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2026 No.7
2026 No.8
2026, 50(7): 073112. doi: 10.1088/1674-1137/ae6da0
Abstract:
Dilatons, the CP-even pseudo-Nambu-Goldstone bosons arising from spontaneous scale symmetry breaking, offer a compelling alternative to axion-like particles (ALPs) yet lack a comprehensive low-energy framework. We address this by constructing a systematic effective field theory (EFT) for the dilaton based on a manifestly scale-invariant regularization scheme. This approach derives universal linear couplings to the trace anomaly while preserving consistent renormalization group evolution. We establish a hierarchical EFT tower connecting the ultraviolet conformal sector to the infrared, encompassing the dilaton-extended SMEFT, low-energy EFT up to dimension-7, and a chiral Lagrangian describing meson and baryon interactions. We perform a comprehensive phenomenological analysis across two distinct mass regimes, where the dilaton manifests as either a conventional particle or a wave-like particle. For MeV-scale dilatons behaving as conventional particles, we obtain constraints from LHC production, semi-invisible B- and K-meson decays, and supernova cooling. For ultralight dilatons acting as dark matter, we project sensitivities for atomic clocks and atom interferometers. This unified EFT framework would pave the way for extended phenomenological studies across the full mass spectrum of the light dilaton.
Dilatons, the CP-even pseudo-Nambu-Goldstone bosons arising from spontaneous scale symmetry breaking, offer a compelling alternative to axion-like particles (ALPs) yet lack a comprehensive low-energy framework. We address this by constructing a systematic effective field theory (EFT) for the dilaton based on a manifestly scale-invariant regularization scheme. This approach derives universal linear couplings to the trace anomaly while preserving consistent renormalization group evolution. We establish a hierarchical EFT tower connecting the ultraviolet conformal sector to the infrared, encompassing the dilaton-extended SMEFT, low-energy EFT up to dimension-7, and a chiral Lagrangian describing meson and baryon interactions. We perform a comprehensive phenomenological analysis across two distinct mass regimes, where the dilaton manifests as either a conventional particle or a wave-like particle. For MeV-scale dilatons behaving as conventional particles, we obtain constraints from LHC production, semi-invisible B- and K-meson decays, and supernova cooling. For ultralight dilatons acting as dark matter, we project sensitivities for atomic clocks and atom interferometers. This unified EFT framework would pave the way for extended phenomenological studies across the full mass spectrum of the light dilaton.
2026, 50(8): 08310. doi: 10.1088/1674-1137/ae68ed
Abstract:
We constructed a four-Higgs-doublet model (4HDM) invariant under D5 symmetry and investigated its complete neutral vacuum structure in detail. Assuming explicit CP conservation in the scalar potential, we examined whether CP symmetry can be spontaneously broken. We provided a complete list of all possible real and complex vacua, along with the constraints on the potential parameters required for each vacuum solution to exist. We also discussed the positive-definiteness conditions that the Hessian must satisfy for each vacuum to be a local minimum of the potential. The results show that, after spontaneous symmetry breaking, some complex vacua lead to spontaneous CP violation in the potential, whereas the remaining complex vacua still preserve CP conservation. Among these CP-violating complex vacua, one can be regarded as the most general form. Furthermore, we discussed the relationship between real and complex vacua.
We constructed a four-Higgs-doublet model (4HDM) invariant under D5 symmetry and investigated its complete neutral vacuum structure in detail. Assuming explicit CP conservation in the scalar potential, we examined whether CP symmetry can be spontaneously broken. We provided a complete list of all possible real and complex vacua, along with the constraints on the potential parameters required for each vacuum solution to exist. We also discussed the positive-definiteness conditions that the Hessian must satisfy for each vacuum to be a local minimum of the potential. The results show that, after spontaneous symmetry breaking, some complex vacua lead to spontaneous CP violation in the potential, whereas the remaining complex vacua still preserve CP conservation. Among these CP-violating complex vacua, one can be regarded as the most general form. Furthermore, we discussed the relationship between real and complex vacua.
2026, 50(7): 073110. doi: 10.1088/1674-1137/ae68ee
Abstract:
The Belle Collaboration has recently reported a measurement of the branching fraction for the semileptonic decay $ B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell $, with $ \ell=e $ or μ. Using the newly available data across the full $ \pi\pi $ invariant-mass spectrum, we determine the non-resonant $ B\to\pi\pi $ transition form factors. We obtain a non-resonant branching fraction $ {\cal B}_N(B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell)=(3.5\pm 1.4^{+4.3}_{-2.4})\times 10^{-5} $. This result indicates that the non-resonant contribution can be comparable in magnitude to the resonant components and should not be treated as a negligible background in precision measurements. Our findings highlight the importance of dedicated experimental efforts at Belle II and LHCb to further probe the non-resonant contribution.
