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2026 No.9
2026, 50(9): 094104. doi: 10.1088/1674-1137/ae7cff
Abstract:
The dynamical double-folding potential (DDFP) model is extended to investigate the α decays of odd-A nuclei in the region $ 78 \le Z \le 90 $. We present a systematic comparison between the deep-well DDFP based on the CDM3Y6 nucleon-nucleon interaction and the pocket-type DDFP based on the Migdal interaction. Both potentials reproduce the experimental α-decay half-lives satisfactorily, with root-mean-square deviations of $ \sigma = 0.212 $ and 0.250, respectively. The two potentials also yield similar trends in α preformation factors ($ P_\alpha $) for both favored and unfavored transitions, reflecting the high sensitivity of $ P_\alpha $ to shell structure and the variation of the proton pairing gap. Furthermore, our analysis demonstrates that the significant difference in the $ P_\alpha $ magnitude between the two potentials stems fundamentally from their distinct treatments of Pauli blocking effects.
The dynamical double-folding potential (DDFP) model is extended to investigate the α decays of odd-A nuclei in the region $ 78 \le Z \le 90 $. We present a systematic comparison between the deep-well DDFP based on the CDM3Y6 nucleon-nucleon interaction and the pocket-type DDFP based on the Migdal interaction. Both potentials reproduce the experimental α-decay half-lives satisfactorily, with root-mean-square deviations of $ \sigma = 0.212 $ and 0.250, respectively. The two potentials also yield similar trends in α preformation factors ($ P_\alpha $) for both favored and unfavored transitions, reflecting the high sensitivity of $ P_\alpha $ to shell structure and the variation of the proton pairing gap. Furthermore, our analysis demonstrates that the significant difference in the $ P_\alpha $ magnitude between the two potentials stems fundamentally from their distinct treatments of Pauli blocking effects.
2026, 50(9): 1-21. doi: 10.1088/1674-1137/ae823d
Abstract:
We investigate the role of the model dependence of the high-density isovector sector in neutron-star matter within a density-dependent relativistic mean-field framework. A 10-dimensional TW-like DD-RMF baseline model is compared with an 11-dimensional ρ-flex extension in which an additional parameter, $ \xi_\rho $, introduces a controlled deformation of the high-density ρ-meson channel while leaving the saturation-point isovector properties unchanged. Bayesian inference is performed for two data combinations: NS+GW, which includes neutron-star mass and radius measurements and GW170817 tidal information, and ALL+GW, which further incorporates low-density χEFT and heavy-ion-collision constraints. For each posterior sample, we construct the beta-equilibrated equation of state, solve the stellar structure and tidal-response equations, and determine the direct-Urca threshold. The Bayesian evidence differences, $ \Delta\ln Z_{\rm{INS}}=-0.23\pm0.08 $ for NS+GW and $ -0.02\pm0.17 $ for ALL+GW, indicate that present data do not statistically require the additional ρ-channel flexibility. The 10D and 11D models yield similar posterior predictions for the beta-equilibrium pressure, sound speed, mass-radius relation, tidal deformability, and maximum mass. In contrast, the 11D extension broadens the allowed ranges of the high-density symmetry energy, proton fraction, direct-Urca threshold density, onset mass, and direct-Urca activation probability. These results demonstrate that current multimessenger constraints primarily restrict the bulk stiffness of beta-equilibrated matter, while residual uncertainty in the high-density isovector sector remains relevant for composition-sensitive and cooling-related observables.
We investigate the role of the model dependence of the high-density isovector sector in neutron-star matter within a density-dependent relativistic mean-field framework. A 10-dimensional TW-like DD-RMF baseline model is compared with an 11-dimensional ρ-flex extension in which an additional parameter, $ \xi_\rho $, introduces a controlled deformation of the high-density ρ-meson channel while leaving the saturation-point isovector properties unchanged. Bayesian inference is performed for two data combinations: NS+GW, which includes neutron-star mass and radius measurements and GW170817 tidal information, and ALL+GW, which further incorporates low-density χEFT and heavy-ion-collision constraints. For each posterior sample, we construct the beta-equilibrated equation of state, solve the stellar structure and tidal-response equations, and determine the direct-Urca threshold. The Bayesian evidence differences, $ \Delta\ln Z_{\rm{INS}}=-0.23\pm0.08 $ for NS+GW and $ -0.02\pm0.17 $ for ALL+GW, indicate that present data do not statistically require the additional ρ-channel flexibility. The 10D and 11D models yield similar posterior predictions for the beta-equilibrium pressure, sound speed, mass-radius relation, tidal deformability, and maximum mass. In contrast, the 11D extension broadens the allowed ranges of the high-density symmetry energy, proton fraction, direct-Urca threshold density, onset mass, and direct-Urca activation probability. These results demonstrate that current multimessenger constraints primarily restrict the bulk stiffness of beta-equilibrated matter, while residual uncertainty in the high-density isovector sector remains relevant for composition-sensitive and cooling-related observables.
