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2027 No.1
2027, 51(1): 015107.
doi:10.1088/1674-1137/aeaa13
Abstract:
We investigate the instability of spinning test particles and the associated classical chaos bound in a spherically symmetric black hole spacetime with two photon spheres. The radial effective potential admits two branches of unstable circular orbits in the near-horizon and far-horizon regions. Although both branches are locally unstable, their Lyapunov exponents have different relationships with the black hole surface gravity. The near-horizon branch satisfies the bound, whereas the far-horizon branch can violate it. We further examine the effects of particle spin, total angular momentum, and black hole parameters. Spin-curvature coupling shifts the unstable orbits and modifies their instability, whereas the total angular momentum and background parameters generally have larger effects. Our results show that the validity of the classical orbital chaos bound is branch dependent.
We investigate the instability of spinning test particles and the associated classical chaos bound in a spherically symmetric black hole spacetime with two photon spheres. The radial effective potential admits two branches of unstable circular orbits in the near-horizon and far-horizon regions. Although both branches are locally unstable, their Lyapunov exponents have different relationships with the black hole surface gravity. The near-horizon branch satisfies the bound, whereas the far-horizon branch can violate it. We further examine the effects of particle spin, total angular momentum, and black hole parameters. Spin-curvature coupling shifts the unstable orbits and modifies their instability, whereas the total angular momentum and background parameters generally have larger effects. Our results show that the validity of the classical orbital chaos bound is branch dependent.
2027, 51(1): 015105.
doi:10.1088/1674-1137/aea1f0
Abstract:
Extreme mass-ratio inspirals (EMRIs), with their long-lived and highly relativistic orbital evolution, can probe strong-field spacetime geometry and provide an important means of testing general relativity. In this work, we investigate EMRI waveforms in a Schwarzschild-like black hole spacetime arising in bumblebee gravity, where Lorentz symmetry breaking (LSB) is characterized by the dimensionless parameterℓ. We construct EMRI waveforms within the Augmented Analytic Kludge (AAK) framework using the modified orbital frequencies and fluxes. We find thatℓsignificantly affects orbital evolution and thereby modifies the waveform. These modifications grow with increasingℓand are further enhanced for more eccentric orbits. Furthermore, using Bayesian analysis, we obtain the posterior distributions of the EMRI parameters withℓincluded. Our results show that all injected source parameters are recovered within their $ 1\,\sigma $ credible intervals. We find that the bumblebee parameterℓcan be constrained with an uncertainty of order $ {\cal{O}}(10^{-4}) $ by LISA.
Extreme mass-ratio inspirals (EMRIs), with their long-lived and highly relativistic orbital evolution, can probe strong-field spacetime geometry and provide an important means of testing general relativity. In this work, we investigate EMRI waveforms in a Schwarzschild-like black hole spacetime arising in bumblebee gravity, where Lorentz symmetry breaking (LSB) is characterized by the dimensionless parameterℓ. We construct EMRI waveforms within the Augmented Analytic Kludge (AAK) framework using the modified orbital frequencies and fluxes. We find thatℓsignificantly affects orbital evolution and thereby modifies the waveform. These modifications grow with increasingℓand are further enhanced for more eccentric orbits. Furthermore, using Bayesian analysis, we obtain the posterior distributions of the EMRI parameters withℓincluded. Our results show that all injected source parameters are recovered within their $ 1\,\sigma $ credible intervals. We find that the bumblebee parameterℓcan be constrained with an uncertainty of order $ {\cal{O}}(10^{-4}) $ by LISA.
2027, 51(1): 015104.
doi:10.1088/1674-1137/ae9c1c
Abstract:
The interaction between spin and gravitational waves causes spinning bodies to deviate from geodesic motion. In this work, we obtain an analytic solution to the Mathisson–Papapetrou–Dixon equations at linear order in spin for plane gravitational-wave spacetimes. Our approach combines a parallel-transported tetrad with the translational Killing symmetries of plane-wave spacetimes, yielding six conserved quantities that fully determine the momentum, spin evolution, and worldline. The resulting transverse and longitudinal motions are expressed in closed form as single integrals over the retarded time, providing a unified, model-independent framework for computing spin–curvature-induced deviations. This analytic solution provides a versatile tool for studying spin-dependent effects in gravitational memory, Penrose-limit geometries, and high-energy scattering regimes.
The interaction between spin and gravitational waves causes spinning bodies to deviate from geodesic motion. In this work, we obtain an analytic solution to the Mathisson–Papapetrou–Dixon equations at linear order in spin for plane gravitational-wave spacetimes. Our approach combines a parallel-transported tetrad with the translational Killing symmetries of plane-wave spacetimes, yielding six conserved quantities that fully determine the momentum, spin evolution, and worldline. The resulting transverse and longitudinal motions are expressed in closed form as single integrals over the retarded time, providing a unified, model-independent framework for computing spin–curvature-induced deviations. This analytic solution provides a versatile tool for studying spin-dependent effects in gravitational memory, Penrose-limit geometries, and high-energy scattering regimes.
2027, 51(1): 015103.
doi:10.1088/1674-1137/aea1ee
Abstract:
We study axial gravitational perturbations of a hairy black hole constructed within the framework of gravitational decoupling and investigate the geometric origin of echo-like late-time signals in this spacetime. We derive the odd-parity master equation and the corresponding effective potential, and compute the quasinormal mode spectrum using frequency-domain and time-domain methods. We show that the axial potential develops a double-peak structure that supports a trapping cavity and gives rise to echo-like waveforms. The representative double-peak configurations also exhibit an unstable--stable--unstable light-ring structure, which provides the null-geodesic counterpart of the trapping cavity in the eikonal limit. Therefore, the echoes are not produced by an artificially imposed near-horizon condition, but instead emerge dynamically from the geometric structure of the effective potential. Our results provide a useful framework for probing black hole hair through gravitational-wave ringdown and for exploring possible observational departures from the standard no-hair paradigm.
We study axial gravitational perturbations of a hairy black hole constructed within the framework of gravitational decoupling and investigate the geometric origin of echo-like late-time signals in this spacetime. We derive the odd-parity master equation and the corresponding effective potential, and compute the quasinormal mode spectrum using frequency-domain and time-domain methods. We show that the axial potential develops a double-peak structure that supports a trapping cavity and gives rise to echo-like waveforms. The representative double-peak configurations also exhibit an unstable--stable--unstable light-ring structure, which provides the null-geodesic counterpart of the trapping cavity in the eikonal limit. Therefore, the echoes are not produced by an artificially imposed near-horizon condition, but instead emerge dynamically from the geometric structure of the effective potential. Our results provide a useful framework for probing black hole hair through gravitational-wave ringdown and for exploring possible observational departures from the standard no-hair paradigm.
2027, 51(1): 015102.
doi:10.1088/1674-1137/ae9b9c
Abstract:
The Lyth bound states that the field excursion of the inflaton must be sub-Planckian, thereby imposing an upper bound on the amplitude of the tensor power spectrum in inflationary scenarios. This bound is conventionally derived under the assumption of a scale-invariant curvature power spectrum,i.e., $ n_s = 1 $. However, astrophysical observations confirm a red-tilted spectrum with $ n_s \lt 1 $. In light of recent results from the Atacama Cosmology Telescope (ACT) DR6, we revisit these constraints using the newly inferred scalar spectral index, $ n_s \simeq 0.9743 $. Incorporating the ACT data yields a different upper bound on the tensor-to-scalar ratiorand clarifies whether non-canonical inflationary scenarios can remain compatible with both CMB observations and a sub-Planckian field excursion. Our result highlights the importance of combining theoretical considerations of the Lyth bound with up-to-date astrophysical data.
The Lyth bound states that the field excursion of the inflaton must be sub-Planckian, thereby imposing an upper bound on the amplitude of the tensor power spectrum in inflationary scenarios. This bound is conventionally derived under the assumption of a scale-invariant curvature power spectrum,i.e., $ n_s = 1 $. However, astrophysical observations confirm a red-tilted spectrum with $ n_s \lt 1 $. In light of recent results from the Atacama Cosmology Telescope (ACT) DR6, we revisit these constraints using the newly inferred scalar spectral index, $ n_s \simeq 0.9743 $. Incorporating the ACT data yields a different upper bound on the tensor-to-scalar ratiorand clarifies whether non-canonical inflationary scenarios can remain compatible with both CMB observations and a sub-Planckian field excursion. Our result highlights the importance of combining theoretical considerations of the Lyth bound with up-to-date astrophysical data.
2027, 51(1): 015101.
doi:10.1088/1674-1137/ae9923
Abstract:
We aim to evaluate the complexity of self-gravitating matter distributions with anisotropic pressure and an electric field. The modified field equations associated with $f(R, G)$ gravity, including the effects of electric charge, and the expressions for the mass function are derived, whereRis the Ricci scalar andGdenotes the Gauss--Bonnet invariant. The concept of complexity, suggested by Herrera and collaborators in 2018, is further elaborated in the context of a charged cylindrically symmetric system by considering the framework of $f(R, G)$ theory and carrying out a comprehensive evaluation of the orthogonal splitting of the Riemann curvature tensor. Among the derived scalars, $Y_{TF}$ is referred to as the complexity factor; it includes the impacts of specific intrinsic features of the fluid, such as variations in energy density, anisotropic pressure, and electric charge. Furthermore, the results obtained in the presence of additional curvature terms corresponding to $f(R, G)$ gravity are studied by establishing a relationship between the Tolman mass, the Weyl scalar, and the complexity factor. This analysis is relevant from an astrophysical perspective, since compact stellar interiors are expected to involve dense matter, pressure anisotropy, electromagnetic effects, and strong-field relativistic corrections. In this context, the complexity factor $Y_{TF}$ provides a geometric diagnostic for measuring how density inhomogeneity, local anisotropy, charge distribution, and modified Gauss--Bonnet corrections influence the internal organization and stability of neutron-star-like compact configurations. The consideration of a polytropic equation of state further connects the proposed scenario with the effective modeling of dense compact-star matter.