The Belle Collaboration has recently reported a measurement of the branching fraction for the semileptonic decay $ B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell $, with $ \ell=e $ or μ. Using the newly available data across the full $ \pi\pi $ invariant-mass spectrum, we determine the non-resonant $ B\to\pi\pi $ transition form factors. We obtain a non-resonant branching fraction $ {\cal B}_N(B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell)=(3.5\pm 1.4^{+4.3}_{-2.4})\times 10^{-5} $. This result indicates that the non-resonant contribution can be comparable in magnitude to the resonant components and should not be treated as a negligible background in precision measurements. Our findings highlight the importance of dedicated experimental efforts at Belle II and LHCb to further probe the non-resonant contribution.
2026, 50(8): 083101. doi: 10.1088/1674-1137/ae6311
Abstract:
The exploration of symmetry laws stands as a cutting-edge direction in modern physics research. This study delves into the examination of P and $\rm CP$ symmetry properties within the charm quark system by analyzing asymmetry parameters in the two-body decay process of $ \Omega_c $. By accounting for the polarization effects of electron and positron beams and employing the helicity formalism, we systematically analyze the decay characteristics of $ \Omega_c $ and its subsequent hyperon decays through specific asymmetry parameters. A comprehensive formulation of the angular distribution for these decay processes has been developed. The research assesses the detection sensitivity of asymmetry parameters in the $ \Omega_c\rightarrow \Omega^-\pi^+ $ decay mode across different experimental conditions, including varying data sample sizes and beam polarization configurations. These results contribute to enriching a theoretical foundation for forthcoming experimental endeavors at the STCF, offering significant implications for symmetry studies in the charm sector.
The exploration of symmetry laws stands as a cutting-edge direction in modern physics research. This study delves into the examination of P and $\rm CP$ symmetry properties within the charm quark system by analyzing asymmetry parameters in the two-body decay process of $ \Omega_c $. By accounting for the polarization effects of electron and positron beams and employing the helicity formalism, we systematically analyze the decay characteristics of $ \Omega_c $ and its subsequent hyperon decays through specific asymmetry parameters. A comprehensive formulation of the angular distribution for these decay processes has been developed. The research assesses the detection sensitivity of asymmetry parameters in the $ \Omega_c\rightarrow \Omega^-\pi^+ $ decay mode across different experimental conditions, including varying data sample sizes and beam polarization configurations. These results contribute to enriching a theoretical foundation for forthcoming experimental endeavors at the STCF, offering significant implications for symmetry studies in the charm sector.
2026, 50(7): 073109. doi: 10.1088/1674-1137/ae5ef8
Abstract:
We present a systematic analysis of the Higgs signal strengths at 125 GeV and 95 GeV in a non-supersymmetric $ U(1)_X $ model with vector-like fermions ($ U(1)_X $ VLFM). This framework extends the Standard Model (SM) by introducing an additional $ U(1)_X $ gauge symmetry, three right-handed neutrinos, two singlet Higgs fields (ϕ and S), and one generation of vector-like quarks and leptons. The scalar fields mix in the neutral CP-even sector, yielding two Higgs-like states around 95 GeV and 125 GeV. We perform a $ \chi^2 $ analysis that combines the Higgs signal strength measurements at 125 GeV from ATLAS and CMS, including the $ \gamma\gamma $, $ WW^* $, $ ZZ^* $, $ b\bar{b} $, and $ \tau\bar{\tau} $ channels, together with the 95 GeV excesses observed in the diphoton and $ b\bar{b} $ final states reported by CMS and LEP. Our results indicate that the $ U(1)_X $ VLFM successfully reproduces the observed signal strengths of the 125 GeV Higgs while simultaneously explaining the 95 GeV excess. The parameters $ g_X $, $ g_{YX} $, $ v_S $, $ v_P $, and the new Yukawa couplings play a crucial role in achieving this consistency.
We present a systematic analysis of the Higgs signal strengths at 125 GeV and 95 GeV in a non-supersymmetric $ U(1)_X $ model with vector-like fermions ($ U(1)_X $ VLFM). This framework extends the Standard Model (SM) by introducing an additional $ U(1)_X $ gauge symmetry, three right-handed neutrinos, two singlet Higgs fields (ϕ and S), and one generation of vector-like quarks and leptons. The scalar fields mix in the neutral CP-even sector, yielding two Higgs-like states around 95 GeV and 125 GeV. We perform a $ \chi^2 $ analysis that combines the Higgs signal strength measurements at 125 GeV from ATLAS and CMS, including the $ \gamma\gamma $, $ WW^* $, $ ZZ^* $, $ b\bar{b} $, and $ \tau\bar{\tau} $ channels, together with the 95 GeV excesses observed in the diphoton and $ b\bar{b} $ final states reported by CMS and LEP. Our results indicate that the $ U(1)_X $ VLFM successfully reproduces the observed signal strengths of the 125 GeV Higgs while simultaneously explaining the 95 GeV excess. The parameters $ g_X $, $ g_{YX} $, $ v_S $, $ v_P $, and the new Yukawa couplings play a crucial role in achieving this consistency.