2026, 50(9): 094103. doi: 10.1088/1674-1137/ae75fc
Abstract:
In this work, the von Neumann entropy has been calculated and employed as a probe to analyse quantum phase transitions (QPTs) within the $ sdg $-Interacting Boson Model ($ sdg $-IBM). The von Neumann entropy between the $s$-boson and $dg$-boson sectors is used as an indicator of QPTs and as a robust observable for the theoretical analysis of the $ _{\phantom{108-1}48}^{108-116}\mathrm{Cd} $ isotopes. The von Neumann entropy correctly characterises the QPT in the ${U_d}\left( 5 \right) \otimes{U_g}\left( 9 \right) \leftrightarrow S O_{sdg}\left( {15} \right)$ transition region. The numerical results show that the $ _{\phantom{1}48}^{108}\mathrm{Cd} $ and $ _{\phantom{1}48}^{116}\mathrm{Cd} $ isotopes are located in the ${U_d}\left( 5 \right) \otimes{U_g}$ and $S O_{sdg}(15)$ limits, respectively.
In this work, the von Neumann entropy has been calculated and employed as a probe to analyse quantum phase transitions (QPTs) within the $ sdg $-Interacting Boson Model ($ sdg $-IBM). The von Neumann entropy between the $s$-boson and $dg$-boson sectors is used as an indicator of QPTs and as a robust observable for the theoretical analysis of the $ _{\phantom{108-1}48}^{108-116}\mathrm{Cd} $ isotopes. The von Neumann entropy correctly characterises the QPT in the ${U_d}\left( 5 \right) \otimes{U_g}\left( 9 \right) \leftrightarrow S O_{sdg}\left( {15} \right)$ transition region. The numerical results show that the $ _{\phantom{1}48}^{108}\mathrm{Cd} $ and $ _{\phantom{1}48}^{116}\mathrm{Cd} $ isotopes are located in the ${U_d}\left( 5 \right) \otimes{U_g}$ and $S O_{sdg}(15)$ limits, respectively.
2026, 50(9): 094102. doi: 10.1088/1674-1137/ae7b17
Abstract:
Theoretical predictions on the optimal reaction energies are essential for producing superheavy elements (SHEs) beyond Og. Owing to the limitation of targets, synthesizing elements 119 and 120 will require beams of $ {}^{50}{\rm{Ti}} $ and/or $ {}^{54}{\rm{Cr}} $ ions. However, is it reliable to theoretically extrapolate from the well-investigated $ {}^{48}{\rm{Ca}} $ induced reactions to those with heavier projectiles? In this work, we answer this question from two perspectives: radial and mass asymmetry degrees of freedom. The Smoluchowski diffusion equation is employed in the mass asymmetry degree of freedom for the first time, in which, by fitting the calculations to experimental evaporation residue cross sections (ERCS) for the reactions of $ {}^{48}{\rm{Ca}} $ as projectiles with the actinide targets, we find a strong linear correlation between the contact distance ($ D_{\rm{cont}} $) and center-of-mass energy excess above the Coulomb barrier ($ E_{\rm{c.m.}}-B_0 $) and introduce a parametrization formula. The calculations based on the fitted formula reproduce the available experimental data of the ERCS satisfactorily. Furthermore, using recent experimental data, we extrapolate the calculation in the reactions $ {}^{50}{\rm{Ti}}+{}^{242}{\rm{Pu}} $, $ {}^{50}{\rm{Ti}}+{}^{244}{\rm{Pu}} $, and $ {}^{54}{\rm{Cr}}+{}^{238}{\rm{U}} $. The calculations reproduce the experimental data rather well within the experimental errors in both perspectives. Our results demonstrate that theoretically extrapolating the projectile from $ ^{48}{\rm{Ca}} $ to $ ^{50}{\rm{Ti}} $ and $ ^{54}{\rm{Cr}} $ for synthesizing SHEs beyond Og is relatively reliable.