We aim to evaluate the complexity of self-gravitating matter distributions with anisotropic pressure and an electric field. The modified field equations associated with $f(R, G)$ gravity, including the effects of electric charge, and the expressions for the mass function are derived, whereRis the Ricci scalar andGdenotes the Gauss--Bonnet invariant. The concept of complexity, suggested by Herrera and collaborators in 2018, is further elaborated in the context of a charged cylindrically symmetric system by considering the framework of $f(R, G)$ theory and carrying out a comprehensive evaluation of the orthogonal splitting of the Riemann curvature tensor. Among the derived scalars, $Y_{TF}$ is referred to as the complexity factor; it includes the impacts of specific intrinsic features of the fluid, such as variations in energy density, anisotropic pressure, and electric charge. Furthermore, the results obtained in the presence of additional curvature terms corresponding to $f(R, G)$ gravity are studied by establishing a relationship between the Tolman mass, the Weyl scalar, and the complexity factor. This analysis is relevant from an astrophysical perspective, since compact stellar interiors are expected to involve dense matter, pressure anisotropy, electromagnetic effects, and strong-field relativistic corrections. In this context, the complexity factor $Y_{TF}$ provides a geometric diagnostic for measuring how density inhomogeneity, local anisotropy, charge distribution, and modified Gauss--Bonnet corrections influence the internal organization and stability of neutron-star-like compact configurations. The consideration of a polytropic equation of state further connects the proposed scenario with the effective modeling of dense compact-star matter.
2027, 51(1): 013001.
doi:10.1088/1674-1137/aea82c
Abstract:
The distribution of heat-producing elements (U, Th, K) within the Moon is critical for understanding its thermal evolution and formation history. Based on a refined lunar interior model, we calculate the lunar antineutrino fluxes from radioactive decays of these elements at two representative detector locations that bracket the expected signal intensity. The maximum flux is found to be slightly lower than the geoneutrino flux for the KamLAND site on Earth, while the minimum flux is approximately a factor of 9 lower than this maximum value. We also compute the expected event rates for lunar antineutrinos using three detection channels.
The distribution of heat-producing elements (U, Th, K) within the Moon is critical for understanding its thermal evolution and formation history. Based on a refined lunar interior model, we calculate the lunar antineutrino fluxes from radioactive decays of these elements at two representative detector locations that bracket the expected signal intensity. The maximum flux is found to be slightly lower than the geoneutrino flux for the KamLAND site on Earth, while the minimum flux is approximately a factor of 9 lower than this maximum value. We also compute the expected event rates for lunar antineutrinos using three detection channels.
2027, 51(1): 015106.
doi:10.1088/1674-1137/aeaa11
Abstract:
We study Hawking emission from the regular magnetic black hole in non-minimal Einstein–Yang–Mills theory. The geometry is supported by a Wu–Yang charge, whose Yang–Mills field couples directly to curvature through the non-minimal susceptibility tensor. This coupling removes the central singularity. In the quasi-stationary approximation, in which the temperature is fixed during the emission of individual quanta, we compute greybody factors for a real massless scalar, an electromagnetic field, and a neutral massless Dirac test field by direct integration of the corresponding one-dimensional scattering equations. We compare these results with those obtained using the higher-order WKB approach and integrate the resulting Hawking spectra. For a representative fixed charge, increasing the non-minimal coupling changes the greybody thresholds only moderately, whereas the Hawking temperature and particle luminosity are strongly suppressed near extremality. A direct separation of temperature and greybody-factor effects shows that cooling accounts for most of the orders-of-magnitude suppression, although modified low-frequency transmission provides an additional reduction near the endpoint. The photon-plus-light-fermion luminosity decreases by many orders of magnitude near the endpoint, and the residual massless flux becomes increasingly fermion dominated.
We study Hawking emission from the regular magnetic black hole in non-minimal Einstein–Yang–Mills theory. The geometry is supported by a Wu–Yang charge, whose Yang–Mills field couples directly to curvature through the non-minimal susceptibility tensor. This coupling removes the central singularity. In the quasi-stationary approximation, in which the temperature is fixed during the emission of individual quanta, we compute greybody factors for a real massless scalar, an electromagnetic field, and a neutral massless Dirac test field by direct integration of the corresponding one-dimensional scattering equations. We compare these results with those obtained using the higher-order WKB approach and integrate the resulting Hawking spectra. For a representative fixed charge, increasing the non-minimal coupling changes the greybody thresholds only moderately, whereas the Hawking temperature and particle luminosity are strongly suppressed near extremality. A direct separation of temperature and greybody-factor effects shows that cooling accounts for most of the orders-of-magnitude suppression, although modified low-frequency transmission provides an additional reduction near the endpoint. The photon-plus-light-fermion luminosity decreases by many orders of magnitude near the endpoint, and the residual massless flux becomes increasingly fermion dominated.
2027, 51(1): 013107.
doi:10.1088/1674-1137/ae9e9c
Abstract:
We investigate the quasinormal modes (QNMs) and greybody factors of dilaton–Euler–Heisenberg (dEH) de Sitter (dS) black holes in string-inspired Euler–Heisenberg gravity. Since the axial gravitational and electromagnetic perturbations decouple, we analyze them independently. By applying the asymptotic iteration method (AIM) together with a sixth-order WKB approximation, we compute the quasinormal frequencies and find excellent agreement between the two methods. We also find that the QNM spectra depend sensitively on the magnetic charge $Q_{\text{m}}$, cosmological constant Λ, and nonlinear coupling $\epsilon$, with a notable topological anomaly appearing in the electromagnetic frequency trajectories. Additionally, larger values of $Q_{\text{m}}$ or the multipole numberlgenerally suppress wave transmission, while the electromagnetic sector with $\epsilon=1$ exhibits an anomalous response.
We investigate the quasinormal modes (QNMs) and greybody factors of dilaton–Euler–Heisenberg (dEH) de Sitter (dS) black holes in string-inspired Euler–Heisenberg gravity. Since the axial gravitational and electromagnetic perturbations decouple, we analyze them independently. By applying the asymptotic iteration method (AIM) together with a sixth-order WKB approximation, we compute the quasinormal frequencies and find excellent agreement between the two methods. We also find that the QNM spectra depend sensitively on the magnetic charge $Q_{\text{m}}$, cosmological constant Λ, and nonlinear coupling $\epsilon$, with a notable topological anomaly appearing in the electromagnetic frequency trajectories. Additionally, larger values of $Q_{\text{m}}$ or the multipole numberlgenerally suppress wave transmission, while the electromagnetic sector with $\epsilon=1$ exhibits an anomalous response.
2027, 51(1): 014103.
doi:10.1088/1674-1137/aeaad4
Abstract:
This work investigates machine-learning approaches for predicting capture cross sections in heavy-ion capture reactions. Three models are implemented: Tabular Prior-data Fitted Network (TabPFN), Gaussian Process Regression (GPR), and Backpropagation Neural Network (BP). All models are trained and tested on capture-cross-section data comprising 566 projectile–target combinations and 14 465 experimental data points. Two data-splitting strategies are adopted: a point-wise random split (subscript P, for interpolation on known systems) and a system-wise split (subscript S, for system-level test-set prediction), both with an 8:2 training-to-test ratio. Under point-wise-split interpolation, $ \mathrm{TabPFN_P} $ achieves the lowest test-set MAE of 0.0720, outperforming $ \mathrm{GPR_P} $ and $ \mathrm{BP_P} $. Under the more challenging system-wise-split protocol, $ \mathrm{TabPFN_S} $ still yields the lowest test-set MAE of 0.1981, whereas $ \mathrm{GPR_S} $ exhibits substantial performance degradation. We further perform leave-one-system-out cross-validation (LOSO-CV) for $ \mathrm{TabPFN_S} $, including ablation experiments that compare the 5-feature baseline with the full 13-feature model to examine the utility of additional entrance-channel-related physical features. The statistics show that 96.1% of unseen projectile–target pairs satisfy $ \overline{\mathrm{MAE}} \le 0.5 $. Binned-residual statistics are also computed to analyze residual distributions across different relative-energy bins. For three fully external local in-distribution test cases involving unseen projectile–target pairs, $ \mathrm{TabPFN_S} $ provides reasonable mean-point predictions together with physically plausible 95% prediction bands. These results indicate that $ \mathrm{TabPFN_S} $ is a promising computational tool for predicting unseen reaction pairs within the parameter domain covered by the training data, especially for systems that are experimentally inaccessible or difficult to measure.