2026, 50(7): 073104. doi: 10.1088/1674-1137/ae5c85
Abstract:
Neutrino Earth tomography provides an observational approach to studying the Earth's deep three-dimensional structure that is distinct from seismology. However, most existing studies still rely on one-dimensional density models and therefore cannot adequately represent lateral heterogeneity within the Earth. To address this issue, this study integrates PREM, CRUST1.0, and HMSL-S06 on a tesseroid grid to construct a non-spherically symmetric three-dimensional Earth density model that includes large low-velocity provinces (LLVPs) in the deep mantle. We also develop a corresponding procedure for extracting neutrino propagation trajectories and derive closed-form expressions for the total mass and axial moment of inertia of the discrete model, which are used as global consistency checks. Within an exact three-flavor oscillation framework, we use public Super-Kamiokande data products to compare the event counts predicted by the three-dimensional model with those from a conventional one-dimensional spherically symmetric model. The results show that, under the present calculation scheme, the differences in the overall event count distributions between the three-dimensional model and the one-dimensional reference model remain limited. This study establishes a three-dimensional calculation framework that can provide a methodological basis for future investigations of how lateral density heterogeneity may affect atmospheric neutrino propagation.
Neutrino Earth tomography provides an observational approach to studying the Earth's deep three-dimensional structure that is distinct from seismology. However, most existing studies still rely on one-dimensional density models and therefore cannot adequately represent lateral heterogeneity within the Earth. To address this issue, this study integrates PREM, CRUST1.0, and HMSL-S06 on a tesseroid grid to construct a non-spherically symmetric three-dimensional Earth density model that includes large low-velocity provinces (LLVPs) in the deep mantle. We also develop a corresponding procedure for extracting neutrino propagation trajectories and derive closed-form expressions for the total mass and axial moment of inertia of the discrete model, which are used as global consistency checks. Within an exact three-flavor oscillation framework, we use public Super-Kamiokande data products to compare the event counts predicted by the three-dimensional model with those from a conventional one-dimensional spherically symmetric model. The results show that, under the present calculation scheme, the differences in the overall event count distributions between the three-dimensional model and the one-dimensional reference model remain limited. This study establishes a three-dimensional calculation framework that can provide a methodological basis for future investigations of how lateral density heterogeneity may affect atmospheric neutrino propagation.
2026, 50(7): 073103. doi: 10.1088/1674-1137/ae5ef7
Abstract:
The internal structure of the light scalar state $ a_0(1450) $ has not been definitively determined; it may comprise multiple possible configurations. Among these, it may be regarded as a $ q\bar{q} $ state. Based on this possibility, we use QCD light-cone sum rules to study the semileptonic decay process $ D \to a_0(1450)\ell \nu_\ell $ with $ \ell=(e, \mu) $ and to test this hypothesis. First, we construct two twist-2 light-cone distribution-amplitude schemes based on the light-cone harmonic-oscillator model, and present their moments $ \langle\xi^{n}\rangle |_{\mu} $ and Gegenbauer moments $ a_{n}(\mu) $ at $ \mu_0=1\; {\rm{GeV}} $ and $ \mu_k= 1.4\; {\rm{GeV}} $ for $ n=(1,3,5) $. In the large-recoil region, we obtain the transition form factors (TFFs): $ f_+^{({\rm{S}}1)}(0) = $$ 0.836_{-0.119}^{+0.116} $, $ f_+^{({\rm{S}}2)}(0)=0.767_{-0.105}^{+0.106} $, and $ f_-(0)=0.630_{-0.077}^{+0.078} $. A simplified series expansion $ z(q^2, t) $ is used to extrapolate the TFFs to the entire physical $ q^2 $ region. For $ q^2=10^{-5} \; {\rm{GeV}}^2 $, we compute the angular distribution of the differential decay width ${{\rm d}\Gamma}/{{\rm d}\cos\theta_\ell }$ over the range $ \cos\theta_\ell \in [-1,1] $. Subsequently, we obtain the differential decay widths and branching fractions for $ D^0 \to a_0(1450)^- \ell^+ \nu_\ell $ and $ D^- \to a_0(1450)^0 \ell^- \bar{\nu}_\ell $, with branching fractions of order $ 10^{-6} $. Finally, we analyze three angular observables for the semileptonic decay process $ D^- \to a_0(1450)^0 \ell^- \bar{\nu}_\ell $: the forward–backward asymmetry $ {\cal{A}}_{\rm{FB}} $, the lepton polarization asymmetry $ {\cal{A}}_{\lambda_\ell} $, and the $ q^2 $-differential flat term $ {\cal{F}}_{\rm{H}} $.