Theoretical predictions on the optimal reaction energies are essential for producing superheavy elements (SHEs) beyond Og. Owing to the limitation of targets, synthesizing elements 119 and 120 will require beams of $ {}^{50}{\rm{Ti}} $ and/or $ {}^{54}{\rm{Cr}} $ ions. However, is it reliable to theoretically extrapolate from the well-investigated $ {}^{48}{\rm{Ca}} $ induced reactions to those with heavier projectiles? In this work, we answer this question from two perspectives: radial and mass asymmetry degrees of freedom. The Smoluchowski diffusion equation is employed in the mass asymmetry degree of freedom for the first time, in which, by fitting the calculations to experimental evaporation residue cross sections (ERCS) for the reactions of $ {}^{48}{\rm{Ca}} $ as projectiles with the actinide targets, we find a strong linear correlation between the contact distance ($ D_{\rm{cont}} $) and center-of-mass energy excess above the Coulomb barrier ($ E_{\rm{c.m.}}-B_0 $) and introduce a parametrization formula. The calculations based on the fitted formula reproduce the available experimental data of the ERCS satisfactorily. Furthermore, using recent experimental data, we extrapolate the calculation in the reactions $ {}^{50}{\rm{Ti}}+{}^{242}{\rm{Pu}} $, $ {}^{50}{\rm{Ti}}+{}^{244}{\rm{Pu}} $, and $ {}^{54}{\rm{Cr}}+{}^{238}{\rm{U}} $. The calculations reproduce the experimental data rather well within the experimental errors in both perspectives. Our results demonstrate that theoretically extrapolating the projectile from $ ^{48}{\rm{Ca}} $ to $ ^{50}{\rm{Ti}} $ and $ ^{54}{\rm{Cr}} $ for synthesizing SHEs beyond Og is relatively reliable.
2026, 50(9): 094002. doi: 10.1088/1674-1137/ae740a
Abstract:
Nucleon-pair correlations play a fundamental role in shaping nuclear structure. Two-nucleon transfer reactions provide a unique probe for investigating pair correlations in nuclei. A recent theoretical study has predicted significant proton-neutron ($pn$) pair correlations in the unconventional $N>Z$ region. To investigate isoscalar $pn$ pair correlations, we measured the 120Sn(α, 6Li)118In reaction in the laboratory angular range from $9^\circ$ to $19^\circ$. Owing to the limited experimental energy resolution, no distinct peak corresponding to the ground state of 118In was observed. By evaluating the low-excitation-energy region, an upper limit of the cross section for populating 118In(g.s.) was extracted, yielding an integrated cross section of $\sigma=0.42 \pm 0.02$ μb. The DWBA calculations for the transfer of a $\pi g_{9/2}\otimes\nu g_{7/2}$ pair using an assumed value of the two-nucleon amplitude (TNA) are consistent with the experimental cross section. The competition between simultaneous and sequential transfer in this heavy system was investigated. A comparison with the 120Sn(α, 6He)118Sn reaction indicates that the $pn$ pair-correlation strength is far weaker than that for neutron-neutron pair condensation.
Nucleon-pair correlations play a fundamental role in shaping nuclear structure. Two-nucleon transfer reactions provide a unique probe for investigating pair correlations in nuclei. A recent theoretical study has predicted significant proton-neutron ($pn$) pair correlations in the unconventional $N>Z$ region. To investigate isoscalar $pn$ pair correlations, we measured the 120Sn(α, 6Li)118In reaction in the laboratory angular range from $9^\circ$ to $19^\circ$. Owing to the limited experimental energy resolution, no distinct peak corresponding to the ground state of 118In was observed. By evaluating the low-excitation-energy region, an upper limit of the cross section for populating 118In(g.s.) was extracted, yielding an integrated cross section of $\sigma=0.42 \pm 0.02$ μb. The DWBA calculations for the transfer of a $\pi g_{9/2}\otimes\nu g_{7/2}$ pair using an assumed value of the two-nucleon amplitude (TNA) are consistent with the experimental cross section. The competition between simultaneous and sequential transfer in this heavy system was investigated. A comparison with the 120Sn(α, 6He)118Sn reaction indicates that the $pn$ pair-correlation strength is far weaker than that for neutron-neutron pair condensation.
2026, 50(9): 094001. doi: 10.1088/1674-1137/ae71a5
Abstract:
The neutron capture cross sections of copper play a crucial role in the s process of stellar nucleosynthesis, the production of the medical isotope $^{64}{\rm{Cu}}$ for positron emission tomography (PET) imaging and radiotherapy, and neutron resonance capture analysis for determining the elemental and isotopic compositions of archaeological and cultural heritage materials. The ${}{\rm{Cu}}({n},\gamma)$ cross section was measured from 1 eV to 700 keV at the Back-n facility of the Chinese Spallation Neutron Source using the time-of-flight (TOF) method. Prompt γ-rays were detected using four ${{\rm{C}}_{6}{\rm{D}}_{6}}$ liquid scintillator detectors, and the data were analyzed using the pulse height weighting technique. The results were generally consistent with the evaluated data in the major library; however, some discrepancies were observed, offering valuable insights into the differences between five prominent evaluated data libraries. The R-matrix SAMMY code was used to extract the resonance parameters for $^{63,65}{\rm{Cu}}$ in the resolved resonance region. Maxwellian-averaged cross sections (MACSs) were calculated within the temperature range relevant to the s process nucleosynthesis model, spanning $kT=5-100$ keV, based on the averaged cross sections in the unresolved resonance region. At $kT=30$ keV, the MACSs values for $^{63}{\rm{Cu}}$ (88.1±8.8 mb) and $^{65}{\rm{Cu}}$ (42.1±4.2 mb) were higher than the corresponding recommendations in the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars.