This work investigates machine-learning approaches for predicting capture cross sections in heavy-ion capture reactions. Three models are implemented: Tabular Prior-data Fitted Network (TabPFN), Gaussian Process Regression (GPR), and Backpropagation Neural Network (BP). All models are trained and tested on capture-cross-section data comprising 566 projectile–target combinations and 14 465 experimental data points. Two data-splitting strategies are adopted: a point-wise random split (subscript P, for interpolation on known systems) and a system-wise split (subscript S, for system-level test-set prediction), both with an 8:2 training-to-test ratio. Under point-wise-split interpolation, $ \mathrm{TabPFN_P} $ achieves the lowest test-set MAE of 0.0720, outperforming $ \mathrm{GPR_P} $ and $ \mathrm{BP_P} $. Under the more challenging system-wise-split protocol, $ \mathrm{TabPFN_S} $ still yields the lowest test-set MAE of 0.1981, whereas $ \mathrm{GPR_S} $ exhibits substantial performance degradation. We further perform leave-one-system-out cross-validation (LOSO-CV) for $ \mathrm{TabPFN_S} $, including ablation experiments that compare the 5-feature baseline with the full 13-feature model to examine the utility of additional entrance-channel-related physical features. The statistics show that 96.1% of unseen projectile–target pairs satisfy $ \overline{\mathrm{MAE}} \le 0.5 $. Binned-residual statistics are also computed to analyze residual distributions across different relative-energy bins. For three fully external local in-distribution test cases involving unseen projectile–target pairs, $ \mathrm{TabPFN_S} $ provides reasonable mean-point predictions together with physically plausible 95% prediction bands. These results indicate that $ \mathrm{TabPFN_S} $ is a promising computational tool for predicting unseen reaction pairs within the parameter domain covered by the training data, especially for systems that are experimentally inaccessible or difficult to measure.
2027, 51(1): 014102.
doi:10.1088/1674-1137/aea548
Abstract:
We employ a full Bayesian analysis with adaptive Metropolis-Hastings Markov chain Monte Carlo (BA-MCMC) sampling to systematically investigate the posterior probability distributions of the strengths of energy terms in optimized nuclear mass models based on Bethe-Weizsäcker variants. Strong correlations among certain energy terms in some mass models are revealed through parameter-degeneracy diagnostics. We analyze selected refined models to identify parameter degeneracies while proposing a new macroscopic-microscopic mass model, BWL, that incorporates quadrupole and high-multipole deformation and shell corrections. All mass models in this work are analyzed and optimized using the BA-MCMC method. Compared with 2242 precise experimental binding energies from AME2020, BWL yields a root-mean-square deviation of 759 keV, with particular improvement in the description of masses in the light-nuclei and actinide regions. BA-MCMC provides robust inference on parameter degeneracy while also serving as an optimization method for future nuclear mass models.
We employ a full Bayesian analysis with adaptive Metropolis-Hastings Markov chain Monte Carlo (BA-MCMC) sampling to systematically investigate the posterior probability distributions of the strengths of energy terms in optimized nuclear mass models based on Bethe-Weizsäcker variants. Strong correlations among certain energy terms in some mass models are revealed through parameter-degeneracy diagnostics. We analyze selected refined models to identify parameter degeneracies while proposing a new macroscopic-microscopic mass model, BWL, that incorporates quadrupole and high-multipole deformation and shell corrections. All mass models in this work are analyzed and optimized using the BA-MCMC method. Compared with 2242 precise experimental binding energies from AME2020, BWL yields a root-mean-square deviation of 759 keV, with particular improvement in the description of masses in the light-nuclei and actinide regions. BA-MCMC provides robust inference on parameter degeneracy while also serving as an optimization method for future nuclear mass models.
2027, 51(1): 014101.
doi:10.1088/1674-1137/aea3e3
Abstract:
The study of dilepton emission from hot hadronic matter provides a unique probe of the properties of the strongly interacting medium created in heavy-ion collisions. In non-central collisions, the presence of magnetic fields can induce anisotropic features in the emission spectrum. While the impact of a magnetic field on the dilepton emission rate has been extensively studied, the detailed higher-order azimuthal anisotropies of the emission rate—characterized by flow coefficients beyond elliptic flow—remain an open question, particularly in the low invariant-mass region, where magnetic-field-induced medium effects are expected to be most pronounced. Here, we investigate the higher-order azimuthal anisotropies of source-level thermal dilepton emission from a magnetized hot hadronic medium. Our results reveal a continuous dilepton spectrum with strong Landau-cut contributions at low invariant masses due to the background magnetic field. The emission rate exhibits significant azimuthal-angle dependence in this region, characterized by the source-level flow coefficients $v_{2,4,6}$. The odd-order coefficients vanish because of symmetry. The elliptic flow coefficient ($v_2$) is positive and exhibits an oscillatory structure at low invariant masses—driven by Landau-level quantization of pions—but is negligible at higher masses. Similar behavior is observed for the higher-order coefficients $v_4$ and $v_6$, with notable structures at low masses and negligible values at higher masses. These results highlight dileptons as sensitive probes of magnetic-field effects in heavy-ion collisions, offering new avenues to constrain the strength of magnetic fields and to unravel the properties and dynamics of hot hadronic matter.
The study of dilepton emission from hot hadronic matter provides a unique probe of the properties of the strongly interacting medium created in heavy-ion collisions. In non-central collisions, the presence of magnetic fields can induce anisotropic features in the emission spectrum. While the impact of a magnetic field on the dilepton emission rate has been extensively studied, the detailed higher-order azimuthal anisotropies of the emission rate—characterized by flow coefficients beyond elliptic flow—remain an open question, particularly in the low invariant-mass region, where magnetic-field-induced medium effects are expected to be most pronounced. Here, we investigate the higher-order azimuthal anisotropies of source-level thermal dilepton emission from a magnetized hot hadronic medium. Our results reveal a continuous dilepton spectrum with strong Landau-cut contributions at low invariant masses due to the background magnetic field. The emission rate exhibits significant azimuthal-angle dependence in this region, characterized by the source-level flow coefficients $v_{2,4,6}$. The odd-order coefficients vanish because of symmetry. The elliptic flow coefficient ($v_2$) is positive and exhibits an oscillatory structure at low invariant masses—driven by Landau-level quantization of pions—but is negligible at higher masses. Similar behavior is observed for the higher-order coefficients $v_4$ and $v_6$, with notable structures at low masses and negligible values at higher masses. These results highlight dileptons as sensitive probes of magnetic-field effects in heavy-ion collisions, offering new avenues to constrain the strength of magnetic fields and to unravel the properties and dynamics of hot hadronic matter.
2027, 51(1): 014002.
doi:10.1088/1674-1137/aea549
Abstract:
The237Np+48Ca reaction was studied using the gas-filled separator DGFRS-2 of the SHE Factory at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research. We observed threeα-decay chains of282Nh and its descendant nuclei278Rg,274Mt, and270Bh terminated by the spontaneous fission of266Db. The half-lifeTαof the isotopes282Nh,278Rg, and270Bh correspond to the values expected from the experimental systematics for the odd-Znuclei; however,Tαfor274Mt exceeds this value by two orders of magnitude. These results are in agreement with those previously measured by Oganessianet al. [Phys. Rev. C76, 011601(R) (2007); Phys. Rev. C106, 064306 (2022)]. Such a significant difference in the measuredTαfor274Mt is observed for the first time for the heaviest nuclei withZ≥ 107. The decay properties of a few heavy odd-Znuclei are compared with the predictions of a cluster model based on a dinuclear system approach, and their corresponding decay schemes are proposed. The reaction cross section is measured to be $0.43^{+0.46}_{-0.25} $ pb, which is consistent with the expectation for the excitation functions of the 3nchannel in48Ca-induced reactions. The upper cross-section limit of the 4nreaction channel is 0.28 pb.
The237Np+48Ca reaction was studied using the gas-filled separator DGFRS-2 of the SHE Factory at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research. We observed threeα-decay chains of282Nh and its descendant nuclei278Rg,274Mt, and270Bh terminated by the spontaneous fission of266Db. The half-lifeTαof the isotopes282Nh,278Rg, and270Bh correspond to the values expected from the experimental systematics for the odd-Znuclei; however,Tαfor274Mt exceeds this value by two orders of magnitude. These results are in agreement with those previously measured by Oganessianet al. [Phys. Rev. C76, 011601(R) (2007); Phys. Rev. C106, 064306 (2022)]. Such a significant difference in the measuredTαfor274Mt is observed for the first time for the heaviest nuclei withZ≥ 107. The decay properties of a few heavy odd-Znuclei are compared with the predictions of a cluster model based on a dinuclear system approach, and their corresponding decay schemes are proposed. The reaction cross section is measured to be $0.43^{+0.46}_{-0.25} $ pb, which is consistent with the expectation for the excitation functions of the 3nchannel in48Ca-induced reactions. The upper cross-section limit of the 4nreaction channel is 0.28 pb.