The internal structure of the light scalar state $ a_0(1450) $ has not been definitively determined; it may comprise multiple possible configurations. Among these, it may be regarded as a $ q\bar{q} $ state. Based on this possibility, we use QCD light-cone sum rules to study the semileptonic decay process $ D \to a_0(1450)\ell \nu_\ell $ with $ \ell=(e, \mu) $ and to test this hypothesis. First, we construct two twist-2 light-cone distribution-amplitude schemes based on the light-cone harmonic-oscillator model, and present their moments $ \langle\xi^{n}\rangle |_{\mu} $ and Gegenbauer moments $ a_{n}(\mu) $ at $ \mu_0=1\; {\rm{GeV}} $ and $ \mu_k= 1.4\; {\rm{GeV}} $ for $ n=(1,3,5) $. In the large-recoil region, we obtain the transition form factors (TFFs): $ f_+^{({\rm{S}}1)}(0) = $$ 0.836_{-0.119}^{+0.116} $, $ f_+^{({\rm{S}}2)}(0)=0.767_{-0.105}^{+0.106} $, and $ f_-(0)=0.630_{-0.077}^{+0.078} $. A simplified series expansion $ z(q^2, t) $ is used to extrapolate the TFFs to the entire physical $ q^2 $ region. For $ q^2=10^{-5} \; {\rm{GeV}}^2 $, we compute the angular distribution of the differential decay width ${{\rm d}\Gamma}/{{\rm d}\cos\theta_\ell }$ over the range $ \cos\theta_\ell \in [-1,1] $. Subsequently, we obtain the differential decay widths and branching fractions for $ D^0 \to a_0(1450)^- \ell^+ \nu_\ell $ and $ D^- \to a_0(1450)^0 \ell^- \bar{\nu}_\ell $, with branching fractions of order $ 10^{-6} $. Finally, we analyze three angular observables for the semileptonic decay process $ D^- \to a_0(1450)^0 \ell^- \bar{\nu}_\ell $: the forward–backward asymmetry $ {\cal{A}}_{\rm{FB}} $, the lepton polarization asymmetry $ {\cal{A}}_{\lambda_\ell} $, and the $ q^2 $-differential flat term $ {\cal{F}}_{\rm{H}} $.
2026, 50(7): 073106. doi: 10.1088/1674-1137/ae62f8
Abstract:
In this work, we focus on the possible linear relationship between short-range correlations (SRCs) and the EMC effect for partons in nuclei. First, we test a linear relationship pertaining to gluons in bound nuclei; it is manifested as a correlation between the slope of the reduced cross-section ratio in deep inelastic scattering (DIS) and the cross-section of sub-threshold $ J/\psi $ photoproduction. For comparison, results from four different global analysis groups of nuclear parton distribution functions (nPDFs) are utilized. These results show a good linear correlation between the gluons in bound nuclei and the slope of the reduced cross-section ratio, consistent with the possible presence of nuclear effects in the gluon distributions. Second, we investigate the linear relationship of quarks in the proton-induced Drell-Yan process. The corresponding results for quarks show strong sensitivity to the parameterizations forms adopted by the different groups. These findings enhance our understanding of the substructure in bound nuclei and provide a valuable reference for future global fitting of nPDFs.
In this work, we focus on the possible linear relationship between short-range correlations (SRCs) and the EMC effect for partons in nuclei. First, we test a linear relationship pertaining to gluons in bound nuclei; it is manifested as a correlation between the slope of the reduced cross-section ratio in deep inelastic scattering (DIS) and the cross-section of sub-threshold $ J/\psi $ photoproduction. For comparison, results from four different global analysis groups of nuclear parton distribution functions (nPDFs) are utilized. These results show a good linear correlation between the gluons in bound nuclei and the slope of the reduced cross-section ratio, consistent with the possible presence of nuclear effects in the gluon distributions. Second, we investigate the linear relationship of quarks in the proton-induced Drell-Yan process. The corresponding results for quarks show strong sensitivity to the parameterizations forms adopted by the different groups. These findings enhance our understanding of the substructure in bound nuclei and provide a valuable reference for future global fitting of nPDFs.
2026, 50(7): 073107. doi: 10.1088/1674-1137/ae62fa
Abstract:
In this work, we present the first computation of the full one-loop electroweak radiative corrections to the process $ \mu^- \mu^+ \to W^\pm W^\mp \to hh $ within the Standard Model (SM). Building upon this, we investigate neutral scalar pair production via vector boson fusion at multi–TeV muon colliders in the framework of the Two-Higgs-Doublet Model (2HDM). In our phenomenological analysis, we introduce an enhancement factor, defined as the ratio of the cross section for SM-like Higgs pair production in the 2HDM to the corresponding SM prediction. This factor is systematically evaluated across the allowed regions of parameter space in both Type-X and Type-Y 2HDMs. Our results indicate that, within the viable Type-X parameter space, this factor can reach a value of 3, whereas it remains between 0.91 and 0.95 across the allowed parameter space of the Type-Y scenario. We observe that the enhancement factor exhibits distinct behaviors in the Type-X and Type-Y 2HDMs. This feature provides a promising opportunity to discriminate between the two scenarios through precision measurements of double Higgs production at future multi–TeV colliders. Furthermore, we perform a detailed scan of the cross sections for both CP-odd and CP-even Higgs pair production over the viable parameter spaces of the Type-X and Type-Y 2HDMs. In the Type-Y scenario, at a center-of-mass (CoM) energy $ \sqrt{s} = 10\; \text{TeV} $ and an integrated luminosity of $ {\cal{L}} = 10000\; \text{fb}^{-1} $, both CP-odd and CP-even Higgs pair production in the $ t\bar{t}b\bar{b} $ final state, with subsequent top-quark decays into leptons and bottom quarks, can be probed with a statistical significance exceeding the $ 2\sigma $ level at several viable parameter points.