The neutron capture cross sections of copper play a crucial role in the s process of stellar nucleosynthesis, the production of the medical isotope $^{64}{\rm{Cu}}$ for positron emission tomography (PET) imaging and radiotherapy, and neutron resonance capture analysis for determining the elemental and isotopic compositions of archaeological and cultural heritage materials. The ${}{\rm{Cu}}({n},\gamma)$ cross section was measured from 1 eV to 700 keV at the Back-n facility of the Chinese Spallation Neutron Source using the time-of-flight (TOF) method. Prompt γ-rays were detected using four ${{\rm{C}}_{6}{\rm{D}}_{6}}$ liquid scintillator detectors, and the data were analyzed using the pulse height weighting technique. The results were generally consistent with the evaluated data in the major library; however, some discrepancies were observed, offering valuable insights into the differences between five prominent evaluated data libraries. The R-matrix SAMMY code was used to extract the resonance parameters for $^{63,65}{\rm{Cu}}$ in the resolved resonance region. Maxwellian-averaged cross sections (MACSs) were calculated within the temperature range relevant to the s process nucleosynthesis model, spanning $kT=5-100$ keV, based on the averaged cross sections in the unresolved resonance region. At $kT=30$ keV, the MACSs values for $^{63}{\rm{Cu}}$ (88.1±8.8 mb) and $^{65}{\rm{Cu}}$ (42.1±4.2 mb) were higher than the corresponding recommendations in the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars.
2026, 50(9): 094101. doi: 10.1088/1674-1137/ae662f
Abstract:
In this study, we develop a framework for producing exotic muonic kaon atoms ($ K\mu $) in semileptonic $ D^{0} $ decays using an effective weak Hamiltonian, a helicity-based treatment of leptonic current, and a nonrelativistic bound-state projection. The resulting branching ratio $ BR(D^{0} \to(K\mu )\nu_{\mu})=2.29\times10^{-10} $ is implemented in a ROOT-based code to estimate yields at a relativistic heavy-ion collider (RHIC), large hadron collider (LHC), and super tau-charm facility (STCF). We demonstrate quantitatively that $ K\mu $ atoms, which are also produced through coalescence in the quark–gluon plasma (QGP), offer a sensitive probe of low-momentum primordial muons and early-time electromagnetic radiation, acting as complementary constraints in an otherwise unexplored phase space for thermal dilepton and photon emission. Newly estimated dissociation cross-sections in detector material indicate that secondary-vertex reconstruction should be experimentally feasible, enabling the clean experimental identification of atoms. Projected yields from QGP coalescence in LHC and RHIC heavy-ion collisions and from $ D^{0} $ decays in LHC high-luminosity $ p+p $ collisions indicate that the first observation of $ K\mu $ atoms is within reach.
In this study, we develop a framework for producing exotic muonic kaon atoms ($ K\mu $) in semileptonic $ D^{0} $ decays using an effective weak Hamiltonian, a helicity-based treatment of leptonic current, and a nonrelativistic bound-state projection. The resulting branching ratio $ BR(D^{0} \to(K\mu )\nu_{\mu})=2.29\times10^{-10} $ is implemented in a ROOT-based code to estimate yields at a relativistic heavy-ion collider (RHIC), large hadron collider (LHC), and super tau-charm facility (STCF). We demonstrate quantitatively that $ K\mu $ atoms, which are also produced through coalescence in the quark–gluon plasma (QGP), offer a sensitive probe of low-momentum primordial muons and early-time electromagnetic radiation, acting as complementary constraints in an otherwise unexplored phase space for thermal dilepton and photon emission. Newly estimated dissociation cross-sections in detector material indicate that secondary-vertex reconstruction should be experimentally feasible, enabling the clean experimental identification of atoms. Projected yields from QGP coalescence in LHC and RHIC heavy-ion collisions and from $ D^{0} $ decays in LHC high-luminosity $ p+p $ collisions indicate that the first observation of $ K\mu $ atoms is within reach.
2026, 50(9): 1-12. doi: 10.1088/1674-1137/ae7702
Abstract:
In this study, we discuss general critical properties of bound states with a one-boson-exchange potential. For simplicity, we first consider a system of two identical scalar particles as an example. The interaction between these two scalar particles is described by the exchange of another massive scalar meson under the instantaneous approximation, which yields the Yukawa potential. A highly accurate numerical method is used to determine the critical mass of the system. The resulting critical mass for the ground state is consistent with values reported in the literature, agreeing to about 35 significant figures. Highly accurate results for the $l=1$ case are also presented, which are significantly more precise than those previously reported in the literature. Furthermore, we extend the discussion to physical hadronic molecular states, for which form factors are introduced in the interaction to describe the structure of hadrons. Our numerical results show that although the binding energies of the hadronic molecular states depend on the cutoff in the form factors, the number of hadronic molecular states is almost independent of the cutoffs over a very wide physically relevant range. This indicates a strong and important property: for physically small couplings, the number of hadronic molecular states is almost solely determined by the coupling constants and the masses of the exchange particles. This highly accurate numerical method can also be straightforwardly applied to higher l cases or other systems.
