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2026 No.3
2026, 50(3): 033101. doi: 10.1088/1674-1137/ae18aa
Abstract:
Inspired by the observation of the ${\eta}_{t}$ meson at the LHC and the promising prospect of the ${\eta}_{t}$ meson available at the approaching HL-LHC, branching ratios for the ${\eta}_{t}$ ${\to}$ $f\bar{f}$, $gg$, ${\gamma}{\gamma}$, $W^{+}W^{-}$, $Z^{0}Z^{0}$, $Z^{0}{\gamma}$, and $Z^{0}H$ decays are roughly estimated. It is found that tens of opposite-charge dilepton events from the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ decay and hundreds of events from the ${\eta}_{t}$ ${\to}$ $Z^{0}H$ ${\to}$ ${\ell}^{+}{\ell}^{-}H$ decay using the single $Z^{0}$ boson tagging method are expected to be accessible. This estimation provides a reference for future experimental study on the ${\eta}_{t}$ meson.
Inspired by the observation of the ${\eta}_{t}$ meson at the LHC and the promising prospect of the ${\eta}_{t}$ meson available at the approaching HL-LHC, branching ratios for the ${\eta}_{t}$ ${\to}$ $f\bar{f}$, $gg$, ${\gamma}{\gamma}$, $W^{+}W^{-}$, $Z^{0}Z^{0}$, $Z^{0}{\gamma}$, and $Z^{0}H$ decays are roughly estimated. It is found that tens of opposite-charge dilepton events from the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ decay and hundreds of events from the ${\eta}_{t}$ ${\to}$ $Z^{0}H$ ${\to}$ ${\ell}^{+}{\ell}^{-}H$ decay using the single $Z^{0}$ boson tagging method are expected to be accessible. This estimation provides a reference for future experimental study on the ${\eta}_{t}$ meson.
2026, 50(3): 033111. doi: 10.1088/1674-1137/ae2b5c
Abstract:
An analytical and numerical systematic study of the neutrino mass matrix with one texture zero is presented in a basis where the charged leptons are diagonal. Under the assumption that neutrinos are Dirac particles, the analysis is conducted in detail for the normal and inverted hierarchy mass spectra. Our study is performed without any approximations, first analytically and then numerically, using current neutrino oscillation data. The analysis constrains the parameter space in such a way that, among the six possible one-texture-zero patterns, only four are favored in the normal hierarchy and one in the inverted hierarchy by current oscillation data at the $3 \sigma$ level. Phenomenological implications for the lepton CP-violating phase and neutrino masses are also explored.
An analytical and numerical systematic study of the neutrino mass matrix with one texture zero is presented in a basis where the charged leptons are diagonal. Under the assumption that neutrinos are Dirac particles, the analysis is conducted in detail for the normal and inverted hierarchy mass spectra. Our study is performed without any approximations, first analytically and then numerically, using current neutrino oscillation data. The analysis constrains the parameter space in such a way that, among the six possible one-texture-zero patterns, only four are favored in the normal hierarchy and one in the inverted hierarchy by current oscillation data at the $3 \sigma$ level. Phenomenological implications for the lepton CP-violating phase and neutrino masses are also explored.
2026, 50(3): 033001. doi: 10.1088/1674-1137/ae2f4e
Abstract:
The Circular Electron Positron Collider (CEPC) is designed to operate at key center-of-mass energies: 91.2 GeV as a Z factory for precision Z boson studies, ≈ 160 GeV at the threshold for W boson pair production, and 240 GeV as a Higgs factory for copious Higgs boson production. It can be upgraded to 360 GeV (CEPC-360 GeV) for enabling top quark-antiquark ($ t\bar{t}$) pair production. Beyond enabling high-precision measurements of the Standard Model (SM), CEPC-360 GeV is uniquely positioned to perform searches for new physics beyond the SM (BSM), serving as a valuable complement to hadron colliders. This paper presents a sensitivity study on the direct pair production of staus and smuons at the CEPC with $ \sqrt{s}$ = 360 GeV, conducted via full Monte Carlo simulation. Under the assumptions of 1.0 ab−1 integrated luminosity and a flat 5% systematic uncertainty, CEPC-360 GeV could potentially discover the combined production of left-handed and right-handed staus up to a mass of 170 GeV (if they exist) or up to 169 for pure left-handed staus and 162 GeV for pure right-handed staus. For direct smuon production, the discovery potential reaches up to 178 GeV under the same conditions.