2027, 51(1): 014001.
doi:10.1088/1674-1137/ae9ea9
Abstract:
High-spin states in95Tc were investigated via the87Rb(12C, $ 4n $)95Tc reaction at a beam energy of 62 MeV using standard in-beamγ-ray spectroscopic techniques. The previously established level scheme was revised and extended through the identification of 42 new transitions. The experimental results are interpreted using large-scale shell-model calculations. Valence-nucleon excitations outside the88Sr core dominate the excited states up to $ J = 33/2 $, corresponding to the maximum angular momentum possible within this restricted space. Of particular interest are the systematics of $ \nu d_{5/2} \rightarrow \nu g_{7/2} $ excitations across the $ N = 56 $ subshell. These systematics show that proton excitations across the $ Z=38 $ subshell, coupled with neutrons in the $ d_{5/2} $ and $ g_{7/2} $ orbitals, are necessary for higher-spin states.
High-spin states in95Tc were investigated via the87Rb(12C, $ 4n $)95Tc reaction at a beam energy of 62 MeV using standard in-beamγ-ray spectroscopic techniques. The previously established level scheme was revised and extended through the identification of 42 new transitions. The experimental results are interpreted using large-scale shell-model calculations. Valence-nucleon excitations outside the88Sr core dominate the excited states up to $ J = 33/2 $, corresponding to the maximum angular momentum possible within this restricted space. Of particular interest are the systematics of $ \nu d_{5/2} \rightarrow \nu g_{7/2} $ excitations across the $ N = 56 $ subshell. These systematics show that proton excitations across the $ Z=38 $ subshell, coupled with neutrons in the $ d_{5/2} $ and $ g_{7/2} $ orbitals, are necessary for higher-spin states.
2027, 51(1): 014003.
doi:10.1088/1674-1137/aea831
Abstract:
We present a systematic study of the reconstructability and directed flow of short-lived hadronic resonances in Au+Au collisions at $\sqrt{s_{NN}}=19.6$ and $200$ GeV using the UrQMD transport model. The reconstructable fractions of $\rho^0$, $K^{*0}$, and $\Lambda(1520)$ are examined as functions of charged-particle multiplicity and resonance lifetime. The results show a clear lifetime-dependent ordering, with shorter-lived resonances exhibiting stronger suppression of reconstructability. The directed-flow analysis reveals clear differences between resonances and their corresponding stable hadrons in mid-central collisions; however, these differences are substantially reduced in peripheral collisions. These results demonstrate that hadronic evolution significantly affects both resonance reconstructability and final-state directed flow, thereby providing complementary probes of the hadronic stage in relativistic heavy-ion collisions.
We present a systematic study of the reconstructability and directed flow of short-lived hadronic resonances in Au+Au collisions at $\sqrt{s_{NN}}=19.6$ and $200$ GeV using the UrQMD transport model. The reconstructable fractions of $\rho^0$, $K^{*0}$, and $\Lambda(1520)$ are examined as functions of charged-particle multiplicity and resonance lifetime. The results show a clear lifetime-dependent ordering, with shorter-lived resonances exhibiting stronger suppression of reconstructability. The directed-flow analysis reveals clear differences between resonances and their corresponding stable hadrons in mid-central collisions; however, these differences are substantially reduced in peripheral collisions. These results demonstrate that hadronic evolution significantly affects both resonance reconstructability and final-state directed flow, thereby providing complementary probes of the hadronic stage in relativistic heavy-ion collisions.
2027, 51(1): 013104.
doi:10.1088/1674-1137/aea284
Abstract:
Describing the proton structure function $ F_2(x,Q^2) $ across the nonperturbative and transition regimes of quantum chromodynamics remains a significant theoretical challenge. We construct a physics-guided phenomenological representation that combines fermion-resonance and Pomeron-like AdS/QCD basis functions with a neural parametrization. The fermion-resonance sector is constrained by the AdS eigenvalue problem and the physical proton mass, while the neural parametrization describes the effective kinematic mixing, the Pomeron normalization, and a regularized log-space correction. For 187 selected SLAC measurements, a fixed training–test partition containing 153 and 34 points, respectively, yields the point-normalized diagnostics $ \chi^2/N_{{\rm{train}}}=0.542 $, $ \chi^2/N_{{\rm{test}}}=1.990 $, and $ \chi^2/N_{{\rm{all}}}=0.805 $. Conditional on the chosen holographic basis, the fitted channel fractions show a continuous transition from Pomeron-like dominance at the lower end of the measuredxrange to fermion-resonance dominance at largerx. The midpoint of the mixing function occurs at $ x\simeq0.187 $, whereas equality of the final channel fractions occurs at $ x\simeq0.226 $. These two definitions identify a transition region of approximately $ x\simeq0.19 $–$ 0.23 $, rather than a unique physical boundary. Although $ \alpha_0\simeq1.08 $ is compatible with the data, fixed-$ \alpha_0 $ refits show that it is not separately identifiable from the flexible Pomeron normalization. Thex-dependent holographic coordinates and associated effective excited scales should therefore be interpreted as basis-dependent effective quantities rather than direct measurements of anx-dependent proton spectrum. A comparison with a data-only neural baseline does not establish a predictive advantage for the holographic basis on the present dataset. The resulting framework thus provides a basis-conditioned phenomenological decomposition of the data, rather than a model-independent extraction of the underlying proton dynamics.
Describing the proton structure function $ F_2(x,Q^2) $ across the nonperturbative and transition regimes of quantum chromodynamics remains a significant theoretical challenge. We construct a physics-guided phenomenological representation that combines fermion-resonance and Pomeron-like AdS/QCD basis functions with a neural parametrization. The fermion-resonance sector is constrained by the AdS eigenvalue problem and the physical proton mass, while the neural parametrization describes the effective kinematic mixing, the Pomeron normalization, and a regularized log-space correction. For 187 selected SLAC measurements, a fixed training–test partition containing 153 and 34 points, respectively, yields the point-normalized diagnostics $ \chi^2/N_{{\rm{train}}}=0.542 $, $ \chi^2/N_{{\rm{test}}}=1.990 $, and $ \chi^2/N_{{\rm{all}}}=0.805 $. Conditional on the chosen holographic basis, the fitted channel fractions show a continuous transition from Pomeron-like dominance at the lower end of the measuredxrange to fermion-resonance dominance at largerx. The midpoint of the mixing function occurs at $ x\simeq0.187 $, whereas equality of the final channel fractions occurs at $ x\simeq0.226 $. These two definitions identify a transition region of approximately $ x\simeq0.19 $–$ 0.23 $, rather than a unique physical boundary. Although $ \alpha_0\simeq1.08 $ is compatible with the data, fixed-$ \alpha_0 $ refits show that it is not separately identifiable from the flexible Pomeron normalization. Thex-dependent holographic coordinates and associated effective excited scales should therefore be interpreted as basis-dependent effective quantities rather than direct measurements of anx-dependent proton spectrum. A comparison with a data-only neural baseline does not establish a predictive advantage for the holographic basis on the present dataset. The resulting framework thus provides a basis-conditioned phenomenological decomposition of the data, rather than a model-independent extraction of the underlying proton dynamics.
2027, 51(1): 013103.
doi:10.1088/1674-1137/ae9f36
Abstract:
We revisit the 95 GeV $\gamma\gamma$ and $\tau\tau$ excesses in the Georgi–Machacek model using a combined fit to a single light $\rm CP$-even custodial singletH. By combining the one-loop renormalization group-improved effective potential and positive-definiteness conditions for vacuum stability with perturbative unitarity, electroweak precision tests,B-physics, and Higgs data, we identify a narrow but viable parameter region. In the allowed region, $\mu_{\gamma\gamma}$ approaches the experimental central value, whereas $\mu_{\tau\tau}$ reaches only $\sim0.5$ (about $1.4\sigma$ below the CMS central value) and remains within the $2\sigma$ interval—providing a good description of the di-photon excess but only a partial accommodation of the di-tau excess. The scenario predicts characteristic patterns in the singlet mixing and triplet vacuum expectation values and is highly testable at the HL-LHC and future lepton colliders through precision $\kappa_V$ measurements and direct exotic searches.
We revisit the 95 GeV $\gamma\gamma$ and $\tau\tau$ excesses in the Georgi–Machacek model using a combined fit to a single light $\rm CP$-even custodial singletH. By combining the one-loop renormalization group-improved effective potential and positive-definiteness conditions for vacuum stability with perturbative unitarity, electroweak precision tests,B-physics, and Higgs data, we identify a narrow but viable parameter region. In the allowed region, $\mu_{\gamma\gamma}$ approaches the experimental central value, whereas $\mu_{\tau\tau}$ reaches only $\sim0.5$ (about $1.4\sigma$ below the CMS central value) and remains within the $2\sigma$ interval—providing a good description of the di-photon excess but only a partial accommodation of the di-tau excess. The scenario predicts characteristic patterns in the singlet mixing and triplet vacuum expectation values and is highly testable at the HL-LHC and future lepton colliders through precision $\kappa_V$ measurements and direct exotic searches.
2027, 51(1): 013102.
doi:10.1088/1674-1137/ae9b9b
Abstract:
The $ \Omega^0_c $ baryon is unique among charmed sextet baryons because it decays through the weak interaction. In this work, we investigate the topological amplitudes of $ \Omega_c^0 $ decays in the $S U(3)_F$ limit. The complete set of tree- and penguin-induced diagrams contributing to $ \Omega_c^0 $ decays into decuplet and octet baryons is presented. The linear relations between the topological amplitudes and the $ S U(3) $ irreducible amplitudes are derived through tensor analysis. Several isospin relations are obtained, and additional relations are derived to test the Körner-Pati-Woo theorem.