In this study, we discuss general critical properties of bound states with a one-boson-exchange potential. For simplicity, we first consider a system of two identical scalar particles as an example. The interaction between these two scalar particles is described by the exchange of another massive scalar meson under the instantaneous approximation, which yields the Yukawa potential. A highly accurate numerical method is used to determine the critical mass of the system. The resulting critical mass for the ground state is consistent with values reported in the literature, agreeing to about 35 significant figures. Highly accurate results for the $l=1$ case are also presented, which are significantly more precise than those previously reported in the literature. Furthermore, we extend the discussion to physical hadronic molecular states, for which form factors are introduced in the interaction to describe the structure of hadrons. Our numerical results show that although the binding energies of the hadronic molecular states depend on the cutoff in the form factors, the number of hadronic molecular states is almost independent of the cutoffs over a very wide physically relevant range. This indicates a strong and important property: for physically small couplings, the number of hadronic molecular states is almost solely determined by the coupling constants and the masses of the exchange particles. This highly accurate numerical method can also be straightforwardly applied to higher l cases or other systems.
2026, 50(9): 1-12. doi: 10.1088/1674-1137/ae740b
Abstract:
Hyperon-antihyperon pairs produced in high-energy electron-positron annihilation constitute a naturally spin-entangled system in the high-energy regime. Recently, a probabilistic amplification of entanglement, termed autodistillation, has been found in the daughter baryon-antibaryon pairs from hyperon decay and is constrained by an upper boundary. This work demonstrates that the quantum entanglement in this process may be accompanied by a decrease, constrained by a lower boundary, but it will not be completely lost. Thus, the entanglement of these systems undergoes redistribution within the phase space during the sequential decays of hyperons, highlighting the important role of hyperon polarization. By using the explicit spin density matrix of baryon pairs, it is also found that the quantumness of the system, characterized by quantum discord, always has the possibility to increase during decay processes, even when entanglement evaluated by concurrence and negativity does not increase.
Hyperon-antihyperon pairs produced in high-energy electron-positron annihilation constitute a naturally spin-entangled system in the high-energy regime. Recently, a probabilistic amplification of entanglement, termed autodistillation, has been found in the daughter baryon-antibaryon pairs from hyperon decay and is constrained by an upper boundary. This work demonstrates that the quantum entanglement in this process may be accompanied by a decrease, constrained by a lower boundary, but it will not be completely lost. Thus, the entanglement of these systems undergoes redistribution within the phase space during the sequential decays of hyperons, highlighting the important role of hyperon polarization. By using the explicit spin density matrix of baryon pairs, it is also found that the quantumness of the system, characterized by quantum discord, always has the possibility to increase during decay processes, even when entanglement evaluated by concurrence and negativity does not increase.
2026, 50(9): 093104. doi: 10.1088/1674-1137/ae71a6
Abstract:
Motivated by the enigmatic vector charmonium-like states, we investigate the strong decay behaviors of four types of vector tetraquark states, which are possible candidates for the $Y(4660)$, within the framework of three-point QCD sum rules based on rigorous quark-hadron duality. We take into account vacuum condensates up to dimension 5 on the QCD side and obtain the hadronic coupling constants and hence the partial decay widths of these states. The predicted total width, $61.5\pm7.3\,{\rm{MeV}}$, is in excellent agreement with the experimental data for the $Y(4660)$, supporting its interpretation as a $[sc][\bar{s}\bar{c}]$ tetraquark state with $J^{PC}=1^{--}$.
Motivated by the enigmatic vector charmonium-like states, we investigate the strong decay behaviors of four types of vector tetraquark states, which are possible candidates for the $Y(4660)$, within the framework of three-point QCD sum rules based on rigorous quark-hadron duality. We take into account vacuum condensates up to dimension 5 on the QCD side and obtain the hadronic coupling constants and hence the partial decay widths of these states. The predicted total width, $61.5\pm7.3\,{\rm{MeV}}$, is in excellent agreement with the experimental data for the $Y(4660)$, supporting its interpretation as a $[sc][\bar{s}\bar{c}]$ tetraquark state with $J^{PC}=1^{--}$.