The Circular Electron Positron Collider (CEPC) is designed to operate at key center-of-mass energies: 91.2 GeV as a Z factory for precision Z boson studies, ≈ 160 GeV at the threshold for W boson pair production, and 240 GeV as a Higgs factory for copious Higgs boson production. It can be upgraded to 360 GeV (CEPC-360 GeV) for enabling top quark-antiquark ($ t\bar{t}$) pair production. Beyond enabling high-precision measurements of the Standard Model (SM), CEPC-360 GeV is uniquely positioned to perform searches for new physics beyond the SM (BSM), serving as a valuable complement to hadron colliders. This paper presents a sensitivity study on the direct pair production of staus and smuons at the CEPC with $ \sqrt{s}$ = 360 GeV, conducted via full Monte Carlo simulation. Under the assumptions of 1.0 ab−1 integrated luminosity and a flat 5% systematic uncertainty, CEPC-360 GeV could potentially discover the combined production of left-handed and right-handed staus up to a mass of 170 GeV (if they exist) or up to 169 for pure left-handed staus and 162 GeV for pure right-handed staus. For direct smuon production, the discovery potential reaches up to 178 GeV under the same conditions.
2026, 50(3): 033109. doi: 10.1088/1674-1137/ae28ea
Abstract:
Off-shell characteristics of pion generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) are examined within the framework of the Nambu–Jona-Lasinio model. In our previous studies, we separately investigated the properties of on-shell pion GPDs and light-front wave functions. Comparing the differences between on-shell and off-shell pion GPDs is particularly intriguing becuase it enables us to explore the effects associated with off-shellness. The absence of crossing symmetry causes the moments of GPDs to incorporate odd powers of the skewness parameter, resulting in new off-shell form factors. Through our calculations, we derived correction functions that account for modifications in pion GPDs attributed to off-shell effects. Unlike their on-shell counterparts, certain properties break down in the off-shell scenario; for example, symmetry properties and polynomiality conditions may no longer hold. In addition, we evaluate off-shell TMDs and compare them with their on-shell equivalents while also investigating their dependence on $ {\boldsymbol{k}}_{\perp} $.
Off-shell characteristics of pion generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) are examined within the framework of the Nambu–Jona-Lasinio model. In our previous studies, we separately investigated the properties of on-shell pion GPDs and light-front wave functions. Comparing the differences between on-shell and off-shell pion GPDs is particularly intriguing becuase it enables us to explore the effects associated with off-shellness. The absence of crossing symmetry causes the moments of GPDs to incorporate odd powers of the skewness parameter, resulting in new off-shell form factors. Through our calculations, we derived correction functions that account for modifications in pion GPDs attributed to off-shell effects. Unlike their on-shell counterparts, certain properties break down in the off-shell scenario; for example, symmetry properties and polynomiality conditions may no longer hold. In addition, we evaluate off-shell TMDs and compare them with their on-shell equivalents while also investigating their dependence on $ {\boldsymbol{k}}_{\perp} $.
2026, 50(3): 033106. doi: 10.1088/1674-1137/ae28e9
Abstract:
Quantum chromodynamics (QCD) is a fundamental theory describing quark interactions. Thus far, various quark models based on QCD have been widely used to study the properties of hadrons, including their structures and mass spectra. However, unlike quantum electrodynamics and Bohr's model of the hydrogen atom, a direct classical analogy is lacking for hadronic structures. This paper presents a classical interpretation of the nonrelativistic quark potential model, providing a more intuitive and visualizable description of strong interactions through the quantitative formulation of color charge and color flux. In addition, we establish the relationship between meson mass and its structural radius in the nonrelativistic framework and estimate key parameters of our model using available data from $ \eta_b(1S) $ and $ \Upsilon(1S) $. Subsequently, we extend this relationship to a broader range of excited meson states and obtain their structural radii, which show good agreement with the root mean square radius or charge radius predicted by QCD calculations.