The $ \Omega^0_c $ baryon is unique among charmed sextet baryons because it decays through the weak interaction. In this work, we investigate the topological amplitudes of $ \Omega_c^0 $ decays in the $S U(3)_F$ limit. The complete set of tree- and penguin-induced diagrams contributing to $ \Omega_c^0 $ decays into decuplet and octet baryons is presented. The linear relations between the topological amplitudes and the $ S U(3) $ irreducible amplitudes are derived through tensor analysis. Several isospin relations are obtained, and additional relations are derived to test the Körner-Pati-Woo theorem.
2027, 51(1): 013101.
doi:10.1088/1674-1137/ae973a
Abstract:
In this paper, chiral Lagrangians with a vector meson nonet are constructed across multiple representations, including those at the next-to-leading order in the vector-field representation, as well as at the next-to-next-to-leading order in the tensor-field and hidden local symmetry representations. For the next-to-leading order octet, redundant terms identified in other literature are also addressed in both the tensor-field and hidden local symmetry representations. Furthermore, the equivalence between the tensor-field and hidden local symmetry representations is examined.
In this paper, chiral Lagrangians with a vector meson nonet are constructed across multiple representations, including those at the next-to-leading order in the vector-field representation, as well as at the next-to-next-to-leading order in the tensor-field and hidden local symmetry representations. For the next-to-leading order octet, redundant terms identified in other literature are also addressed in both the tensor-field and hidden local symmetry representations. Furthermore, the equivalence between the tensor-field and hidden local symmetry representations is examined.
2027, 51(1): 011002.
doi:10.1088/1674-1137/aea53f
Abstract:
The neutrino mass ordering remains unresolved because long-baseline oscillation measurements are entangled with the unknown CP phase $ \delta_{\rm CP} $; a collider probe free from this degeneracy would provide a qualitatively distinct and complementary test. We show that, when the long-lived charged particle producing a displaced-lepton signal at the High-Luminosity LHC is also the mediator responsible for Majorana neutrino masses—theshared-coupling condition—the Casas–Ibarra parametrization determines the lepton flavor ratio $ N_e/N_\mu $ of time-delayed leptons solely in terms of Pontecorvo–Maki–Nakagawa–Sakata (PMNS) mixing parameters. Within the resultingshared-coupling classof models, the ratio is fixed by oscillation data and is independent of all beyond-Standard-Model mass and coupling parameters, up to calculable corrections bounded by charged-lepton-flavor-violation data, yielding $ N_e/N_\mu = 0.140 $ for the Normal and 2.11 for the Inverted Hierarchy—a separation of more than an order of magnitude between the two predictions. This prediction holds identically across the Scotogenic model, the Type-III seesaw, the inverse and linear seesaw, and lepton-portal dark matter, and it is stable against oscillation-parameter uncertainties and detector-efficiency variations, which cancel in the ratio. A single efficiency-corrected decision criterion identifies the hierarchy, and explicit signal-yield estimates combined with an exact Poisson test show that $ {\cal{O}}(25) $ displaced-lepton events suffice for a $ 3\sigma $ discrimination with the timing infrastructure already under construction at CMS and ATLAS—so that a positive long-lived-particle signal would simultaneously resolve the mass ordering, with no dependence on $ \delta_{\rm CP} $.
The neutrino mass ordering remains unresolved because long-baseline oscillation measurements are entangled with the unknown CP phase $ \delta_{\rm CP} $; a collider probe free from this degeneracy would provide a qualitatively distinct and complementary test. We show that, when the long-lived charged particle producing a displaced-lepton signal at the High-Luminosity LHC is also the mediator responsible for Majorana neutrino masses—theshared-coupling condition—the Casas–Ibarra parametrization determines the lepton flavor ratio $ N_e/N_\mu $ of time-delayed leptons solely in terms of Pontecorvo–Maki–Nakagawa–Sakata (PMNS) mixing parameters. Within the resultingshared-coupling classof models, the ratio is fixed by oscillation data and is independent of all beyond-Standard-Model mass and coupling parameters, up to calculable corrections bounded by charged-lepton-flavor-violation data, yielding $ N_e/N_\mu = 0.140 $ for the Normal and 2.11 for the Inverted Hierarchy—a separation of more than an order of magnitude between the two predictions. This prediction holds identically across the Scotogenic model, the Type-III seesaw, the inverse and linear seesaw, and lepton-portal dark matter, and it is stable against oscillation-parameter uncertainties and detector-efficiency variations, which cancel in the ratio. A single efficiency-corrected decision criterion identifies the hierarchy, and explicit signal-yield estimates combined with an exact Poisson test show that $ {\cal{O}}(25) $ displaced-lepton events suffice for a $ 3\sigma $ discrimination with the timing infrastructure already under construction at CMS and ATLAS—so that a positive long-lived-particle signal would simultaneously resolve the mass ordering, with no dependence on $ \delta_{\rm CP} $.
2027, 51(1): 013113.
doi:10.1088/1674-1137/aea106
Abstract:
The recent Belle II evidence for $ B^+ \to K^+ \nu \bar{\nu} $, combined with a suppressed branching fraction ratio $ R \equiv {\cal{B}}(B^0 \to K^{*0} \nu \bar{\nu}) / {\cal{B}}(B^+ \to K^+ \nu \bar{\nu}) $, requires new physics that contributes to both left- and right-handed vector operators. We perform a systematic topological classification of one-loop completions that radiatively generate both operators without tree-level mediation, and construct two minimal benchmark scenarios: a scalar-rich model and a fermion-rich model. Evaluating these frameworks under specific benchmark mass schemes and four distinct flavor structures, we find a generic anti-correlation, where enhancing one decay channel typically suppresses the other. A notable exception is a decoupled flavor configuration within the scalar-rich model, which yields simultaneous constructive interference, reducingRby 3.83% while satisfying all complementary flavor bounds. Under a universal coupling assumption, the scalar-rich model yields exact cancellation in the charged mode, highlighting the non-trivial interplay between flavor structure and loop-generated Wilson coefficients.
The recent Belle II evidence for $ B^+ \to K^+ \nu \bar{\nu} $, combined with a suppressed branching fraction ratio $ R \equiv {\cal{B}}(B^0 \to K^{*0} \nu \bar{\nu}) / {\cal{B}}(B^+ \to K^+ \nu \bar{\nu}) $, requires new physics that contributes to both left- and right-handed vector operators. We perform a systematic topological classification of one-loop completions that radiatively generate both operators without tree-level mediation, and construct two minimal benchmark scenarios: a scalar-rich model and a fermion-rich model. Evaluating these frameworks under specific benchmark mass schemes and four distinct flavor structures, we find a generic anti-correlation, where enhancing one decay channel typically suppresses the other. A notable exception is a decoupled flavor configuration within the scalar-rich model, which yields simultaneous constructive interference, reducingRby 3.83% while satisfying all complementary flavor bounds. Under a universal coupling assumption, the scalar-rich model yields exact cancellation in the charged mode, highlighting the non-trivial interplay between flavor structure and loop-generated Wilson coefficients.
2027, 51(1): 013112.
doi:10.1088/1674-1137/aea10c
Abstract:
We consider heavy neutral bosons in the 3-3-1 model with axionlike particles (331ALP), including the Higgs boson and the $ Z^\prime $ boson, which lie beyond the Standard Model (SM). Based on gluon-gluon fusion at the LHC, we investigate cross-section signals in the parameter-space region consistent with current experimental limits on lepton-flavor-violating decays, including processes involving charged leptons and the Higgs boson, and we provide predictions of $ m_{h_2}\geq 630 \; {\rm{GeV}} $. A new gauge boson, denoted by $ Z^{\prime} $, is constrained to have a mass above $ 5.1 \; {\rm{TeV}} $ by analyzing the cross sections of $ Z^{\prime} $-mediated processes in combination with experimental limits from searches for high-mass dilepton resonances at ATLAS and CMS. We also consider the stability of odd-$ Z_2 $ particles, with $ Z_2 $ assumed to be a residual symmetry after spontaneous symmetry-breaking stages, to identify dark matter candidates in the model. By investigating the dark matter relic density within experimentally allowed limits, we establish a relationship between the dark matter mass and the axion-breaking scale.
We consider heavy neutral bosons in the 3-3-1 model with axionlike particles (331ALP), including the Higgs boson and the $ Z^\prime $ boson, which lie beyond the Standard Model (SM). Based on gluon-gluon fusion at the LHC, we investigate cross-section signals in the parameter-space region consistent with current experimental limits on lepton-flavor-violating decays, including processes involving charged leptons and the Higgs boson, and we provide predictions of $ m_{h_2}\geq 630 \; {\rm{GeV}} $. A new gauge boson, denoted by $ Z^{\prime} $, is constrained to have a mass above $ 5.1 \; {\rm{TeV}} $ by analyzing the cross sections of $ Z^{\prime} $-mediated processes in combination with experimental limits from searches for high-mass dilepton resonances at ATLAS and CMS. We also consider the stability of odd-$ Z_2 $ particles, with $ Z_2 $ assumed to be a residual symmetry after spontaneous symmetry-breaking stages, to identify dark matter candidates in the model. By investigating the dark matter relic density within experimentally allowed limits, we establish a relationship between the dark matter mass and the axion-breaking scale.