In this work, we present the first computation of the full one-loop electroweak radiative corrections to the process $ \mu^- \mu^+ \to W^\pm W^\mp \to hh $ within the Standard Model (SM). Building upon this, we investigate neutral scalar pair production via vector boson fusion at multi–TeV muon colliders in the framework of the Two-Higgs-Doublet Model (2HDM). In our phenomenological analysis, we introduce an enhancement factor, defined as the ratio of the cross section for SM-like Higgs pair production in the 2HDM to the corresponding SM prediction. This factor is systematically evaluated across the allowed regions of parameter space in both Type-X and Type-Y 2HDMs. Our results indicate that, within the viable Type-X parameter space, this factor can reach a value of 3, whereas it remains between 0.91 and 0.95 across the allowed parameter space of the Type-Y scenario. We observe that the enhancement factor exhibits distinct behaviors in the Type-X and Type-Y 2HDMs. This feature provides a promising opportunity to discriminate between the two scenarios through precision measurements of double Higgs production at future multi–TeV colliders. Furthermore, we perform a detailed scan of the cross sections for both CP-odd and CP-even Higgs pair production over the viable parameter spaces of the Type-X and Type-Y 2HDMs. In the Type-Y scenario, at a center-of-mass (CoM) energy $ \sqrt{s} = 10\; \text{TeV} $ and an integrated luminosity of $ {\cal{L}} = 10000\; \text{fb}^{-1} $, both CP-odd and CP-even Higgs pair production in the $ t\bar{t}b\bar{b} $ final state, with subsequent top-quark decays into leptons and bottom quarks, can be probed with a statistical significance exceeding the $ 2\sigma $ level at several viable parameter points.
2026, 50(7): 073108. doi: 10.1088/1674-1137/ae62fc
Abstract:
We study the equation of state (EoS) of QCD matter in a bottom-up holographic setup that combines an Einstein-Maxwell-dilaton (EMD) sector with an improved Karch-Katz-Son-Stephanov (KKSS) flavor action. In the probe approximation, we perform an inverse reconstruction of the model functions by parameterizing them with neural networks and solving the EMD equations via a differentiable ODE solver (a neural ODE framework), calibrating the model to a reference thermodynamic table for $(2+1)$-flavor QCD at finite temperature and finite baryon chemical potential. The reconstructed model functions are then parameterized and kept fixed across thermodynamic states. Next, viewing the EMD sector as an effective description of pure Yang-Mills theory, we fix its parameters by fitting the $\mu_B=0$ lattice pure-glue EoS using a hybrid optimization strategy. Finally, we go beyond the probe limit and solve the coupled EMD+KKSS equations with back-reaction, using the pure-glue-calibrated EMD sector as a fixed input and varying the KKSS couplings to compare with the $\mu_B=0$ two-flavor lattice EoS. We find a visible mismatch and a high-temperature behavior in which the back-reacted dimensionless ratios approach a nearly $\beta_1$-insensitive plateau close to the pure-glue baseline, providing a simple structural diagnostic for the present flavor-sector truncation.
We study the equation of state (EoS) of QCD matter in a bottom-up holographic setup that combines an Einstein-Maxwell-dilaton (EMD) sector with an improved Karch-Katz-Son-Stephanov (KKSS) flavor action. In the probe approximation, we perform an inverse reconstruction of the model functions by parameterizing them with neural networks and solving the EMD equations via a differentiable ODE solver (a neural ODE framework), calibrating the model to a reference thermodynamic table for $(2+1)$-flavor QCD at finite temperature and finite baryon chemical potential. The reconstructed model functions are then parameterized and kept fixed across thermodynamic states. Next, viewing the EMD sector as an effective description of pure Yang-Mills theory, we fix its parameters by fitting the $\mu_B=0$ lattice pure-glue EoS using a hybrid optimization strategy. Finally, we go beyond the probe limit and solve the coupled EMD+KKSS equations with back-reaction, using the pure-glue-calibrated EMD sector as a fixed input and varying the KKSS couplings to compare with the $\mu_B=0$ two-flavor lattice EoS. We find a visible mismatch and a high-temperature behavior in which the back-reacted dimensionless ratios approach a nearly $\beta_1$-insensitive plateau close to the pure-glue baseline, providing a simple structural diagnostic for the present flavor-sector truncation.
2026, 50(7): 073105. doi: 10.1088/1674-1137/ae5f08
Abstract:
In this work, we investigate the production and decay of molecular states with quark content $cc\bar c\bar q$ and $J^P=1^+$ using a phenomenological analysis and an effective Lagrangian approach. Based on an SU(3) flavor-symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of ${\eta_c D^*}$ and ${J/\psi D^*}$. Our results indicate that the production branching ratio in $B_c$ decays is sizable: it can be of order $10^{-4}$ for the molecular configuration ${{\eta}_cD^*}$ and $10^{-5}$ for the molecule ${J/\psi D^*}$. In addition, we find that the decay widths of the two molecular configurations ${{\eta}_cD^*}$ and ${J/\psi D^*}$ are not significant, at the level of ${\cal{O}}$($\text{MeV}$).
