rm d}y $ , $ \Delta {\rm d}N/{\rm d}y $ , and $ \Delta {\rm d}v_{1}/{\rm d}y $ forπ,K, andp, and influence their system-size dependence. The effect is most prominent on the $ v_1 $ value of protons and non-trivial for kaons; the $ v_1 $ value of pions remains largely unchanged. These findings provide insights into the interplay among particle production mechanisms, baryon transport, and directed flow in heavy-ion collisions.

SU(3) analysis forB(E2) anomaly

Yu-xin Cheng, De-hao Zhao, Yue-yang Shao, Li Gong, Tao Wang, Xiao-shen Kang

2025, 49(10): 104105. doi:10.1088/1674-1137/aded05

Abstract:
The concept of ''SU(3) analysis'' is proposed for theB(E2) anomaly based on various mechanisms reported recently. TheB(E2) anomaly is analyzed in theSU(3) symmetry limit. According to the results of the analysis, theSU(3) third-order interaction $ [L\times Q \times L]^{(0)} $ can generate the level-crossing phenomenon for any mechanism, which is vital for the emergence of theB(E2) anomaly. Thus, this anomaly is found to be related with theSU(3) symmetry. TheB(E2) anomaly in $ ^{^{168}} {\rm{Os}}$ is also analyzed.

Nucleon-Δ elastic cross section in isospin-asymmetric nuclear medium with inclusion of scalar-isovectorδmeson field

Manzi Nan, Pengcheng Li, Wei Zuo, Qingfeng Li

2025, 49(9): 094112. doi:10.1088/1674-1137/add8fd

Abstract:
The production, dynamic evolution, and decay of $ \Delta $ particles play a crucial role in understanding the properties of high baryon density nuclear matter in intermediate-energy heavy-ion collisions. In this study, energy-, density-, and isospin-dependent nucleon- $ \Delta $ elastic cross sections ( $ \sigma^{*}_{N \Delta} $ ) were studied within the framework of the relativistic Boltzmann-Uehling-Uhlenbeck transport theory, in which the $ \delta $ meson field is considered in addition to the $ \sigma $ , $ \omega $ , and $ \rho $ meson fields. The results show that the $ \delta $ and $ \rho $ meson related exchange terms have a nonnegligible contribution to $ \sigma^{*}_{N \Delta} $ compared to only considering the $ \rho $ meson exchange terms, although there is a significant cancellation of the cross section among these meson exchange terms. In addition, owing to the different effects of the medium correction on the effective masses of neutrons, protons, and differently charged $ \Delta $ s, the individual $ \sigma^{*}_{N \Delta} $ exhibits an ordered isospin-asymmetry ( $ \alpha $ ) dependence, and $ \sigma^{*}_{n\Delta} $ and $ \sigma^{*}_{p\Delta} $ have opposite $ \alpha $ dependencies. Moreover, the $ \alpha $ dependence of the ratio $ R(\alpha)=\sigma^{*}(\alpha)/\sigma^{*}(\alpha=0) $ for $ n\Delta $ reaction channels satisfies $ n\Delta^{++}>n\Delta^{+}>n\Delta^{0}>n\Delta^{-} $ , while for $ p\Delta $ , it satisfies $ p\Delta^{-}>p\Delta^{0}>p\Delta^{+}>p\Delta^{++} $ . In addition, the results indicate that the isospin effect on $ \sigma^{*}_{N \Delta} $ , which is mostly caused by the isovector $ \rho $ and $ \delta $ meson fields, is still significant at densities up to three times the normal nuclear density. Finally, a parametrization of the energy-, density-, and isospin-dependent $ N\Delta $ elastic cross sections is proposed based on the microscopic calculated results. Thus, the in-medium $ \sigma^{*}_{N \Delta} $ in the energy range of $ \sqrt{s} $ =2.3~3.0 GeV can be properly described.

Fixing effective range parameters in elasticα-¹²C scattering: impact on resonant 2₄⁺state of¹⁶O andS_E2factor of¹²C(α,γ)¹⁶O