Quantum chromodynamics (QCD) is a fundamental theory describing quark interactions. Thus far, various quark models based on QCD have been widely used to study the properties of hadrons, including their structures and mass spectra. However, unlike quantum electrodynamics and Bohr's model of the hydrogen atom, a direct classical analogy is lacking for hadronic structures. This paper presents a classical interpretation of the nonrelativistic quark potential model, providing a more intuitive and visualizable description of strong interactions through the quantitative formulation of color charge and color flux. In addition, we establish the relationship between meson mass and its structural radius in the nonrelativistic framework and estimate key parameters of our model using available data from $ \eta_b(1S) $ and $ \Upsilon(1S) $. Subsequently, we extend this relationship to a broader range of excited meson states and obtain their structural radii, which show good agreement with the root mean square radius or charge radius predicted by QCD calculations.
One-loop expressions for ${H^\pm \rightarrow W^\pm Z} $ and their implications at muon-TeV colliders
2026, 50(3): 033108. doi: 10.1088/1674-1137/ae2660
Abstract:
One-loop contributions for the decay process $ H^{\pm} \rightarrow W^{\pm}Z $ within the Two-Higgs-Doublet Model (THDM) are computed in the general $ {\cal{R}}_{\xi} $ gauge, and its phenomenological applications at future muon–TeV colliders are investigated. Analytic results are confirmed by several consistency tests, including those of ξ-independence, renormalization-scale stability, and the ultraviolet finiteness of the one-loop amplitude. We first perform an updated parameter scan of the Type-X THDM in phenomenological studies. The production of charged Higgs boson pairs at future muon–TeV colliders is then investigated through two processes: $ \mu^+\mu^- \rightarrow H^+H^- \rightarrow W^{\pm}W^{\mp}Zh $ and $ \mu^+\mu^- \rightarrow \gamma\gamma \rightarrow H^+H^- \rightarrow W^{\pm}W^{\mp}Zh $. Both signal events and their significance are evaluated considering the corresponding Standard Model backgrounds. We find that the signal significances can exceed $ 5\sigma $ at several benchmark points in the viable parameter space of the Type-X THDM.
One-loop contributions for the decay process $ H^{\pm} \rightarrow W^{\pm}Z $ within the Two-Higgs-Doublet Model (THDM) are computed in the general $ {\cal{R}}_{\xi} $ gauge, and its phenomenological applications at future muon–TeV colliders are investigated. Analytic results are confirmed by several consistency tests, including those of ξ-independence, renormalization-scale stability, and the ultraviolet finiteness of the one-loop amplitude. We first perform an updated parameter scan of the Type-X THDM in phenomenological studies. The production of charged Higgs boson pairs at future muon–TeV colliders is then investigated through two processes: $ \mu^+\mu^- \rightarrow H^+H^- \rightarrow W^{\pm}W^{\mp}Zh $ and $ \mu^+\mu^- \rightarrow \gamma\gamma \rightarrow H^+H^- \rightarrow W^{\pm}W^{\mp}Zh $. Both signal events and their significance are evaluated considering the corresponding Standard Model backgrounds. We find that the signal significances can exceed $ 5\sigma $ at several benchmark points in the viable parameter space of the Type-X THDM.
2026, 50(3): 033105. doi: 10.1088/1674-1137/ae2454
Abstract:
Higgs self-coupling is crucial to understand the structure of the scalar potential and the mechanism of electroweak symmetry breaking. In this study, we utilize a deep neural network based on a particle Transformer model that relies on an attention mechanism to comprehensively analyze the measured trilinear Higgs self-coupling through Higgs pair production with subsequent decay into four b-quarks ($ HH\to b\bar{b}b\bar{b} $) at the LHC. The model processes the full event-level information as input and bypasses explicit jet pairing. It also serves as an event classifier. At HL-LHC, our approach constrains $ \kappa_\lambda $ to $ (-0.25,\,5.41) $ at 68% CL, and thus achieved an improvement of ~44% in precision over conventional cut-based analyses. The results of a comparison against alternative machine learning architectures demonstrate the outstanding performance of the Transformer-based model owing to its ability to capture correlations in high-dimensional collision data with the help of the attention mechanism. These findings highlight the potential of attention-based networks and end-to-end event classifiers in collider phenomenology.