2027, 51(1): 013111.
doi:10.1088/1674-1137/aea287
Abstract:
The equation of state of hot and dense, strongly interacting quark matter plays a fundamental role in many areas. However, owing to the nonperturbative nature of strong interactions, a reliable treatment remains under debate. We use a symmetry-preserving treatment of a vector $\otimes$ vector contact interaction to study related issues at nonzero temperature or quark chemical potential, and we carefully compare a three-momentum cutoff with a proper-time regularization scheme. The numerical results show that the character of the phase transition in the present model depends sensitively on the regularization scheme and parameter choices.
The equation of state of hot and dense, strongly interacting quark matter plays a fundamental role in many areas. However, owing to the nonperturbative nature of strong interactions, a reliable treatment remains under debate. We use a symmetry-preserving treatment of a vector $\otimes$ vector contact interaction to study related issues at nonzero temperature or quark chemical potential, and we carefully compare a three-momentum cutoff with a proper-time regularization scheme. The numerical results show that the character of the phase transition in the present model depends sensitively on the regularization scheme and parameter choices.
2027, 51(1): 013110.
doi:10.1088/1674-1137/ae97ec
Abstract:
The symmetry properties of the phase diagram of dense quark matter composed ofuanddquarks with three colors have been investigated within the framework of massless (3+1)-dimensional Nambu–Jona-Lasinio (NJL) and QCD models. It turns out that, in the presence of baryon $ \mu_B $, isospin $ \mu_I $, chiral $ \mu_5 $, and chiral isospin $ \mu_{I5} $ chemical potentials, the Lagrangians of these models are invariant under the so-called dual transformation $ {\cal{D}} $. In this paper, it has been shown that the path-integration measure of the corresponding partition functions is also invariant under $ {\cal{D}} $. Consequently, the thermodynamic potentials of the NJL model (or QCD) are dually symmetric. In particular, this means that in the full $ (\mu_B,\mu_I,\mu_5,\mu_{I5}) $ phase portraits of these models, the chiral symmetry breaking (CSB) and charged pion condensation (PC) phases are arranged dually conjugately (or symmetrically) with respect to each other. Dual symmetry between the CSB and charged PC phases of quark matter is a fundamental property of massless dense QCD; it should be observed within the framework of any approximation to the QCD phase diagram, and it has important implications for studies of the phase structure.
The symmetry properties of the phase diagram of dense quark matter composed ofuanddquarks with three colors have been investigated within the framework of massless (3+1)-dimensional Nambu–Jona-Lasinio (NJL) and QCD models. It turns out that, in the presence of baryon $ \mu_B $, isospin $ \mu_I $, chiral $ \mu_5 $, and chiral isospin $ \mu_{I5} $ chemical potentials, the Lagrangians of these models are invariant under the so-called dual transformation $ {\cal{D}} $. In this paper, it has been shown that the path-integration measure of the corresponding partition functions is also invariant under $ {\cal{D}} $. Consequently, the thermodynamic potentials of the NJL model (or QCD) are dually symmetric. In particular, this means that in the full $ (\mu_B,\mu_I,\mu_5,\mu_{I5}) $ phase portraits of these models, the chiral symmetry breaking (CSB) and charged pion condensation (PC) phases are arranged dually conjugately (or symmetrically) with respect to each other. Dual symmetry between the CSB and charged PC phases of quark matter is a fundamental property of massless dense QCD; it should be observed within the framework of any approximation to the QCD phase diagram, and it has important implications for studies of the phase structure.
2027, 51(1): 013105.
doi:10.1088/1674-1137/aea108
Abstract:
The nature of the recently observed $K(1690)$ state, reported by the COMPASS Collaboration as a candidate strange crypto-exotic meson with $J^P=0^-$, remains unclear. In this work, we investigate whether it can be described by local meson-meson currents within the framework of QCD sum rules. We construct a set of independent local color-singlet meson-meson interpolating currents with $J^P=0^-$ and analyze their QCD sum rules. For the currents that admit reliable Borel windows, the extracted effective mass scales are consistently in the range of $2.0-2.3\;\mathrm{GeV}$, significantly above the experimental mass of the $K(1690)$. Within the standard pole-plus-continuum framework, none of the selected local currents yields a separately resolved low-lying pole compatible with the COMPASS signal. These results indicate that the selected local color-singlet meson-meson currents do not isolate the $K(1690)$ signal within the present framework, while leaving open the possibility of more extended molecular dynamics and other configurations beyond the present analysis.
The nature of the recently observed $K(1690)$ state, reported by the COMPASS Collaboration as a candidate strange crypto-exotic meson with $J^P=0^-$, remains unclear. In this work, we investigate whether it can be described by local meson-meson currents within the framework of QCD sum rules. We construct a set of independent local color-singlet meson-meson interpolating currents with $J^P=0^-$ and analyze their QCD sum rules. For the currents that admit reliable Borel windows, the extracted effective mass scales are consistently in the range of $2.0-2.3\;\mathrm{GeV}$, significantly above the experimental mass of the $K(1690)$. Within the standard pole-plus-continuum framework, none of the selected local currents yields a separately resolved low-lying pole compatible with the COMPASS signal. These results indicate that the selected local color-singlet meson-meson currents do not isolate the $K(1690)$ signal within the present framework, while leaving open the possibility of more extended molecular dynamics and other configurations beyond the present analysis.
2027, 51(1): 013106.
doi:10.1088/1674-1137/ae9928
Abstract:
We present a lattice QCD spectroscopy study of the conjecturedH-dibaryon in five channels at nine temperatures ranging from $T/T_c =0.24$ to $T/T_c = 1.90$. The five channels are the flavor singlet, flavor 27-plet, $\Lambda \Lambda$, $N \Xi$, and $\Sigma \Sigma$. Five interpolating operators are employed, one for each channel. The simulations are performed on anisotropic lattices with $N_f=2+1$ flavors of clover fermions at a quark mass corresponding to $m_\pi=384(4)\, {\rm MeV} $. The thermal ensembles were provided by the FASTSUM collaboration and the zero-temperature ensembles by the Hadspec collaboration. The simulations show that theH-dibaryon mass in the 27-plet channel is the largest across the nine temperatures, whereas the mass in the $\Sigma \Sigma $ channel is the smallest. We also calculate the spectral density of theH-dibaryon correlation function for the five channels. The spectral density distributions of the five channels exhibit similar behavior. The mass differences $\Delta m = m_H - 2\,m_{\Lambda} $ between theH-dibaryon and a Λ pair at $T/T_c =0.24 $ for the five channels are also estimated. The results show that $\Delta m $ is positive for the 27-plet and $\Lambda \Lambda$ channels, whereas $\Delta m $ is negative for the singlet, $N \Xi$, and $\Sigma \Sigma$ channels. These findings are limited, however, by the use of a single spatial volume and a relatively large quark mass.
We present a lattice QCD spectroscopy study of the conjecturedH-dibaryon in five channels at nine temperatures ranging from $T/T_c =0.24$ to $T/T_c = 1.90$. The five channels are the flavor singlet, flavor 27-plet, $\Lambda \Lambda$, $N \Xi$, and $\Sigma \Sigma$. Five interpolating operators are employed, one for each channel. The simulations are performed on anisotropic lattices with $N_f=2+1$ flavors of clover fermions at a quark mass corresponding to $m_\pi=384(4)\, {\rm MeV} $. The thermal ensembles were provided by the FASTSUM collaboration and the zero-temperature ensembles by the Hadspec collaboration. The simulations show that theH-dibaryon mass in the 27-plet channel is the largest across the nine temperatures, whereas the mass in the $\Sigma \Sigma $ channel is the smallest. We also calculate the spectral density of theH-dibaryon correlation function for the five channels. The spectral density distributions of the five channels exhibit similar behavior. The mass differences $\Delta m = m_H - 2\,m_{\Lambda} $ between theH-dibaryon and a Λ pair at $T/T_c =0.24 $ for the five channels are also estimated. The results show that $\Delta m $ is positive for the 27-plet and $\Lambda \Lambda$ channels, whereas $\Delta m $ is negative for the singlet, $N \Xi$, and $\Sigma \Sigma$ channels. These findings are limited, however, by the use of a single spatial volume and a relatively large quark mass.
2027, 51(1): 1-6.
doi:10.1088/1674-1137/aea82b
Abstract:
The production rates of $ \Xi^{-}/\bar{\Xi}^{+} $ baryons in energy-ranked jets produced from $ Z\to{\rm{hadrons}} $ decays are measured using $ 3.2 $ million hadronicZdecay events recorded by the DELPHI experiment. Jets are reconstructed using the Durham algorithm with $ y_{{\rm{cut}}}=0.005 $. Quark- and gluon-enriched jet samples are obtained by ranking the jet energies in three-jet events. The softest jet is found to produce fewer $ \Xi^{-}/\bar{\Xi}^{+} $ and less energetic baryons than the other jets. The ratio of $ \Xi^{-}/\bar{\Xi}^{+} $ production rates in gluon and quark jets, each normalized to the corresponding mean charged-particle multiplicity, is measured to be $ 1.21 \pm 0.18\; {\rm{(stat.)}} \pm 0.26\; {\rm{(syst.)}} $. This result is consistent with the JETSET expectation and the OPAL measurements of $ K_S^0 $ and Λ productions inZdecays. This study presents the first measurement of the gluon-to-quark production ratio for baryons containing twosquarks, providing new insights into strange-quark production and hadronization. Future $ e^{+}e^{-} $ colliders such as CEPC and FCCee will provide much largerZ-boson samples and enable far more precise studies of the subject.