Shung-Ichi Ando

2025, 49(9): 094107. doi:10.1088/1674-1137/addaae

Abstract:
Elasticα-¹²C scattering for $ l=2 $ andE2 transition of radiativeαcapture on¹²C and¹²C(α,γ)¹⁶O are studied in cluster effective field theory. Owing to the problem in fixing the asymptotic normalization coefficient (ANC) of the subthreshold $ 2_1^+ $ state of¹⁶O or, equivalently, the effective range parameters of the $ 2_1^+ $ state, from the elastic scattering data, we introduced the conditions that lead to a large value of the ANC in this study. We also introducedd-wave phase shift data of the elastic scattering up to theαenergy, $ E_\alpha=10 $ MeV, which contain the resonant $ 2_4^+ $ state of¹⁶O. Applying these conditions, the parameters of theSmatrix of the elastic scattering for $ l=2 $ were fitted to the phase shift data, and the fitted parameters were employed in the calculation of the astrophysical $ S_{E2} $ factor of¹²C(α,γ)¹⁶O; we extrapolated the $ S_{E2} $ factor to the Gamow-peak energy, $ E_G=0.3 $ MeV. We found that the aforementioned conditions lead to significant effects in the observables of the $ 2_4^+ $ state of¹⁶O and the estimate of the $ S_{E2} $ factor at $ E_G $ and confirmed that the ANC of the $ 2_1^+ $ of¹⁶O cannot be determined by the phase shift data for $ l=2 $ .

Ab initiostudy of shell evolution in neutron-rich Si, S, Ar, and Ca isotopes nearN= 32 and 34

Qi Yuan, Liu-Yuan Shen, Meng-Ran Xie, Hong-Hui Li, Jian-Guo Li, Xing Xu, Wei Zuo

2025, 49(9): 094104. doi:10.1088/1674-1137/add5dd

Abstract:
Shell evolution is crucial for understanding nuclear structures across the nuclear chart. In this work, we employed theab initiovalence space in-medium similarity renormalization group with chiral nucleon-nucleon and three-nucleon interactions to study neutron-rich Si, S, Ar, and Ca isotopes, particularly focusing on nuclei near $ N=32, 34 $ . We systematically analyzed both neutron and proton shell evolutions by examining the excitation energies of the first $ 2^+ $ states and the effective single-particle energies. Our calculations show that the $ N=32 $ sub-shell gradually weakens as protons are removed from the doubly magic nucleus $ ^{52} {\rm{Ca}}$ , eventually disappearing in $ ^{46} {\rm{Si}}$ . Conversely, the strength of the $ N=34 $ sub-shell is enhanced with the removal of protons from $ ^{54} {\rm{Ca}}$ . Furthermore, our results indicate the existence of the proton $ Z=14 $ sub-shell in neutron-rich Si isotopes. These findings suggest that $ ^{48} {\rm{Si}}$ is a doubly magic nucleus, with the excitation energy of the first $ 2^+ $ state around 2.49 MeV, which is approximately 400 keV higher than that of $ ^{54} {\rm{Ca}}$ . This value is comparable to those of other well-known exotic doubly magic nuclei, such as $ ^{52} {\rm{Ca}}$ and $ ^{78} {\rm{Ni}}$ , which is of great interest for further experiments at RIB facilities. In addition, we predicted the low-lying spectra of neutron-rich Si, S, and Ar isotopes, providing new insights for future experiments.

Study of QCD critical point with the effect of three-nucleon correlations on light nuclei yield ratios using PYTHIA8/Angantyr

Zuman Zhang, Ning Yu, Sha Li, Shuang Li, Siyu Tang, Meimei Zhang

2025, 49(9): 094106. doi:10.1088/1674-1137/add10f

Abstract:
This study utilizes the PYTHIA8 Angantyr model to systematically investigate the effects of three nucleons correlation $C_{n^2p}$ on the light nuclei yield ratio $N_tN_p/N_d^2$ for Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV. The analysis explores this property across different rapidity ranges, collision centralities, and collision energies, while also examining the roles of multi-parton interactions (MPI) and color reconnection (CR) mechanisms. The light nuclei yield ratio remains stable with changes in rapidity coverage and collision centrality but slightly increases with rising collision energy. The impact of CR on the light nuclei yield ratio depends on the presence of MPI; when MPI is turned off, CR has no effect. Additionally, the three-nucleon correlation enhances the light nuclei yield ratio for both central and peripheral collisions. However, the non-monotonic energy dependence observed in experiments, the peak at $\sqrt{s_{\mathrm{NN}}}=20\sim30$ GeV reported by the STAR experiment, cannot be explained by the Angantyr model owing to its lack of key mechanisms related to the quark-gluon plasma (QGP). Nevertheless, the Angantyr model serves as an important baseline for studying collision behaviors in the absence of QGP effects.

Constraint on symmetry energy slope using neutron skins of⁴⁸Ca,⁶⁴Ni,¹²⁴Sn, and²⁰⁸Pb and its impact on neutron star radius

Yu Huang, Kai-Xuan Huang, Zu-Xing Yang, Xiao-Lin Tu, Jin-Niu Hu, Jing-Tao Zhang, Ji-Feng Han

2025, 49(9): 094005. doi:10.1088/1674-1137/add9fd

Abstract:
We constrain the symmetry energy slopeLat the saturation density using the neutron skin values of⁴⁸Ca,⁶⁴Ni,¹²⁴Sn, and²⁰⁸Pb determined by various experiments. The resultingLof 50(6) MeV is consistent with the world-averaged value from different observables and methodologies. The implications of newly constrainedLon the radius determinations of 1.4 solar-mass neutron stars are also discussed based on the established $ R_{1.4}$ -Llinear relationships by the DD-ME2 and TW99 EoS families.