Higgs self-coupling is crucial to understand the structure of the scalar potential and the mechanism of electroweak symmetry breaking. In this study, we utilize a deep neural network based on a particle Transformer model that relies on an attention mechanism to comprehensively analyze the measured trilinear Higgs self-coupling through Higgs pair production with subsequent decay into four b-quarks ($ HH\to b\bar{b}b\bar{b} $) at the LHC. The model processes the full event-level information as input and bypasses explicit jet pairing. It also serves as an event classifier. At HL-LHC, our approach constrains $ \kappa_\lambda $ to $ (-0.25,\,5.41) $ at 68% CL, and thus achieved an improvement of ~44% in precision over conventional cut-based analyses. The results of a comparison against alternative machine learning architectures demonstrate the outstanding performance of the Transformer-based model owing to its ability to capture correlations in high-dimensional collision data with the help of the attention mechanism. These findings highlight the potential of attention-based networks and end-to-end event classifiers in collider phenomenology.
2026, 50(3): 033102. doi: 10.1088/1674-1137/ae1afd
Abstract:
We study a feebly interacting massive particle realization of the Scotogenic Dirac Model in which the lightest neutral fermion $ N_1 $ serves as a dark matter (DM) candidate produced via the freeze-in or super-WIMP mechanism. The model generates Dirac neutrino masses at one loop, resulting in a rank-2 mass matrix that predicts one almost massless neutrino. We analyze the DM relic density for various next-to-lightest odd particles (NLOPs), finding that coannihilation effects and enhanced annihilation channels are crucial for achieving the correct thermal freeze-out abundance of the NLOP. We provide a detailed analysis of the model's implications for the effective number of relativistic species, $ \Delta N_{{\rm{eff}}} $, which receives contributions from both a thermal bath of right-handed neutrinos and non-thermal energy injection due to late NLOP decays. Through an extensive parameter scan, we identify the viable parameter space for all NLOP candidates that satisfies constraints from the DM relic density, lepton flavor violation, Big Bang nucleosynthesis, cosmic microwave background, and $ \Delta N_{{\rm{eff}}} $.
We study a feebly interacting massive particle realization of the Scotogenic Dirac Model in which the lightest neutral fermion $ N_1 $ serves as a dark matter (DM) candidate produced via the freeze-in or super-WIMP mechanism. The model generates Dirac neutrino masses at one loop, resulting in a rank-2 mass matrix that predicts one almost massless neutrino. We analyze the DM relic density for various next-to-lightest odd particles (NLOPs), finding that coannihilation effects and enhanced annihilation channels are crucial for achieving the correct thermal freeze-out abundance of the NLOP. We provide a detailed analysis of the model's implications for the effective number of relativistic species, $ \Delta N_{{\rm{eff}}} $, which receives contributions from both a thermal bath of right-handed neutrinos and non-thermal energy injection due to late NLOP decays. Through an extensive parameter scan, we identify the viable parameter space for all NLOP candidates that satisfies constraints from the DM relic density, lepton flavor violation, Big Bang nucleosynthesis, cosmic microwave background, and $ \Delta N_{{\rm{eff}}} $.
2026, 50(3): 034106. doi: 10.1088/1674-1137/ae1f7a
Abstract:
Recently, the very small $B(E2;2_{1}^{+}\rightarrow0_{1}^{+})$ value of 7(4) W.u. in $^{166}{\rm{Os}}$ was found experimentally. This result is much smaller than the values of 74(13) W.u. and 97(9) W.u. in the adjacent nuclei $^{168,170}{\rm{Os}}$. Using the newly proposed technique called "$ S U$(3) analysis" and the new explanatory framework for the SU(3) anomaly, the $B(E2;2_{1}^{+}\rightarrow0_{1}^{+})$ anomaly in $^{166}{\rm{Os}}$ is studied for the first time. Four results are used to fit the experimental data in $^{166,168,170}{\rm{Os}}$ successfully. This implies that the level-crossing or level-anticrossing explanation is applicable.