The production rates of $ \Xi^{-}/\bar{\Xi}^{+} $ baryons in energy-ranked jets produced from $ Z\to{\rm{hadrons}} $ decays are measured using $ 3.2 $ million hadronicZdecay events recorded by the DELPHI experiment. Jets are reconstructed using the Durham algorithm with $ y_{{\rm{cut}}}=0.005 $. Quark- and gluon-enriched jet samples are obtained by ranking the jet energies in three-jet events. The softest jet is found to produce fewer $ \Xi^{-}/\bar{\Xi}^{+} $ and less energetic baryons than the other jets. The ratio of $ \Xi^{-}/\bar{\Xi}^{+} $ production rates in gluon and quark jets, each normalized to the corresponding mean charged-particle multiplicity, is measured to be $ 1.21 \pm 0.18\; {\rm{(stat.)}} \pm 0.26\; {\rm{(syst.)}} $. This result is consistent with the JETSET expectation and the OPAL measurements of $ K_S^0 $ and Λ productions inZdecays. This study presents the first measurement of the gluon-to-quark production ratio for baryons containing twosquarks, providing new insights into strange-quark production and hadronization. Future $ e^{+}e^{-} $ colliders such as CEPC and FCCee will provide much largerZ-boson samples and enable far more precise studies of the subject.
2027, 51(1): 013115.
doi:10.1088/1674-1137/ae8f25
Abstract:
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are recast as differential equations for sector-wise generating functions, allowing the reduction problem to be studied within a non-commutative algebra of differential operators rather than solely through relations among individual integrals. This perspective yields an iterative algorithm that generates candidate equations, extracts symbolic reduction rules, updates the active rule set, and verifies completeness on the lattice of integral indices. We illustrate the method using the sunset topology, planar and non-planar massless double-box topologies, representative subsectors, and a degenerate example in which the top sector contains no master integral. Collectively, these examples demonstrate how symbolic reduction rules, descendant equations, and completeness criteria can be organized within a single algebraic framework.
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are recast as differential equations for sector-wise generating functions, allowing the reduction problem to be studied within a non-commutative algebra of differential operators rather than solely through relations among individual integrals. This perspective yields an iterative algorithm that generates candidate equations, extracts symbolic reduction rules, updates the active rule set, and verifies completeness on the lattice of integral indices. We illustrate the method using the sunset topology, planar and non-planar massless double-box topologies, representative subsectors, and a degenerate example in which the top sector contains no master integral. Collectively, these examples demonstrate how symbolic reduction rules, descendant equations, and completeness criteria can be organized within a single algebraic framework.
2027, 51(1): 1-15.
doi:10.1088/1674-1137/aea8f3
Abstract:
In the N-B-LSSM, we calculate the electric dipole moments (EDMs) of leptons and the neutron at the one-loop level using the mass insertion approximation (MIA). In the Standard Model (SM), charge-parity (CP) violation originates solely from the single phase of the Cabibbo–Kobayashi–Maskawa (CKM) matrix, and the predicted EDMs of leptons and the neutron are well below the current experimental upper limits. Thus, EDMs serve as sensitive probes of CP-violating phases in new physics. The N-B-LSSM extends the Minimal Supersymmetric Standard Model (MSSM) by introducing right-handed neutrino superfields and additional singlet Higgs superfields, thereby enriching the particle spectrum and the sources of CP violation. We derive one-loop analytical expressions for lepton and quark EDMs and show their dependence on model parameters such as $ g_{YB} $, $ \theta_{\mu_H} $, $ \theta_{1'} $, $ \theta_{BB'} $, and $ \tan\beta $. Numerical analyses demonstrate that EDM measurements strongly constrain the CP-violating parameter space of the N-B-LSSM and reveal the sensitivity of lepton and neutron EDMs to the extended gauge interactions and supersymmetric parameters. This study provides a systematic theoretical tool and numerical reference for exploring CP violation and new physics within the N-B-LSSM.
In the N-B-LSSM, we calculate the electric dipole moments (EDMs) of leptons and the neutron at the one-loop level using the mass insertion approximation (MIA). In the Standard Model (SM), charge-parity (CP) violation originates solely from the single phase of the Cabibbo–Kobayashi–Maskawa (CKM) matrix, and the predicted EDMs of leptons and the neutron are well below the current experimental upper limits. Thus, EDMs serve as sensitive probes of CP-violating phases in new physics. The N-B-LSSM extends the Minimal Supersymmetric Standard Model (MSSM) by introducing right-handed neutrino superfields and additional singlet Higgs superfields, thereby enriching the particle spectrum and the sources of CP violation. We derive one-loop analytical expressions for lepton and quark EDMs and show their dependence on model parameters such as $ g_{YB} $, $ \theta_{\mu_H} $, $ \theta_{1'} $, $ \theta_{BB'} $, and $ \tan\beta $. Numerical analyses demonstrate that EDM measurements strongly constrain the CP-violating parameter space of the N-B-LSSM and reveal the sensitivity of lepton and neutron EDMs to the extended gauge interactions and supersymmetric parameters. This study provides a systematic theoretical tool and numerical reference for exploring CP violation and new physics within the N-B-LSSM.
2027, 51(1): 013108.
doi:10.1088/1674-1137/ae9927
Abstract:
We present a joint factorization and resummation study of the energy-energy correlator (EEC) and thrust in $ e^+e^- $ collisions. An analysis of the joint kinematic distribution reveals five relevant regimes that govern how the global event shape constrains local energy correlations. In the collinear limit ($ z \to 0 $), we show that the global thrust boundary strongly constrains the jet substructure, necessitating a sub-jet refactorization. In the back-to-back limit ($ z \to 1 $), the coexistence of $ {\rm{SCET}}_{{\rm{I}}} $ and $ {\rm{SCET}}_{{\rm{II}}} $ soft scales requires the $ {\rm{SCET}}_{+} $ framework. We derive the factorization theorems for all five regimes and calculate the corresponding differential jet functions at one-loop order. By cleanly separating the overlapping soft and collinear modes, our framework provides a systematic factorization description of the EEC under global thrust constraints in the singular limits.
We present a joint factorization and resummation study of the energy-energy correlator (EEC) and thrust in $ e^+e^- $ collisions. An analysis of the joint kinematic distribution reveals five relevant regimes that govern how the global event shape constrains local energy correlations. In the collinear limit ($ z \to 0 $), we show that the global thrust boundary strongly constrains the jet substructure, necessitating a sub-jet refactorization. In the back-to-back limit ($ z \to 1 $), the coexistence of $ {\rm{SCET}}_{{\rm{I}}} $ and $ {\rm{SCET}}_{{\rm{II}}} $ soft scales requires the $ {\rm{SCET}}_{+} $ framework. We derive the factorization theorems for all five regimes and calculate the corresponding differential jet functions at one-loop order. By cleanly separating the overlapping soft and collinear modes, our framework provides a systematic factorization description of the EEC under global thrust constraints in the singular limits.
2027, 51(1): 013109.
doi:10.1088/1674-1137/aea285
Abstract:
We investigate the discovery potential for a singly produced vector-like top quarkTin the $T\to tZ$ decay channel at future muon-proton ($\mu p$) colliders, considering three benchmark center-of-mass energies: $\sqrt{s}=5.29$, $6.48$, and $9.16$ TeV. The baseline signal final state consists of a semileptonic top decay $t\to bW\to b\ell\nu$ and a hadronic $Z\to q\bar{q}$ decay, in which the collimated quark pair from theZboson is reconstructed as a single large-radius fat jetJ. Full detector-level Monte Carlo simulations are performed for both the signal process and the dominant Standard Model backgrounds. We derive the $5\sigma$ discovery contours and the $95\%$ confidence-level exclusion limits in the two-dimensional parameter space spanned by the VLQ mass $m_T$ and the effective coupling $g^*$. A comparison with the $T\to Wb$ channel and with searches at other collider facilities shows that the $T\to tZ$ decay mode provides complementary sensitivity and offers unique advantages for probing high-mass vector-likeTquarks in the boosted-jet topology.
We investigate the discovery potential for a singly produced vector-like top quarkTin the $T\to tZ$ decay channel at future muon-proton ($\mu p$) colliders, considering three benchmark center-of-mass energies: $\sqrt{s}=5.29$, $6.48$, and $9.16$ TeV. The baseline signal final state consists of a semileptonic top decay $t\to bW\to b\ell\nu$ and a hadronic $Z\to q\bar{q}$ decay, in which the collimated quark pair from theZboson is reconstructed as a single large-radius fat jetJ. Full detector-level Monte Carlo simulations are performed for both the signal process and the dominant Standard Model backgrounds. We derive the $5\sigma$ discovery contours and the $95\%$ confidence-level exclusion limits in the two-dimensional parameter space spanned by the VLQ mass $m_T$ and the effective coupling $g^*$. A comparison with the $T\to Wb$ channel and with searches at other collider facilities shows that the $T\to tZ$ decay mode provides complementary sensitivity and offers unique advantages for probing high-mass vector-likeTquarks in the boosted-jet topology.