2026, 50(9): 1-13. doi: 10.1088/1674-1137/ae76fa
Abstract:
A dark photon is an Abelian gauge boson arising from a new $ U(1)_D $ gauge symmetry, coupled to the Standard Model through kinetic mixing. The mixing parameter ϵ induces an effective coupling to the electromagnetic current, while $ g_\chi $ couples the dark photon to a stable dark matter particle χ. We study $ J/\psi $ two-body and four-body decays mediated by a light dark photon ($ m_U \lt 3.0 $ GeV) within the non-relativistic QCD (NRQCD) framework, considering both visible decays of the dark photon into SM fermions and invisible decays into dark sector particles. We investigate the detection sensitivity of BESIII and STCF experiments to the dark photon mass $ m_U $ and kinetic mixing parameter ϵ. Our results show that, for two-body final states with $ m_U<2m_\chi $, BESIII sets ϵ upper limits of $ 9.3\times10^{-4} $ and $ 7.6\times10^{-4} $ for lepton-pair and hadronic signals, respectively, while STCF yields $ 3.7\times10^{-4} $ and $ 3.1\times10^{-4} $. For invisible decays ($ m_U\ge 2m_\chi $), BESIII achieves an ϵ limit of $ 1.4\times10^{-3} $ in the mass range $ 0.3\sim0.8 $ GeV, and STCF reaches $ 2.3\times10^{-4} $ in $ 0.3\sim1.9 $ GeV; no signals are expected in other mass regions, and visible decays are severely suppressed throughout. For four-body decay channels, BESIII yields an ϵ upper limit of $ 7.6\times10^{-5} $ for $ m_U<2.2 $ GeV, whereas STCF achieves $ 1.2\times10^{-5} $ over the full mass range. When $ m_U\ge 2m_\chi $, visible modes are nearly excluded; BESIII and STCF set ϵ limits from invisible decays of $ 8.8\times10^{-5} $ for $ m_U \lt 2.4 $ GeV and $ 1.4\times10^{-5} $ for $ m_U \lt 2.8 $ GeV, respectively, with no detectable signals at higher masses. Except for the limit of $ 9.3\times10^{-4} $, all the above ϵ bounds lie in regions that are not currently excluded by collider experiments. Compared with the constraints from two-body final state processes, the limits derived from four-body decay channels lie well below existing experimental bounds, providing supportive references for constraining this parameter in BESIII and STCF experiments. Numerical results for the decay ratios $ \Gamma/\Gamma_{J/\psi} $, expected event numbers, significance $ S/\sqrt{B} $, and $ p_T $ distributions are presented where applicable.
A dark photon is an Abelian gauge boson arising from a new $ U(1)_D $ gauge symmetry, coupled to the Standard Model through kinetic mixing. The mixing parameter ϵ induces an effective coupling to the electromagnetic current, while $ g_\chi $ couples the dark photon to a stable dark matter particle χ. We study $ J/\psi $ two-body and four-body decays mediated by a light dark photon ($ m_U \lt 3.0 $ GeV) within the non-relativistic QCD (NRQCD) framework, considering both visible decays of the dark photon into SM fermions and invisible decays into dark sector particles. We investigate the detection sensitivity of BESIII and STCF experiments to the dark photon mass $ m_U $ and kinetic mixing parameter ϵ. Our results show that, for two-body final states with $ m_U<2m_\chi $, BESIII sets ϵ upper limits of $ 9.3\times10^{-4} $ and $ 7.6\times10^{-4} $ for lepton-pair and hadronic signals, respectively, while STCF yields $ 3.7\times10^{-4} $ and $ 3.1\times10^{-4} $. For invisible decays ($ m_U\ge 2m_\chi $), BESIII achieves an ϵ limit of $ 1.4\times10^{-3} $ in the mass range $ 0.3\sim0.8 $ GeV, and STCF reaches $ 2.3\times10^{-4} $ in $ 0.3\sim1.9 $ GeV; no signals are expected in other mass regions, and visible decays are severely suppressed throughout. For four-body decay channels, BESIII yields an ϵ upper limit of $ 7.6\times10^{-5} $ for $ m_U<2.2 $ GeV, whereas STCF achieves $ 1.2\times10^{-5} $ over the full mass range. When $ m_U\ge 2m_\chi $, visible modes are nearly excluded; BESIII and STCF set ϵ limits from invisible decays of $ 8.8\times10^{-5} $ for $ m_U \lt 2.4 $ GeV and $ 1.4\times10^{-5} $ for $ m_U \lt 2.8 $ GeV, respectively, with no detectable signals at higher masses. Except for the limit of $ 9.3\times10^{-4} $, all the above ϵ bounds lie in regions that are not currently excluded by collider experiments. Compared with the constraints from two-body final state processes, the limits derived from four-body decay channels lie well below existing experimental bounds, providing supportive references for constraining this parameter in BESIII and STCF experiments. Numerical results for the decay ratios $ \Gamma/\Gamma_{J/\psi} $, expected event numbers, significance $ S/\sqrt{B} $, and $ p_T $ distributions are presented where applicable.