Constraining explosive nucleosynthesis by indirect reaction methods at storage rings using unstable beams in batch mode

G. de Angelis, F. Recchia, J. Glorius, J. Gerl, B. Jurado, Xiao-Lin Tu, Jian-Ling Lou, S. Carollo, C. Berthelot, N. Watwood, B. P. Kay, P. Aguilera, M. L. Avila, J. Benito Garcia, K. Bhatt, D. Brugnara, K. A. Chipps, A. Couture, A. Demerdjiev, G.D. Dimitrova, S. Dutta, A. Ertoprak, R. Escudeiro, S. J. Freeman, F. Galtarossa, E. Geleva, B. Gongora Servin, A. Gottardo, A. Hall-Smith, J. Henderson, C. Hoffman, R. O. Hughes, H. Jayatissa, M. La Commara, G. Leckenby, S. M. Lenzi, D. Mengoni, M. R. Mumpower, W. J. Ong, M. Paul, J. Pellumaj, C. Domingo-Pardo, R. M. Perez Vidal, S. Pigliapoco, A. Ratkiewicz, K. Rezynkina, S. Rocca, D. K. Sharp, Yang Sun, T. L. Tang, D. Tonev, I. A. Tolstukhin, G. Wendell Misch, M. Williams, B. Wloch, Fan-Fei Zeng

2025, 49(9): 094004. doi:10.1088/1674-1137/add877

Abstract:
Nuclear reaction studies on unstable isotopes can strongly help in improving our understanding of nucleosynthesis in stars. Indirect approaches to determining astrophysical reaction rates are increasingly common-place and undergoing continuous refinement. Of particular interest is the use of such indirect techniques at storage rings, which, among other aspects, allow to recycle rare unstable beams. We propose to investigate the reaction rates of astrophysical interest using indirect methods (surrogate, Trojan horse,etc.) in reverse kinematics at the IMP-CAS storage ring. Long lived radioactive ion beams, produced remotely, can be accelerated, and made to interact with light targets. The proposed reactions are⁸⁵Kr(p, p’γ),⁸⁵Kr(d, pγ), constraining the neutron flux in an s-process branching point,⁷⁹Se(p, p’γ),⁷⁹Se(d, pγ), constraining the temperature in s-process nucleosyntheses, and⁵⁹Fe(d, pγ), constraining core collapse supernovae.

Development status of efficiency improvement at the Rare-RI Ring facility

Y. Yamaguchi, A. Yano, T. Ohnishi, Y. Abe, N. Chandrakumar, G. Hudson-Chang, N. Imai, Y. Kikuchi, N. Kitamura, R. Kojima, J. Li, T. Moriguchi, D. Nagae, S. Naimi, S. Nishizawa, A. Ozawa, F. Suzaki, K. Takiura, N. Tomioka, R. Tuchiya, M. Wakasugi, K. Watanabe, T. Yamaguchi, R. Yokoyama, H. Zhang

2025, 49(9): 094002. doi:10.1088/1674-1137/add25d

Abstract:
The rare radioactive-isotope (RI) ring is an isochronous storage ring for deriving the masses of extremely short-lived rare RIs. Since the successful commissioning experiment in 2015, the time of flight mass measurement technique has been established through test experiments using unstable nuclei with well-known masses. The experiments for unknown masses were started in 2018. While conducting experiments, we continue to develop equipment to further improve the efficiency and precision of mass measurements. The upgraded kicker system can generate a magnetic field with an extractable duration equivalent to the revolution time of the ring. This is essential for extracting extremely rare events as well as shortening the measurement time compared with that in the initial experiments. New steering magnets make it possible to eliminate an uncertain vertical beam deviation that occurs upstream. As a result, we confirm that the extraction yield is increased. A new resonant Schottky pick-up is able to detect single particles in timeframes on the order of milliseconds. It will be useful not only for beam diagnostics but also for lifetime measurement experiments of extremely short-lived rare RIs planned as a future application.