2027, 51(1): 1-18.
doi:10.1088/1674-1137/aea286
Abstract:
We investigate the QCD corrections to the loop-induced decays of the heavy $\rm CP$-even Higgs boson, $H \to V\gamma$ ($V = Z, \gamma$), within the framework of the Type-I Two-Higgs-Doublet Model (THDM). Owing to the similarity of the underlying loop topologies, the two decay channels exhibit closely correlated behavior. After imposing the relevant phenomenological constraints, we evaluate the decay widths for 5000 viable parameter points at next-to-leading order (NLO) in QCD under the alignment limit. The $H\to\gamma\gamma$ width exceeds that of $H\to Z\gamma$ by roughly a factor of four. Both are dominated by the top-quark loop: theWcontribution vanishes in the alignment limit, and the charged-Higgs loop is suppressed throughout most of the viable parameter space. The corrections exhibit a pronounced dependence on the heavy Higgs boson mass $m_H$, reaching a maximum in the vicinity of the $t\bar{t}$ production threshold. To elucidate the individual parameter dependences, dedicated benchmark scenarios are analyzed, revealing that the decay widths decrease monotonically with increasing $\tan\beta$ while increasing with $m_H$. The QCD corrections for both decay modes typically range from approximately $-20$% to $+20$%, with larger corrections in the non-alignment scenario: in the $H\to\gamma\gamma$ channel, they reach up to $+38$% at large $\tan\beta$, and in the $H\to Z\gamma$ channel, they cross zero and become positive. The $\rm CP$ selection rule forces the $t\bar{t}$ pair into aP-wave configuration at threshold, which strongly suppresses the Coulomb corrections and ensures the perturbative stability of the fixed-order prediction. A comparison with ATLAS limits shows that current data do not yet constrain the parameter space, whereas the ${\cal{O}}$(15%) NLO corrections may become relevant for interpreting exclusion bounds at the HL-LHC.
We investigate the QCD corrections to the loop-induced decays of the heavy $\rm CP$-even Higgs boson, $H \to V\gamma$ ($V = Z, \gamma$), within the framework of the Type-I Two-Higgs-Doublet Model (THDM). Owing to the similarity of the underlying loop topologies, the two decay channels exhibit closely correlated behavior. After imposing the relevant phenomenological constraints, we evaluate the decay widths for 5000 viable parameter points at next-to-leading order (NLO) in QCD under the alignment limit. The $H\to\gamma\gamma$ width exceeds that of $H\to Z\gamma$ by roughly a factor of four. Both are dominated by the top-quark loop: theWcontribution vanishes in the alignment limit, and the charged-Higgs loop is suppressed throughout most of the viable parameter space. The corrections exhibit a pronounced dependence on the heavy Higgs boson mass $m_H$, reaching a maximum in the vicinity of the $t\bar{t}$ production threshold. To elucidate the individual parameter dependences, dedicated benchmark scenarios are analyzed, revealing that the decay widths decrease monotonically with increasing $\tan\beta$ while increasing with $m_H$. The QCD corrections for both decay modes typically range from approximately $-20$% to $+20$%, with larger corrections in the non-alignment scenario: in the $H\to\gamma\gamma$ channel, they reach up to $+38$% at large $\tan\beta$, and in the $H\to Z\gamma$ channel, they cross zero and become positive. The $\rm CP$ selection rule forces the $t\bar{t}$ pair into aP-wave configuration at threshold, which strongly suppresses the Coulomb corrections and ensures the perturbative stability of the fixed-order prediction. A comparison with ATLAS limits shows that current data do not yet constrain the parameter space, whereas the ${\cal{O}}$(15%) NLO corrections may become relevant for interpreting exclusion bounds at the HL-LHC.
2027, 51(1): 013114.
doi:10.1088/1674-1137/ae9f38
Abstract:
We investigate in detail the discovery potential of the doubly charged Higgs boson at the Compact Linear Collider in $ e^-e^- $, $ e^-\gamma $, $ \gamma\gamma $, and $ e^+e^- $ collision modes within the Higgs triplet model, using two extreme benchmark points as representatives of the Yukawa-like and gauge-like regions. In the Yukawa-like region, the most promising production mechanism is single production in $ e^-e^- $ and $ e^-\gamma $ collisions. Given the subsequent decay of the doubly charged Higgs boson into a same-sign lepton pair, CLIC can achieve a statistical significance well beyond the discovery threshold within the parameter space allowed by experimental constraints. In the gauge-like region, using the $ \ell^{\pm}\ell^{\pm} + \geq 3j $ final state, CLIC exhibits robust discovery potential for the doubly charged Higgs boson up to a mass of approximately $ 1.2\; \mathrm{TeV} $. We also investigate the search for doubly charged Higgs bosons at the HL-LHC. Our results demonstrate that CLIC offers greater advantages and superior discovery potential for the doubly charged Higgs boson compared with the HL-LHC.
We investigate in detail the discovery potential of the doubly charged Higgs boson at the Compact Linear Collider in $ e^-e^- $, $ e^-\gamma $, $ \gamma\gamma $, and $ e^+e^- $ collision modes within the Higgs triplet model, using two extreme benchmark points as representatives of the Yukawa-like and gauge-like regions. In the Yukawa-like region, the most promising production mechanism is single production in $ e^-e^- $ and $ e^-\gamma $ collisions. Given the subsequent decay of the doubly charged Higgs boson into a same-sign lepton pair, CLIC can achieve a statistical significance well beyond the discovery threshold within the parameter space allowed by experimental constraints. In the gauge-like region, using the $ \ell^{\pm}\ell^{\pm} + \geq 3j $ final state, CLIC exhibits robust discovery potential for the doubly charged Higgs boson up to a mass of approximately $ 1.2\; \mathrm{TeV} $. We also investigate the search for doubly charged Higgs bosons at the HL-LHC. Our results demonstrate that CLIC offers greater advantages and superior discovery potential for the doubly charged Higgs boson compared with the HL-LHC.
2027, 51(1): 011001.
doi:10.1088/1674-1137/aeaa0f
Abstract:
$ X(2370) $ lies in the mass region of the lowest pseudoscalar glueball predicted by lattice quantum chromodynamics (QCD) studies, and its decay properties are similar to those of $ \eta_c $. A previous lattice QCD study clearly shows that the pseudoscalar glueball ($ G_{0^-} $) and lowest pseudoscalar charmonium state ($ c\bar{c}(0^-) $) can mix with a small mixing angleθ. Therefore, $ X(2370) $ and $ \eta_c $ could be admixtures of $ G_{0^-} $ and $ c\bar{c}(0^-) $. Although $ {\rm{Br}}(J/\psi\to\gamma\eta_c) $ is insensitive to small values of $ \sin\theta $, $ {\rm{Br}}(J/\psi\to \gamma X(2370)) $ can be greatly enhanced by mixing because of the considerably larger kinematic factor for $ J/\psi\to \gamma X(2370) $ and the substantially larger transition form factor for $ J/\psi\to \gamma (c\bar{c}(0^{-})) $. Based on the value of $ \sin\theta $, $ {\rm{Br}}(J/\psi\to \gamma X(2370)) $ can be considerably larger than the branching fraction for a pure pseudoscalar glueball, namely, $ 2.3(8)\times 10^{-4} $, as predicted by a quenched lattice QCD calculation. This amplification mechanism helps explain the large production rate of $ X(2370) $ in $ J/\psi $ radiative decay, and the BESIII Collaboration results favor a small mixing angle of $ {\cal{O}}(1^\circ) $ if the mixing picture applies here.
$ X(2370) $ lies in the mass region of the lowest pseudoscalar glueball predicted by lattice quantum chromodynamics (QCD) studies, and its decay properties are similar to those of $ \eta_c $. A previous lattice QCD study clearly shows that the pseudoscalar glueball ($ G_{0^-} $) and lowest pseudoscalar charmonium state ($ c\bar{c}(0^-) $) can mix with a small mixing angleθ. Therefore, $ X(2370) $ and $ \eta_c $ could be admixtures of $ G_{0^-} $ and $ c\bar{c}(0^-) $. Although $ {\rm{Br}}(J/\psi\to\gamma\eta_c) $ is insensitive to small values of $ \sin\theta $, $ {\rm{Br}}(J/\psi\to \gamma X(2370)) $ can be greatly enhanced by mixing because of the considerably larger kinematic factor for $ J/\psi\to \gamma X(2370) $ and the substantially larger transition form factor for $ J/\psi\to \gamma (c\bar{c}(0^{-})) $. Based on the value of $ \sin\theta $, $ {\rm{Br}}(J/\psi\to \gamma X(2370)) $ can be considerably larger than the branching fraction for a pure pseudoscalar glueball, namely, $ 2.3(8)\times 10^{-4} $, as predicted by a quenched lattice QCD calculation. This amplification mechanism helps explain the large production rate of $ X(2370) $ in $ J/\psi $ radiative decay, and the BESIII Collaboration results favor a small mixing angle of $ {\cal{O}}(1^\circ) $ if the mixing picture applies here.
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