Recently, the very small $B(E2;2_{1}^{+}\rightarrow0_{1}^{+})$ value of 7(4) W.u. in $^{166}{\rm{Os}}$ was found experimentally. This result is much smaller than the values of 74(13) W.u. and 97(9) W.u. in the adjacent nuclei $^{168,170}{\rm{Os}}$. Using the newly proposed technique called "$ S U$(3) analysis" and the new explanatory framework for the SU(3) anomaly, the $B(E2;2_{1}^{+}\rightarrow0_{1}^{+})$ anomaly in $^{166}{\rm{Os}}$ is studied for the first time. Four results are used to fit the experimental data in $^{166,168,170}{\rm{Os}}$ successfully. This implies that the level-crossing or level-anticrossing explanation is applicable.
2026, 50(3): 034003. doi: 10.1088/1674-1137/ae1f06
Abstract:
The 26Mg$(p,\,\gamma)$27Al reaction, as part of the Mg-Al cycle, is closely related to the abundance ratio of 26Al to 27Al in stars. It also has a direct connection to the Mg-Al anti-correlation observed in globular clusters (GCs). Its reaction rate is determined by multiple known and unknown low-energy resonances. In this work, we measured the angular distributions of the proton transfer reaction 26Mg(7Li, 6He)27Al populating three levels at excitation energies from 8.324 MeV to 8.597 MeV using the HI-13 tandem accelerator and a high-precision magnetic spectrograph. Proton spectroscopic factors were extracted from the angular distributions corresponding to these three states, and the resonance strengths contributing to the reaction rate were updated. At the same time, the latest calculated reaction rate shows that the result for the 52.8 keV resonance significantly increases the total reaction rate at $T_{9}<0.03$.
The 26Mg$(p,\,\gamma)$27Al reaction, as part of the Mg-Al cycle, is closely related to the abundance ratio of 26Al to 27Al in stars. It also has a direct connection to the Mg-Al anti-correlation observed in globular clusters (GCs). Its reaction rate is determined by multiple known and unknown low-energy resonances. In this work, we measured the angular distributions of the proton transfer reaction 26Mg(7Li, 6He)27Al populating three levels at excitation energies from 8.324 MeV to 8.597 MeV using the HI-13 tandem accelerator and a high-precision magnetic spectrograph. Proton spectroscopic factors were extracted from the angular distributions corresponding to these three states, and the resonance strengths contributing to the reaction rate were updated. At the same time, the latest calculated reaction rate shows that the result for the 52.8 keV resonance significantly increases the total reaction rate at $T_{9}<0.03$.
2026, 50(3): 034002. doi: 10.1088/1674-1137/ae2263
Abstract:
This paper presents the development and validation of China’s first benchmark measurement system for neutron leakage time-of-flight (TOF) spectra using a 252Cf spontaneous fission source and spherical polyethylene sample. EJ-309 and CLYC scintillation detectors were used for neutron detection, and a shadow cone was employed for background suppression. Notably, the SiC detector was, for the first time on this platform, applied as the start-time signal generator in TOF spectrum measurement. The TOF spectrum covering the energy range of 0.15−8.00 MeV was measured, and the results were systematically compared with evaluated data from four major nuclear libraries: ENDF/B-VIII.1, JEFF-3.3, JENDL-5, and CENDL-3.2. The comparison revealed strong agreement across the full spectrum, with calculated to experimental (C/E) deviations remaining within 5% in the high-energy region and within 13% at low energies. These results verify the system’s stability and suitability for integral experiments. The established benchmark platform provides a strong technical foundation for future neutron nuclear data validation, particularly in shielding applications and the improvement of fission-spectrum nuclear databases.
This paper presents the development and validation of China’s first benchmark measurement system for neutron leakage time-of-flight (TOF) spectra using a 252Cf spontaneous fission source and spherical polyethylene sample. EJ-309 and CLYC scintillation detectors were used for neutron detection, and a shadow cone was employed for background suppression. Notably, the SiC detector was, for the first time on this platform, applied as the start-time signal generator in TOF spectrum measurement. The TOF spectrum covering the energy range of 0.15−8.00 MeV was measured, and the results were systematically compared with evaluated data from four major nuclear libraries: ENDF/B-VIII.1, JEFF-3.3, JENDL-5, and CENDL-3.2. The comparison revealed strong agreement across the full spectrum, with calculated to experimental (C/E) deviations remaining within 5% in the high-energy region and within 13% at low energies. These results verify the system’s stability and suitability for integral experiments. The established benchmark platform provides a strong technical foundation for future neutron nuclear data validation, particularly in shielding applications and the improvement of fission-spectrum nuclear databases.