Contrasting features of parton energy loss in heavy-ion collisions at RHIC and LHC

Thomas Marshall, Philip Suh, Gang Wang, Huan Zhong Huang

2025, 49(9): 094001. doi:10.1088/1674-1137/adcf0f

Abstract:
Energetic quarks and gluons lose energy as they traverse the hot and dense medium created in high-energy heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC). The nuclear modification factor ( $ R_{AA} $ ) of leading particles quantifies parton energy loss in such collisions, with the particle spectrum in $ p+p $ collisions as a reference. Previous $ R_{AA} $ measurements at RHIC energies have revealed an approximately constant trend at high transverse momenta ( $ p_{T} $ ), implying a scenario where parton energy loss, $ \Delta p_{T} $ , scales proportionally with $ p_{T} $ , a feature naively expected from energy loss dynamics in elastic collisions. In this study, we investigate the LHC $ R_{AA} $ measurements that exhibit a pronounced $ p_{T} $ dependence of $ R_{AA} $ for various particle species, and our analysis attributes this behavior to $ \Delta p_T $ being approximately proportional to $ \sqrt{p_{T}} $ . These distinct features are consistent with model calculations of dominant radiative energy loss dynamics at LHC, in contrast to the dominance of collisional energy loss at RHIC. Additionally, the linear increase of the fractional energy loss with medium density at different $ p_{T} $ magnitudes affirms our previous empirical observation that the magnitude of the energy loss depends more strongly on the initial entropy density than the parton's path length through the medium. Implications on the dynamical scenarios of parton energy loss and future experimental investigations are also discussed.

α-decay half-lives of superheavy nuclei within a one-parameter model

Li-Qian Qi, Hong-Min Wang, Jian-Po Cui, Yan-Zhao Wang, Jian-Zhong Gu

2025, 49(9): 094102. doi:10.1088/1674-1137/addcc8

Abstract:
Theα-decay half-lives of superheavy nuclei (SHN) with charge numbers $ Z \geq 104 $ are investigated by employing a phenomenological one-parameter model based on quantum-mechanical tunneling through a potential barrier, where both the centrifugal and overlapping effects have been considered. It is shown that the experimentalα-decay half-lives of the 81 SHN are reproduced well. Moreover, the order of magnitude for theα-particle preformation probability inside a parent nucleus ( $S_{ {\alpha }} $ ) is found to be $ 10^{-2} $ . Then, within this model, the $S_{ {\alpha }} $ values andα-decay half-lives ofZ= 118−120 isotopes are predicted by inputting theα-decay energies ( $ Q_{\alpha } $ ) extracted from the relativistic continuum Hartree-Bogoliubov (RCHB) theory, Duflo-Zuker 19 (DZ19, where 19 denotes the number of fitting parameters) model, improved Weizsacker-Skyrme (lMWS) model, and machine learning (ML) approach. By analyzing the evolutions of $ Q_{\alpha } $ , $S_{ {\alpha} }$ andα-decay half-lives ofZ= 118−120 isotopes with the neutron numberNof the parent nucleus, it is found that the shell effect atN= 184 is evident for all nuclear mass models. Meanwhile, for the case of the RCHB,N= 172 is determined as a submagic number. However, the submagic number atN= 172 is replaced byN= 178 for the ML approach.

Analysis of the outer crust of neutron stars using the Brueckner-Hartree-Fock method

Zhi-Rui Jiang, Zeng-Hua Li, Hans-Josef Schulze

2025, 49(9): 094109. doi:10.1088/1674-1137/ade4a0

Abstract:
We study the properties of the outer crust of nonaccreting cold neutron stars using a liquid-drop model based on a microscopic Brueckner-Hartree-Fock energy-density functional. We calculate an extended nuclear mass table, particularly near the neutron drip line. Combined with the latest experimental binding energies from AME2020, we determine the sequence of equilibrium nuclei and construct the equation of state for the outer crust. Various properties of the outer crust are calculated in detail and compared with those from other crust models.

Effective decay rates of nuclei in astrophysical environments

Chao Dong, Zhi-Hong Li, Ge-Xing Li, Yun-Ju Li, Na Song, Chen Chen, Jun-Wen Tian, Jia-Ying-Hao Li, Zhi-Cheng Zhang, Hui-Ling Tian, Mei-Yue-Nan Ma

2025, 49(9): 094110. doi:10.1088/1674-1137/adcf11

Abstract:
Nuclearβ-decay plays a pivotal role at various stages of stellar evolution. However, the effective decay rates of nuclei in astrophysical environments may differ significantly from their laboratory values. This paper presents a detailed methodology for calculating nuclear half-life under the influence of temperature, electron density, ionization, and incomplete thermal equilibrium. We analyze the impact of astrophysical conditions on theβ-decay of²⁶Al,⁵⁹Fe,⁷⁹Se, and²⁰⁵Pb, revealing substantial variations in their effective half-lives within stellar environments. These changes lead to significant differences in nucleosynthetic yields, underscoring the critical importance of accounting for environmental effects when modeling nuclear decay rates.