In this work, we investigate the production and decay of molecular states with quark content $cc\bar c\bar q$ and $J^P=1^+$ using a phenomenological analysis and an effective Lagrangian approach. Based on an SU(3) flavor-symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of ${\eta_c D^*}$ and ${J/\psi D^*}$. Our results indicate that the production branching ratio in $B_c$ decays is sizable: it can be of order $10^{-4}$ for the molecular configuration ${{\eta}_cD^*}$ and $10^{-5}$ for the molecule ${J/\psi D^*}$. In addition, we find that the decay widths of the two molecular configurations ${{\eta}_cD^*}$ and ${J/\psi D^*}$ are not significant, at the level of ${\cal{O}}$($\text{MeV}$).
2026, 50(7): 073003. doi: 10.1088/1674-1137/ae643e
Abstract:
We report stronger evidence for the $X(7200)$ state and markedly improved measurements of the $X(6900)$ resonance parameters based on a combined analysis of the di-$J/\psi$ mass spectrum using published data from LHCb, ATLAS, and CMS. Through simultaneous fits to the datasets from all three experiments, we observe the $X(6900)$ with overwhelming significance ($>12\sigma$) and determine its mass and width with improved precision. For the $X(7200)$, we find consistent signals across multiple interference models, with significances ranging from $3.7\sigma$ to $6.6\sigma$; in the best-fit model (the CMS three-resonance scheme), the significance reaches $6.6\sigma$, providing substantially stronger evidence for this state. Our results underscore the essential role of interference effects in fully charmed tetraquark spectroscopy and offer new constraints on their production mechanisms at the LHC.
We report stronger evidence for the $X(7200)$ state and markedly improved measurements of the $X(6900)$ resonance parameters based on a combined analysis of the di-$J/\psi$ mass spectrum using published data from LHCb, ATLAS, and CMS. Through simultaneous fits to the datasets from all three experiments, we observe the $X(6900)$ with overwhelming significance ($>12\sigma$) and determine its mass and width with improved precision. For the $X(7200)$, we find consistent signals across multiple interference models, with significances ranging from $3.7\sigma$ to $6.6\sigma$; in the best-fit model (the CMS three-resonance scheme), the significance reaches $6.6\sigma$, providing substantially stronger evidence for this state. Our results underscore the essential role of interference effects in fully charmed tetraquark spectroscopy and offer new constraints on their production mechanisms at the LHC.
2026, 50(7): 073001. doi: 10.1088/1674-1137/ae5c70
Abstract:
A sensitivity study of $ \bar{K}_1(1270) $ decay-mode measurements is performed using semileptonic D-meson decays. The BESIII experiment is used as a case study, in which a simultaneous analysis of $ \bar{K}_1(1270) $ decays to the four three-body final states $ K^-\pi^+\pi^- $, $ K^-\pi^+\pi^0 $, $ K_S^0\pi^+\pi^- $, and $ K_S^0\pi^-\pi^0 $ is presented, and a model-independent determination of $ {\cal{B}}(\bar{K}_1(1270)\to \bar K\pi\pi) $ that does not require detailed knowledge of intermediate resonant contributions is proposed.
A sensitivity study of $ \bar{K}_1(1270) $ decay-mode measurements is performed using semileptonic D-meson decays. The BESIII experiment is used as a case study, in which a simultaneous analysis of $ \bar{K}_1(1270) $ decays to the four three-body final states $ K^-\pi^+\pi^- $, $ K^-\pi^+\pi^0 $, $ K_S^0\pi^+\pi^- $, and $ K_S^0\pi^-\pi^0 $ is presented, and a model-independent determination of $ {\cal{B}}(\bar{K}_1(1270)\to \bar K\pi\pi) $ that does not require detailed knowledge of intermediate resonant contributions is proposed.
2026, 50(7): 073101. doi: 10.1088/1674-1137/ae5884
Abstract:
Femtoscopy offers a sensitive probe of hadron emission sources and hadronic interactions. In this study, we examine relativistic corrections to scattering phase shifts and correlation functions using the two-body Dirac equation framework. We analyze the impact of the Darwin term and spin-dependent potentials, showing that these relativistic effects, especially spin-related interactions, significantly enhance the proton-proton correlation function. Our findings emphasize the necessity of including relativistic corrections for precise femtoscopic analyses.
Femtoscopy offers a sensitive probe of hadron emission sources and hadronic interactions. In this study, we examine relativistic corrections to scattering phase shifts and correlation functions using the two-body Dirac equation framework. We analyze the impact of the Darwin term and spin-dependent potentials, showing that these relativistic effects, especially spin-related interactions, significantly enhance the proton-proton correlation function. Our findings emphasize the necessity of including relativistic corrections for precise femtoscopic analyses.