2026, 50(3): 034107. doi: 10.1088/1674-1137/ae1de6
Abstract:
The $ \pi d_{5/2} $ rotational bands in odd-even nuclei 117,119,121,123,125Cs are systematically investigated using the cranked shell model (CSM) with the pairing correlations modeled with a particle number conserving (PNC) method. In this PNC method, the particle number is conserved exactly while considering the blocking effects. The experimental observations of the $ \pi d_{5/2} $ bands with two upbendings for 117,119Cs and one backbending for 125Cs are reproduced very well by the PNC-CSM method. Furthermore, $ \pi d_{5/2} $ configuration bands with two upbendings for 121Cs and one backbending for 123Cs are predicted by the PNC-CSM calculations. The difference between the lighter 117,119,121Cs and heavier 123,125Cs isotopes is caused by the evolution of single-particle orbitals near the Fermi surface, and the high-j low-Ω orbital $ \pi [550]1/2 $ plays an important role. The proton shell gap of lighter isotopes is at $ Z=50 $, whereas it appears at $ Z=48 $ for heavier ones. For lighter isotopes 117,119,121Cs, the first upbending is primarily due to the off-diagonal contributions of protons $ j_{x}(\pi5/2^{-}[532]\pi3/2^{-}[541]) $ and $ j_{x}(\pi1/2^{-}[550]\pi3/2^{-}[541]) $. The second upbending is mainly effected by the off-diagonal contributions of neutrons $ j_{x}(\nu7/2^{-}[523] \nu5/2^{-}[532]) $ and $ j_{x}(\nu3/2^{-}[541] \nu5/2^{-}[532]) $ for 117,119Cs and $ j_{x}(\nu1/2^{-}[541] \nu5/2^{-}[532]) $ for 121Cs, respectively. For heavier isotopes such as 123,125Cs, the backbending is attributed mainly to the diagonal parts of proton $ j_{x}(\pi1/2^{-}[550]) $ and neutron $ \nu7/2^{-}[523] $ orbital related terms of diagonal $ j_{x}(\nu7/2^{-}[523]) $ and off-diagonal $ j_{x}(\nu7/2^{-}[523] \nu5/2^{-}[532]) $ contributions.
The $ \pi d_{5/2} $ rotational bands in odd-even nuclei 117,119,121,123,125Cs are systematically investigated using the cranked shell model (CSM) with the pairing correlations modeled with a particle number conserving (PNC) method. In this PNC method, the particle number is conserved exactly while considering the blocking effects. The experimental observations of the $ \pi d_{5/2} $ bands with two upbendings for 117,119Cs and one backbending for 125Cs are reproduced very well by the PNC-CSM method. Furthermore, $ \pi d_{5/2} $ configuration bands with two upbendings for 121Cs and one backbending for 123Cs are predicted by the PNC-CSM calculations. The difference between the lighter 117,119,121Cs and heavier 123,125Cs isotopes is caused by the evolution of single-particle orbitals near the Fermi surface, and the high-j low-Ω orbital $ \pi [550]1/2 $ plays an important role. The proton shell gap of lighter isotopes is at $ Z=50 $, whereas it appears at $ Z=48 $ for heavier ones. For lighter isotopes 117,119,121Cs, the first upbending is primarily due to the off-diagonal contributions of protons $ j_{x}(\pi5/2^{-}[532]\pi3/2^{-}[541]) $ and $ j_{x}(\pi1/2^{-}[550]\pi3/2^{-}[541]) $. The second upbending is mainly effected by the off-diagonal contributions of neutrons $ j_{x}(\nu7/2^{-}[523] \nu5/2^{-}[532]) $ and $ j_{x}(\nu3/2^{-}[541] \nu5/2^{-}[532]) $ for 117,119Cs and $ j_{x}(\nu1/2^{-}[541] \nu5/2^{-}[532]) $ for 121Cs, respectively. For heavier isotopes such as 123,125Cs, the backbending is attributed mainly to the diagonal parts of proton $ j_{x}(\pi1/2^{-}[550]) $ and neutron $ \nu7/2^{-}[523] $ orbital related terms of diagonal $ j_{x}(\nu7/2^{-}[523]) $ and off-diagonal $ j_{x}(\nu7/2^{-}[523] \nu5/2^{-}[532]) $ contributions.