Fermion masses and mixing inSO(10) GUT with a universal two-zero texture

Gao-Xiang Fang, Ye-Ling Zhou

2025, 49(10): 103107. doi:10.1088/1674-1137/ade6d7

Abstract:
We apply a universal two-zero texture (UTZT) to all mass matrices for matter in its flavor space within theSO(10) GUT framework. This texture can be realized by assigning different charges to each family in a $ Z_6 $ symmetry. By fixing the charged fermion masses at their best-fit values, we fit the remaining nine precisely measured observables (three angles and one CP-violating phase in quark mixing, three angles in lepton mixing, and two neutrino mass-squared differences) with seven model parameters. The model fits all data on fermion masses and mixing accurately, and the leptonic CP-violating phase is predicted to lie in the range $ (90^\circ, 230^\circ) $ . The model further predicts the right-handed neutrino masses, with the lightest and heaviest ones being on orders of $ 10^9 $ and $ 10^{12} $ GeV, respectively. Gauge unification and proton decay were checked under the assumption of a breaking chain with two intermediate symmetries above the electroweak scale. The result indicates that $ \alpha_{\rm{GUT}} $ varies in the range of (0.022,0.032) as long as the assumption of an economical choice of Higgs contents is fulfilled, and $ M_{\rm{GUT}} $ should be bigger than $ 4.5\times 10^{15} $ GeV to meet the Super-K bound. We report on the effective mass $ m_{ee} $ for neutrinoless double beta decay, which provides a possibility to test grand unification with neutrinoless double beta decay experiments.

Exploring the two-body strong decay properties of the possible ${\boldsymbol\Lambda_{\boldsymbol c}\boldsymbol K^{*}}$ and ${\boldsymbol\Sigma_{\boldsymbol c}\boldsymbol K^{(*)}}$ molecules

Jin-Yu Huo, Rui Chen

2025, 49(10): 103108. doi:10.1088/1674-1137/adec4e

Abstract:
In this work, we apply the effective Lagrangian approach to investigate the two-body strong decay behaviors of the possible $ \Lambda_c K^* $ and $ \Sigma_c K^{(*)} $ molecules as predicted in our previous study [Phys. Rev. D108, 054011 (2023)]. Our results indicate that the decay width for the coupled $ \Sigma_c K / \Lambda_c K^* / \Sigma_c K^* $ molecule with $ I(J^P) = 1/2(1/2^-) $ is on the order of several MeV, with the $ D_s N $ channel being dominant. For the coupled $ \Lambda_c K^* / \Sigma_c K^* $ molecule with $ 1/2(1/2^-, 3/2^-) $ , the decay widths are on the order of tens of MeV, with the dominant channels being $ \Sigma_c K $ and $ \Sigma_c^* K $ , respectively. For the $ \Sigma_c K^* $ molecules with $ 1/2(1/2^-) $ , the decay width can reach one hundred MeV, with $ \Sigma_c K $ and $ \Lambda_c K $ being the dominant decay channels. The decay widths for the $ \Sigma_c K^* $ molecules with $ 1/2(3/2^-) $ and $ 3/2(1/2^-) $ are on the order of tens of MeV, with the dominant decay modes being $ \Sigma_c^* K $ and $ \Sigma_c K $ , respectively. The branching ratios for all the discussed channels exhibit slight dependence on the binding energies.

Analysis of the form factors ofB_c→D^(*),D_s^(*)and relevant nonleptonic decays

Bin Wu, Guo-Liang Yu, Zhi-Gang Wang, Ze Zhou, Jie Lu

2025, 49(10): 103109. doi:10.1088/1674-1137/ade95d

Abstract:
This study is devoted to calculating the form factors of $B_c \to D^{*}$ , $B_c \to D$ , $B_c \to D_s^{*}$ , and $B_c \to D_s$ transitions in the framework of three-point QCD sum rules. At the QCD side, the contributions of $\langle\overline{q}q\rangle$ , $\langle\overline{q}g_{s}\sigma Gq\rangle$ , $\langle g_{s}^{2}G^{2}\rangle$ , $\langle g^{3}f_{abc}G^{3}\rangle$ , and $\langle\overline{q}q\rangle \langle g_{s}^{2}G^{2}\rangle$ are taken into account. With the obtained form factors, the decay widths and branching ratios of several two-body nonleptonic decay processes, $B_c \to \eta_c D^{*}$ , $\eta_c D$ , $ J/\psi D^{*}$ , $ J/\psi D$ , $\eta_c D_s^{*}$ , $\eta_c D_s$ , $J/\psi D_s^{*}$ , and $J/\psi D_s$ , are predicted. These results on the form factors and decay properties of the $B_c$ meson provide useful information for us to study the heavy-quark dynamical behavior.