2026, 50(7): 074102. doi: 10.1088/1674-1137/ae5ef4
Abstract:
This paper addresses a long-standing problem in astrophysics—the origin of the solar system abundance of the proton-rich isotope $ ^{94}\text{Mo} $ by proposing a valuable novel mechanism. The main contribution of this work is that it challenges the traditional view of "$ ^{94}\text{Mo} $ as a pure p-process nuclide". For the first time, it demonstrates that within the s-process environment of low-mass AGB stars, a new s-process path ($ ^{93}\text{Zr} \rightarrow $ $ ^{93}\text{Nb} $ $ \rightarrow ^{94}\text{Nb} \rightarrow ^{94}\text{Mo} $) for producing $ ^{94}\text{Mo} $ can be opened, enabled by the significant enhancement of the effective decay rates of $ ^{93}\text{Zr} $ and $ ^{94}\text{Nb} $ due to the high-temperature astrophysical environment. The results show that this s-process channel can contribute up to a maximum of approximately 10.6% to the solar system abundance of $ ^{94}\text{Mo} $. This work provides a new s-process perspective on the origin of $ ^{94}\text{Mo} $ and has implications for reevaluating the sources of other "shielded" p-nuclei.
This paper addresses a long-standing problem in astrophysics—the origin of the solar system abundance of the proton-rich isotope $ ^{94}\text{Mo} $ by proposing a valuable novel mechanism. The main contribution of this work is that it challenges the traditional view of "$ ^{94}\text{Mo} $ as a pure p-process nuclide". For the first time, it demonstrates that within the s-process environment of low-mass AGB stars, a new s-process path ($ ^{93}\text{Zr} \rightarrow $ $ ^{93}\text{Nb} $ $ \rightarrow ^{94}\text{Nb} \rightarrow ^{94}\text{Mo} $) for producing $ ^{94}\text{Mo} $ can be opened, enabled by the significant enhancement of the effective decay rates of $ ^{93}\text{Zr} $ and $ ^{94}\text{Nb} $ due to the high-temperature astrophysical environment. The results show that this s-process channel can contribute up to a maximum of approximately 10.6% to the solar system abundance of $ ^{94}\text{Mo} $. This work provides a new s-process perspective on the origin of $ ^{94}\text{Mo} $ and has implications for reevaluating the sources of other "shielded" p-nuclei.
2026, 50(7): 074103. doi: 10.1088/1674-1137/ae62ff
Abstract:
We report a systematic study and predictions of medium-induced modifications in charge-dependent jet substructure using the charge-weighted Energy-Energy Correlators (EEC) in 0−10% central Pb+Pb collisions at $ \sqrt{s_{NN}} = 5.02\ {\rm{TeV}} $. Charged-hadron jets, as well as flavor-separated quark- and gluon-initiated jets with momenta of 40−60 GeV and R = 0.4, are analyzed. The ratio of the charge-weighted distribution to the inclusive EEC, which reflects the magnitude of charge correlations, is uniformly negative, demonstrating the dominance of opposite-charge pairs due to charge conservation. A clear flavor dependence is observed: gluon-initiated jets exhibit weaker opposite-charge correlations in the transition and small-RL regions than quark-initiated jets, but stronger opposite-charge correlations at larger RL. In Pb+Pb collisions, the A+A-to-p+p ratio for charge correlations exhibits a universal, flavor-independent pattern: jet quenching enhances opposite-charge correlations at small angles while suppressing them at large angles, leading to a steeper RL dependence of charge correlations in A+A and indicating more rapid decorrelation as RL increases. A distinctive V-shaped modification, together with a plateau-like enhancement, appears in the transition and small-RL regions, independent of jet flavor. By factorizing the EEC into the charged-hadron–pair multiplicity and the average energy-weighting distribution, we identify an enhanced but smeared energy weighting of opposite-charge pairs at small RL as the origin of this modification. These observations indicate that medium-induced broadening of parton-level splittings in the hot, dense medium dissociates the charged di-hadron pairs (such as $ \pi^+\pi^{-} $) present in p+p collisions. The plateau-like enhancement of charge correlations is also found to be unrelated to selection-bias effects.
We report a systematic study and predictions of medium-induced modifications in charge-dependent jet substructure using the charge-weighted Energy-Energy Correlators (EEC) in 0−10% central Pb+Pb collisions at $ \sqrt{s_{NN}} = 5.02\ {\rm{TeV}} $. Charged-hadron jets, as well as flavor-separated quark- and gluon-initiated jets with momenta of 40−60 GeV and R = 0.4, are analyzed. The ratio of the charge-weighted distribution to the inclusive EEC, which reflects the magnitude of charge correlations, is uniformly negative, demonstrating the dominance of opposite-charge pairs due to charge conservation. A clear flavor dependence is observed: gluon-initiated jets exhibit weaker opposite-charge correlations in the transition and small-RL regions than quark-initiated jets, but stronger opposite-charge correlations at larger RL. In Pb+Pb collisions, the A+A-to-p+p ratio for charge correlations exhibits a universal, flavor-independent pattern: jet quenching enhances opposite-charge correlations at small angles while suppressing them at large angles, leading to a steeper RL dependence of charge correlations in A+A and indicating more rapid decorrelation as RL increases. A distinctive V-shaped modification, together with a plateau-like enhancement, appears in the transition and small-RL regions, independent of jet flavor. By factorizing the EEC into the charged-hadron–pair multiplicity and the average energy-weighting distribution, we identify an enhanced but smeared energy weighting of opposite-charge pairs at small RL as the origin of this modification. These observations indicate that medium-induced broadening of parton-level splittings in the hot, dense medium dissociates the charged di-hadron pairs (such as $ \pi^+\pi^{-} $) present in p+p collisions. The plateau-like enhancement of charge correlations is also found to be unrelated to selection-bias effects.