2026, 50(9): 093102. doi: 10.1088/1674-1137/ae6ed2
Abstract:
We propose a novel realization of the linear seesaw model with a non-invertible selection rule, assisted by $\mathbb{Z}_3$ symmetry. In our framework, Dirac mass matrices are generated at the one-loop level, breaking the non-invertible symmetry, while the symmetry remains intact at tree level. In addition to active neutrino masses, the model exhibits rich and testable phenomenology, including non-unitarity constraints, lepton flavor violation, lepton anomalous magnetic moments, and a dark matter candidate. After describing our model, we carry out a numerical analysis and present results for our physical parameters.
We propose a novel realization of the linear seesaw model with a non-invertible selection rule, assisted by $\mathbb{Z}_3$ symmetry. In our framework, Dirac mass matrices are generated at the one-loop level, breaking the non-invertible symmetry, while the symmetry remains intact at tree level. In addition to active neutrino masses, the model exhibits rich and testable phenomenology, including non-unitarity constraints, lepton flavor violation, lepton anomalous magnetic moments, and a dark matter candidate. After describing our model, we carry out a numerical analysis and present results for our physical parameters.
2026, 50(9): 1-16. doi: 10.1088/1674-1137/ae68ef
Abstract:
In this work, we present a systematic study of the event characteristics and underlying physics relevant to neutrino-antineutrino discrimination in atmospheric neutrino charged-current interactions in large liquid scintillator detectors. This study encompasses the primary neutrino interactions, the subsequent secondary interactions of final-state particles, and the ensuing neutron captures. We investigate in detail the properties of final-state charged leptons and hadrons, deriving distinct distributions of inelasticity and neutron-capture multiplicity for both neutrino and antineutrino interactions. These distributions are used to quantify the performance of neutrino-antineutrino discrimination. Our findings lay the groundwork for atmospheric neutrino oscillation studies in large liquid scintillator detectors, particularly for determining the neutrino mass ordering.
In this work, we present a systematic study of the event characteristics and underlying physics relevant to neutrino-antineutrino discrimination in atmospheric neutrino charged-current interactions in large liquid scintillator detectors. This study encompasses the primary neutrino interactions, the subsequent secondary interactions of final-state particles, and the ensuing neutron captures. We investigate in detail the properties of final-state charged leptons and hadrons, deriving distinct distributions of inelasticity and neutron-capture multiplicity for both neutrino and antineutrino interactions. These distributions are used to quantify the performance of neutrino-antineutrino discrimination. Our findings lay the groundwork for atmospheric neutrino oscillation studies in large liquid scintillator detectors, particularly for determining the neutrino mass ordering.
2026, 50(9): 093103. doi: 10.1088/1674-1137/ae6da1
Abstract:
In this work, we propose a method for quantifying the difference between nuclear parton distribution functions in different nuclei and parton distribution functions in free nucleons using relative entropy (also known as the Kullback-Leibler divergence), a measure widely employed in quantum information theory. By introducing certain constraints and the ''minimum relative entropy'' hypothesis, we can determine the shape of the structure function in the intermediate-x region, which is closely connected to the renowned EMC effect. For quark structure functions, our results are consistent with the latest global fits to experimental data. This agreement suggests that the relative entropy-based methodology may provide novel insights into nucleon structure, particularly in cases where experimental data and theoretical QCD constraints are limited, such as those relevant to gluon nPDFs. Therefore, we apply this methodology to gluon nPDFs, analyzing the results from two commonly used global fitting groups, EPPS21 and nNNPDF3.0. Our analysis suggests that the central values of EPPS21 align more closely with the ''minimum relative entropy'' hypothesis. This finding underscores the utility of the proposed method and provides a valuable reference for future global fits of nPDFs.
In this work, we propose a method for quantifying the difference between nuclear parton distribution functions in different nuclei and parton distribution functions in free nucleons using relative entropy (also known as the Kullback-Leibler divergence), a measure widely employed in quantum information theory. By introducing certain constraints and the ''minimum relative entropy'' hypothesis, we can determine the shape of the structure function in the intermediate-x region, which is closely connected to the renowned EMC effect. For quark structure functions, our results are consistent with the latest global fits to experimental data. This agreement suggests that the relative entropy-based methodology may provide novel insights into nucleon structure, particularly in cases where experimental data and theoretical QCD constraints are limited, such as those relevant to gluon nPDFs. Therefore, we apply this methodology to gluon nPDFs, analyzing the results from two commonly used global fitting groups, EPPS21 and nNNPDF3.0. Our analysis suggests that the central values of EPPS21 align more closely with the ''minimum relative entropy'' hypothesis. This finding underscores the utility of the proposed method and provides a valuable reference for future global fits of nPDFs.
2026, 50(9): 093101. doi: 10.1088/1674-1137/ae740d
Abstract:
We investigate the frame dependence of distribution functions within the framework of generalized chiral kinetic theory. Based on the derived transformation rules governing the choice of frame, we analytically obtain the global equilibrium solutions in the presence of vorticity and electromagnetic fields. Our results show that, under the assumption of varying electromagnetic fields, these equilibrium solutions can be uniquely determined.