Copositive criteria for a two-component dark matter model

Xin-Xin Qi, Hao Sun

2025, 49(10): 103101. doi:10.1088/1674-1137/ade4b7

Abstract:
In this study, we investigate a two-component scalar dark matter framework featuring two singlet scalar fields as dark matter candidates. To ensure vacuum stability, we employ copositive criteria for the scalar potential. We analyze four distinct copositive scenarios characterized by specific negative parameter configurations using direct detection constraints. A comprehensive parameter space scan is performed under joint constraints from the observed dark matter relic density and direct detection experiments. The different signs of couplings not only correspond to different copositive criteria but also contribute to different parameter spaces caused by interference. The allowed values of quartic couplings are different for the four different cases; however, they all require the new Higgs to play a dominant role in determining dark matter relic density within the viable parameter space.

ProbingZ/Wpole physics at high-energy muon colliders via vector-boson-fusion processes

Hao-Qiao Li, Hai-Ning Yan, Jiayin Gu, Xiao-Ze Tan

2025, 49(10): 103102. doi:10.1088/1674-1137/addfcd

Abstract:
A future $ e^+e^- $ collider could run at theZ-pole to perform important electroweak (EW) precision measurements, but such a run may not be viable for a future muon collider. However, this can be compensated for by measuring other EW processes utilizing the high energy and large luminosity of the muon collider. In this paper, we consider the measurements of the vector boson fusion processes of $ WW/WZ/W\gamma $ to a pair of fermions (along with a $ \nu_{\mu}\bar{\nu}_{\mu} $ or $ \nu_{\mu}\mu^+/\bar{\nu}_{\mu}\mu^- $ pair) at a high-energy muon collider and study their potential for probing EW observables. We consider two run scenarios for the muon collider with center-of-mass energies of 10 and 30 TeV, respectively, and focus on the processes involving $ f=b,c,\tau $ and the dimension-6 operators that directly modify the corresponding fermions coupling to the $ Z/W $ bosons. The invariant mass distribution of the $ f\bar{f} $ pair helps to separate the events from the $ Z/W $ and high-energy resonances, whereas the polar angle of the outing fermion provides additional information. Through a chi-squared analysis on the binned distributions and combining the information from theWWand $ WZ/W\gamma $ fusion processes, all relevant Wilson coefficients can be constrained simultaneously. The precision surpasses the current EW measurement constraints and is even competitive with future $ e^+e^- $ colliders. Our analysis can be included in a more complete framework that is required to fully determine the potential of muon colliders in EW precision measurements.

CP violations and branching ratios forB_c⁺→D_(s)⁺π⁺π⁻(K⁺K⁻) from interference of the vector mesons in Perturbative QCD

Kun Shuai Ye, Gang Lü, Na Wang, Jian Chai, Xin-Heng Guo

2025, 49(9): 093108. doi:10.1088/1674-1137/add523

Abstract:
Within the framework of the perturbative QCD approach utilizing $k_T$ factorization, we investigated the CP violation and branching ratios in the decay processes of $B_{c}^{+}\to D_{(s)} ^{+}V(V\rightarrow\pi^{+}\pi^{-})$ and $B_{c}^{+}\to D_{(s)}^{+}V(V\rightarrow K^{+}K^{-})$ , where V denotes the three vector mesons $\rho^0$ ,ω, andϕ. During the $V\to \pi^+\pi^-$ and $V\to K^+K^-$ decay processes, we incorporated the $\rho^{0}-\omega-\phi$ mixing mechanism to describe the amplitudes of these quasi-two-body decays. Within the interference region of the three vector particles, we observed distinct changes in both CP violations and branching ratios. Furthermore, our study presents evidence for local CP violations and branching ratios that warrants further experimental investigation.