2026, 50(3): 034004. doi: 10.1088/1674-1137/ae1cb1
Abstract:
In this work, differential cross sections of $ \gamma $-ray emission produced in nuclear reactions induced by 14.1 MeV neutrons are measured for the 4.439 MeV line from carbon, as well as for 10 individual $ \gamma $-ray lines from aluminum, 6 from silicon, 8 from calcium, 16 from titanium, 6 from chromium, and 14 from iron. The measurements were conducted using the tagged neutron method with four LaBr3(Ce) scintillation detectors positioned at angles of 25°, 45°, 60°, and 70° relative to the generator target – sample center axis. A neutron generator that can produce 16 separate beams of tagged neutrons was employed, which combined with the detector system, enabled the determination of differential cross-sections for 64 distinct angle values in the range of 17° to 89°. To simplify data visualization, the angular distributions were divided into 5° intervals, with weighted mean values of the angle and differential cross-section calculated for each interval. Corrections for multiple neutron scattering and attenuation, $ \gamma $-ray attenuation, and total detection efficiency computed using GEANT4 were accounted for in the cross-section calculations. Additional measurements were performed to validate the correction calculations. The total $ \gamma $-ray emission cross-sections were obtained by approximating the angular distributions with even-order Legendre polynomial expansions up to the 6th degree, followed by integration over the full solid angle. The total systematic error for the obtained data was estimated as 9.1%.
In this work, differential cross sections of $ \gamma $-ray emission produced in nuclear reactions induced by 14.1 MeV neutrons are measured for the 4.439 MeV line from carbon, as well as for 10 individual $ \gamma $-ray lines from aluminum, 6 from silicon, 8 from calcium, 16 from titanium, 6 from chromium, and 14 from iron. The measurements were conducted using the tagged neutron method with four LaBr3(Ce) scintillation detectors positioned at angles of 25°, 45°, 60°, and 70° relative to the generator target – sample center axis. A neutron generator that can produce 16 separate beams of tagged neutrons was employed, which combined with the detector system, enabled the determination of differential cross-sections for 64 distinct angle values in the range of 17° to 89°. To simplify data visualization, the angular distributions were divided into 5° intervals, with weighted mean values of the angle and differential cross-section calculated for each interval. Corrections for multiple neutron scattering and attenuation, $ \gamma $-ray attenuation, and total detection efficiency computed using GEANT4 were accounted for in the cross-section calculations. Additional measurements were performed to validate the correction calculations. The total $ \gamma $-ray emission cross-sections were obtained by approximating the angular distributions with even-order Legendre polynomial expansions up to the 6th degree, followed by integration over the full solid angle. The total systematic error for the obtained data was estimated as 9.1%.
2026, 50(3): 034105. doi: 10.1088/1674-1137/ae1c29
Abstract:
In the framework of effective field theory, we derive the formula for the decay width of neutrinoless double beta-decay with the S-matrix theory, considering only the contribution from the exchange of light neutrinos. Our results agree with previous derivations for a left-right symmetric model. Detailed analyses of the nuclear matrix elements for 76Ge, 82Se, 130Te, and 136Xe from the quasi-particle random phase approximation method with realistic force and large-scale shell model calculations are performed. We compare the results of two many-body approaches and discuss possible origins of the deviation. We also compare our results with those from the so-called master formula, and observe good agreement between the two schemes. A deviation of the q-term in our scheme compared with the counterpart in the master formula can be explained by the distortion of the electron wave function under the static Coulomb field. We also provide constraints for the low energy effective field theory Wilson coefficients $ C_{VL}^{(6)} $ and $ C_{VR}^{(6)} $ from current experimental limits.