We investigate the frame dependence of distribution functions within the framework of generalized chiral kinetic theory. Based on the derived transformation rules governing the choice of frame, we analytically obtain the global equilibrium solutions in the presence of vorticity and electromagnetic fields. Our results show that, under the assumption of varying electromagnetic fields, these equilibrium solutions can be uniquely determined.
2026, 50(9): 1-9. doi: 10.1088/1674-1137/ae740c
Abstract:
We investigate the polarized images of an equatorial emitting ring around a rotating Konoplya-Zhidenko non-Kerr black hole, which incorporates an additional deformation parameter. This deformation parameter, η, permits the spin parameter to exceed the upper bound imposed by the standard Kerr black hole. Our results indicate that the polarized images depend not only on the magnetic field configuration, fluid velocity, and observer inclination angle, but also on the spin and deformation parameters. As the deformation parameter increases, the polarization intensity decreases monotonically. Conversely, the magnitude of the Electric Vector Position Angle (EVPA) increases with η. Furthermore, we observe that η may induce subtle yet discernible azimuthal separation features, potentially distinguishing its effects from those of the spin parameter and the magnetic field orientation angle. Nevertheless, these features remain difficult to resolve under current observational conditions and will require verification by future high-resolution facilities such as the next-generation Event Horizon Telescope (ngEHT).
We investigate the polarized images of an equatorial emitting ring around a rotating Konoplya-Zhidenko non-Kerr black hole, which incorporates an additional deformation parameter. This deformation parameter, η, permits the spin parameter to exceed the upper bound imposed by the standard Kerr black hole. Our results indicate that the polarized images depend not only on the magnetic field configuration, fluid velocity, and observer inclination angle, but also on the spin and deformation parameters. As the deformation parameter increases, the polarization intensity decreases monotonically. Conversely, the magnitude of the Electric Vector Position Angle (EVPA) increases with η. Furthermore, we observe that η may induce subtle yet discernible azimuthal separation features, potentially distinguishing its effects from those of the spin parameter and the magnetic field orientation angle. Nevertheless, these features remain difficult to resolve under current observational conditions and will require verification by future high-resolution facilities such as the next-generation Event Horizon Telescope (ngEHT).
2026, 50(9): 091001. doi: 10.1088/1674-1137/ae74bd
Abstract:
γ-ray pulsar halos are produced by electron-positron pairs that diffuse away from the pulsar and scatter off background photons. Their morphology serves as an ideal probe for studying cosmic-ray propagation on scales of several tens of parsecs. However, the number of firmly identified pulsar halos remains limited, primarily because current γ-ray experiments, constrained by angular resolution, struggle to resolve the diffusion signatures of distant candidates ($>1$ kpc). In this work, we investigate the prospects for identifying pulsar halo candidates through morphological discrimination using simulations of two advanced γ-ray experiments: the Kilometer Square Array of the Large High Altitude Air Shower Observatory (LHAASO-KM2A) and the Cherenkov Telescope Array (CTA, under construction). Using mock observations with realistic instrumental responses, we quantitatively assess the ability of each experiment to distinguish diffusion-based halo morphologies from alternative spatial models. Our analysis indicates that if the angular resolution of LHAASO-KM2A could be improved by 40%, it would be capable of resolving several prominent pulsar halo candidates, namely the halos around pulsars J1831-0952, J0248+6021, and J0359+5414. CTA holds an advantage in resolving the morphology of sources beyond $\approx1.5$ kpc owing to its superb angular resolution. By extending exposure times to hundreds of hours, CTA is expected to achieve morphological identification for all known pulsar halo candidates.
γ-ray pulsar halos are produced by electron-positron pairs that diffuse away from the pulsar and scatter off background photons. Their morphology serves as an ideal probe for studying cosmic-ray propagation on scales of several tens of parsecs. However, the number of firmly identified pulsar halos remains limited, primarily because current γ-ray experiments, constrained by angular resolution, struggle to resolve the diffusion signatures of distant candidates ($>1$ kpc). In this work, we investigate the prospects for identifying pulsar halo candidates through morphological discrimination using simulations of two advanced γ-ray experiments: the Kilometer Square Array of the Large High Altitude Air Shower Observatory (LHAASO-KM2A) and the Cherenkov Telescope Array (CTA, under construction). Using mock observations with realistic instrumental responses, we quantitatively assess the ability of each experiment to distinguish diffusion-based halo morphologies from alternative spatial models. Our analysis indicates that if the angular resolution of LHAASO-KM2A could be improved by 40%, it would be capable of resolving several prominent pulsar halo candidates, namely the halos around pulsars J1831-0952, J0248+6021, and J0359+5414. CTA holds an advantage in resolving the morphology of sources beyond $\approx1.5$ kpc owing to its superb angular resolution. By extending exposure times to hundreds of hours, CTA is expected to achieve morphological identification for all known pulsar halo candidates.
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