ProbingD_s^*-meson longitudinal twist-2 LCDA

Si-Hai Zhang, Tao Zhong, Hai-Bing Fu, Ya-Xiong Wang, Wan-Bing Luo

2025, 49(9): 093104. doi:10.1088/1674-1137/add683

Abstract:
In this study, we continue an investigation of the semileptonic decays $ B_s\to D_s^*\ell \bar\nu_{\ell} $ . First, we derive the moments of the $ D_s^* $ -meson longitudinal leading-twist light-cone distribution amplitude (LCDA) based on QCD sum rules within the background field theory framework. Considering the contributions of the vacuum condensates up to dimension-six, its first ten non-zero $ \xi $ -moments at the initial scale $ \mu_0 = 1.3\; {\rm{GeV}} $ are $ \langle \xi^{\|, 1}_{2; D_s^*} \rangle|_{\mu_0} = -0.302_{-0.046}^{+0.038} $ , $ \langle\xi^{\|, 2}_{2;D_s^*}\rangle|_{\mu_0} = +0.229_{-0.034}^{+0.039} $ , $ \langle\xi^{\|, 3}_{2;D_s^*}\rangle|_{\mu_0} = -0.121_{-0.019}^{+0.015} $ , $ \langle\xi^{\|, 4}_{2;D_s^*}\rangle|_{\mu_0} = +0.101_{-0.014}^{+0.017} $ , $ \langle\xi^{\|, 5}_{2; D_s^*} \rangle|_{\mu_0} = -0.066_{-0.010}^{+0.009} $ , $ \langle\xi^{\|, 6}_{2;D_s^*}\rangle|_{\mu_0} = +0.053_{-0.007}^{+0.009} $ , $ \langle\xi^{\|, 7}_{2;D_s^*}\rangle|_{\mu_0} = -0.041_{-0.007}^{+0.006} $ , $ \langle\xi^{\|, 8}_{2;D_s^*}\rangle|_{\mu_0} = +0.037_{-0.005}^{+0.006} $ , $ \langle\xi^{\|, 9}_{2; D_s^*} \rangle|_{\mu_0} = -0.026_{-0.004}^{+0.003} $ , and $ \langle\xi^{\|, 10}_{2;D_s^*}\rangle|_{\mu_0} = +0.025_{-0.004}^{+0.004} $ . We also construct the $ D_s^* $ -meson longitudinal leading-twist LCDA by using the light-cone harmonic oscillator model. Then, using the above moments, we fix the model parameters $ \alpha_{2;D_s^*} $ and $ B_1^{2;D_s^*} $ using the least squares method and apply them to calculate $ B_s \to D_s^* $ transition form factors $ A_1(q^2), A_2(q^2) $ and $ V(q^2) $ that are derived using the QCD light-cone sum rules. In the large recoil region, we obtain $ A_1(0) = 0.632_{-0.135}^{+0.228}, A_2(0) = 0.706_{-0.092}^{+0.109} $ , and $ V(0) = 0.647_{-0.069}^{+0.076} $ . These form factors are then extrapolated to the allowed whole physical $ q^2 $ -region through the simplified series expansion. Finally, we obtain the branching fractions for the two decay channels of $ B_s\to D_s^*\ell\bar\nu_\ell $ , $ {\cal{B}}(B_s^0 \to D_s^{*+}e^-\bar\nu_e) = (5.45_{-1.57}^{+2.15})\times 10^{-2} $ and $ {\cal{B}}(B_s^0 \to D_s^{*+}\mu^-\bar\nu_\mu) = $ $ (5.43_{-1.57}^{+2.14})\times 10^{-2} $ . In addition, we present the CKM matrix element $ |V_{cb}| $ by matching the LHCb Collaboration branching fraction, yielding a value of $ |V_{cb}| = (40.11_{-7.49}^{+6.54})\times 10^{-3} $ .

Rotation effect on the thermodynamics of QCD matter

Fei Sun, Shuang Li, Rui Wen, Anping Huang, Wei Xie

2025, 49(9): 093105. doi:10.1088/1674-1137/add25e

Abstract:
In this study, we investigated the impact of rotation on the thermodynamic properties of QCD matter using the three-flavor NJL model. We examined the dependencies of key thermodynamic quantities, such as the trace anomaly, specific heat, speed of sound, angular momentum, and moment of inertia, on temperature, quark chemical potential, and angular velocity. Our main finding is that the speed of sound exhibits a nonmonotonic behavior as the angular velocity varies.

Probing type II seesaw leptogenesis through lepton flavor violation

Chengcheng Han, Yijun Han, Sihui Huang, Zhanhong Lei

2025, 49(9): 093103. doi:10.1088/1674-1137/ade079

Abstract:
Lepton flavor violation (LFV) offers a powerful probe of physics beyond the Standard Model, particularly in models addressing neutrino masses and the baryon asymmetry of the universe. In this study, we investigate LFV processes within the framework of type II seesaw leptogenesis, where the Standard Model is extended by an $S U(2)_L$ triplet Higgs field. We focus on key LFV processes, including $\mu^+\to e^+\gamma$ , $\mu^+ \to e^+e^-e^+$ , and $\mu \rightarrow e$ conversion in nuclei, deriving stringent constraints on the parameter space from current experimental data. We scan the 3σrange of neutrino oscillation parameters and identify the most conservative bounds consistent with existing measurements. Our results reveal that the MEG experiment currently provides the most stringent constraints in the normal ordering (NO) scenario, while the SINDRUM experiment offers comparable sensitivity in the inverted ordering (IO) case. Future experiments, such as MEG II, Mu3e, Mu2e, and COMET, are predicted to significantly improve the sensitivity, testing larger regions of the parameter space.