In the framework of effective field theory, we derive the formula for the decay width of neutrinoless double beta-decay with the S-matrix theory, considering only the contribution from the exchange of light neutrinos. Our results agree with previous derivations for a left-right symmetric model. Detailed analyses of the nuclear matrix elements for 76Ge, 82Se, 130Te, and 136Xe from the quasi-particle random phase approximation method with realistic force and large-scale shell model calculations are performed. We compare the results of two many-body approaches and discuss possible origins of the deviation. We also compare our results with those from the so-called master formula, and observe good agreement between the two schemes. A deviation of the q-term in our scheme compared with the counterpart in the master formula can be explained by the distortion of the electron wave function under the static Coulomb field. We also provide constraints for the low energy effective field theory Wilson coefficients $ C_{VL}^{(6)} $ and $ C_{VR}^{(6)} $ from current experimental limits.
2026, 50(3): 035101. doi: 10.1088/1674-1137/ae210d
Abstract:
In this study, we investigate Lyapunov exponents of chaos for both massless and charged particles around a non-linear electrodynamics black hole and explore their relationships with a phase transition and chaos bound of this black hole. Our results indicate that these exponents can effectively reveal the phase transition. Specifically, during the phase transition, violation of the chaos bound occurs solely within a stable branch of a small black hole. Moreover, the violations are observed regardless of whether the phase transition takes place.
In this study, we investigate Lyapunov exponents of chaos for both massless and charged particles around a non-linear electrodynamics black hole and explore their relationships with a phase transition and chaos bound of this black hole. Our results indicate that these exponents can effectively reveal the phase transition. Specifically, during the phase transition, violation of the chaos bound occurs solely within a stable branch of a small black hole. Moreover, the violations are observed regardless of whether the phase transition takes place.
2026, 50(3): 035102. doi: 10.1088/1674-1137/ae1aff
Abstract:
We investigate the shadow image of rotating black holes in Kalb-Ramond gravity using backward ray-tracing techniques. We consider two primary emission models: a spherical source and a optically and geometrically thin accretion disk. The results show that enhanced black hole rotation parameter a amplifies the shadow's departure from circular symmetry, whereas spontaneous Lorentz symmetry-breaking parameters ${\cal{G}}$ and λ suppress the shadow radius. For accretion disk models, observer inclination angle $\theta_o$ predominantly governs the inner shadow morphology and photon ring brightness asymmetry, while a, ${\cal{G}}$, and λ primarily modulate the inner shadow scale. An increase in $\theta_o$ induces a morphological transition of the inner shadow from a circular to a D-shaped geometry, accompanied by enhanced brightness in a crescent-shaped region on the left side. Meanwhile, increasing the values of a, ${\cal{G}}$, or λ decrease the dimensions of the shadow. Furthermore, higher inclination angles $\theta_o$ further enhance spectral differentiation, that is, low inclination angles exhibit exclusively redshifted emission. Additionally, those at high inclination angles produce blueshifted components in both direct and lensed images. These characteristic signatures provide observational discriminators between rotating Kalb-Ramond black holes and alternative spacetime.
We investigate the shadow image of rotating black holes in Kalb-Ramond gravity using backward ray-tracing techniques. We consider two primary emission models: a spherical source and a optically and geometrically thin accretion disk. The results show that enhanced black hole rotation parameter a amplifies the shadow's departure from circular symmetry, whereas spontaneous Lorentz symmetry-breaking parameters ${\cal{G}}$ and λ suppress the shadow radius. For accretion disk models, observer inclination angle $\theta_o$ predominantly governs the inner shadow morphology and photon ring brightness asymmetry, while a, ${\cal{G}}$, and λ primarily modulate the inner shadow scale. An increase in $\theta_o$ induces a morphological transition of the inner shadow from a circular to a D-shaped geometry, accompanied by enhanced brightness in a crescent-shaped region on the left side. Meanwhile, increasing the values of a, ${\cal{G}}$, or λ decrease the dimensions of the shadow. Furthermore, higher inclination angles $\theta_o$ further enhance spectral differentiation, that is, low inclination angles exhibit exclusively redshifted emission. Additionally, those at high inclination angles produce blueshifted components in both direct and lensed images. These characteristic signatures provide observational discriminators between rotating Kalb-Ramond black holes and alternative spacetime.
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