HEP ML LAB: An end-to-end framework for applying machine learning to phenomenology studies

Jing Li, Hao Sun

2025, 49(9): 093106. doi:10.1088/1674-1137/addcc9

Abstract:
Recent years have seen the development and growth of machine learning in high-energy physics. However, additional effort is required to continue exploring the use of machine learning to its full potential. To simplify the application of the existing algorithms and neural networks and to advance the reproducibility of the analysis, we developed HEP ML LAB ( $ \mathrm{hml}$ ), a Python-based, end-to-end framework for phenomenology studies. It covers the complete workflow from event generation to performance evaluation, and provides a consistent style of use for different approaches. We propose an observable naming convention to streamline the data extraction and conversion processes. In the KERAS style, we provide the traditional cut-and-count and boosted decision trees together with neural networks. We take the $W^+ $ tagging as an example and evaluate all built-in approaches with the metrics of significance and background rejection. With its modular design, HEP ML LAB is easy to extend and customize, and can be used as a tool for both beginners and experienced researchers.

A three-body form factor at sub-leading power in the high-energy limit: planar contributions

Yishuai Guo, Zhi-Feng Liu, Mingming Lu, Tianya Xia, Li-Lin Yang

2025, 49(9): 093102. doi:10.1088/1674-1137/addcc7

Abstract:
We analyzed two-loop planar contributions to a three-body form factor at next-to-leading power in the high-energy limit, where the masses of the external particles are much smaller than their energies. Calculations were performed by exploiting differential equations for the expansion coefficients, both to facilitate linear relations among them and to derive their analytic expressions. The results are expressed in terms of generalized polylogarithms involving a few simple symbol letters. Our method can readily be applied to calculations of non-planar contributions as well. Our results provide crucial information for establishing sub-leading factorization theorems for massive scattering amplitudes in the high-energy limit.

A unitary coupled-channel approach toJ/ψradiative decay to pseudoscalar pairs

Yang-hong Lu, Jia-jun Wu, Bei-jiang Liu, Xiao-yan Shen

2025, 49(9): 093107. doi:10.1088/1674-1137/ade4a2

Abstract:
We present a comprehensive theoretical approach for describing the amplitude of the processes $ J/\psi \to \gamma ab $ , whereaandbare pseudoscalar mesons. Our approach systematically incorporates final-state rescattering between the pseudoscalar pair $ ab $ , contributions from intermediate resonances, and coupled-channel effects via rescattering ofawith an intermediate state $ \bar{X} $ (which subsequently decays to $ \gamma b $ ). This formalism ensures unitarity in the two-body rescattering amplitude and dynamically dressed couplings between resonances and the pseudoscalar pair. Using a toy model, we perform numerical calculations and demonstrate that coupled-channel effects significantly influence the lineshape of the invariant mass spectrum of the final states. These findings highlight the necessity of including coupled-channel dynamics in interpretations of $ J/\psi $ radiative decays.

Parameterization of zero-skewness unpolarized GPDs

Hossein Vaziri, Mohammad Reza Shojaei

2025, 49(9): 093101. doi:10.1088/1674-1137/add923

Abstract:
Recent parameterizations of parton distribution functions (PDFs) have led to the determination of the gravitational form factors pertaining to the dependence of nucleons on their generalized parton distributions (GPDs) in the limit $\xi \to 0 $ . This study aims to obtain the flavor division of nucleon electromagnetic and gravitational form factors using the VS24 ansatz and two PDFs at the $ N^3L0 $ approximation in GPDs. The PDFs and GPD formalism enable the calculation of various form factors of nucleons in different approximations, as well as the calculation of the electric radius of nucleons. The study, despite its high approximation complexity, enhances the accuracy of calculations and aligns them more closely with experimental values.

Moments from momentum derivatives in lattice QCD

Zhuoyi Pang, Jian-Hui Zhang, Dian-Jun Zhao

2025, 49(10): 101001. doi:10.1088/1674-1137/aded04

Abstract:
We show that the traditional moments approach in lattice quantum chromodynamics based on operator product expansion can be realized such that it utilizes derivatives in momentum rather than in distance. This avoids power divergent mixings, and thus allows to extract moments order by order to all orders in principle. Further, by exploiting the symmetry of lattice matrix elements, we can determine the even and odd moments separately. As a demonstrative example, we determine the first three moments beyond the tensor charge $ g_T$ of the isovector quark transversity distribution in the nucleon.