2026, 50(8): 084101. doi: 10.1088/1674-1137/ae6b21
Abstract:
We investigate the impacts of strong magnetic fields on neutrino transport in core-collapse supernovae (CCSNe) using the leakage scheme. The magnetic field quantizes the momentum of electrons and positrons, resulting in the modification of weak-interaction cross sections and the chemical potentials of electrons and positrons. We derive a formula for the neutrino leakage scheme, including these two impacts, and perform 1D CCSN simulations with $ {\tt{GR1D}}$. Magnetic field strengths from $ 10^{16} $ G to $ 10^{17} $ G were applied during the postbounce phase. The results show that neutrino opacities are enhanced due to the amplified interaction rates, with stronger effects on antineutrinos. This leads to larger neutrinosphere radii, longer neutrino trapping timescales, reduced peak luminosities, and delayed peak energies.
We investigate the impacts of strong magnetic fields on neutrino transport in core-collapse supernovae (CCSNe) using the leakage scheme. The magnetic field quantizes the momentum of electrons and positrons, resulting in the modification of weak-interaction cross sections and the chemical potentials of electrons and positrons. We derive a formula for the neutrino leakage scheme, including these two impacts, and perform 1D CCSN simulations with $ {\tt{GR1D}}$. Magnetic field strengths from $ 10^{16} $ G to $ 10^{17} $ G were applied during the postbounce phase. The results show that neutrino opacities are enhanced due to the amplified interaction rates, with stronger effects on antineutrinos. This leads to larger neutrinosphere radii, longer neutrino trapping timescales, reduced peak luminosities, and delayed peak energies.
2026, 50(8): 084104. doi: 10.1088/1674-1137/ae662d
Abstract:
We explore the interplay between the magnetic field and non-extensivity in shaping the complex heavy-quark potential in the quark-gluon plasma via the dielectric permittivity. Within the real-time formalism with hard-thermal-loop resummation, we determine the non-extensive corrections to the gluon self-energy and the resummed gluon propagator in the Keldysh representation, and we apply these results to compute the medium's dielectric permittivity. Our study shows that increases in the magnetic field and in non-extensivity enhance screening and flatten the real part of the potential, whereas they affect the imaginary part in opposite ways. When the gluon-loop contribution to the gluon self-energy is excluded, the imaginary part of the potential exhibits pronounced anisotropy in the presence of a magnetic field, especially at small quark-antiquark separations, while non-extensivity can weaken this anisotropy. When the gluon-loop contribution is included, the degree of anisotropy of the imaginary part of the potential is largely reduced and becomes nearly insensitive to non-extensive effects. These results pave the way for further studies of the properties of heavy quarkonia in a magnetized, non-extensive quark-gluon plasma.
We explore the interplay between the magnetic field and non-extensivity in shaping the complex heavy-quark potential in the quark-gluon plasma via the dielectric permittivity. Within the real-time formalism with hard-thermal-loop resummation, we determine the non-extensive corrections to the gluon self-energy and the resummed gluon propagator in the Keldysh representation, and we apply these results to compute the medium's dielectric permittivity. Our study shows that increases in the magnetic field and in non-extensivity enhance screening and flatten the real part of the potential, whereas they affect the imaginary part in opposite ways. When the gluon-loop contribution to the gluon self-energy is excluded, the imaginary part of the potential exhibits pronounced anisotropy in the presence of a magnetic field, especially at small quark-antiquark separations, while non-extensivity can weaken this anisotropy. When the gluon-loop contribution is included, the degree of anisotropy of the imaginary part of the potential is largely reduced and becomes nearly insensitive to non-extensive effects. These results pave the way for further studies of the properties of heavy quarkonia in a magnetized, non-extensive quark-gluon plasma.
2026, 50(8): 084103. doi: 10.1088/1674-1137/ae6633
Abstract:
The proton drip-line marks the limiting location where the proton binding energy vanishes. Ground-state proton emission is a signature of having crossed this drip line. We determine the locations of the proton drip-line for odd-Z nuclei along isotopic chains toward the neutron-deficient side based on experimentally measured nuclear masses and proton emission half-lives. The odd-odd characteristics and a plateau at $N = Z$ in the region $33 \leq Z \leq 47$ of proton drip-line nuclei are presented. In addition, the proper inclusion of the angular momentum l of the emitted proton is essential for accurately calculating the proton emission energy from half-life.
The proton drip-line marks the limiting location where the proton binding energy vanishes. Ground-state proton emission is a signature of having crossed this drip line. We determine the locations of the proton drip-line for odd-Z nuclei along isotopic chains toward the neutron-deficient side based on experimentally measured nuclear masses and proton emission half-lives. The odd-odd characteristics and a plateau at $N = Z$ in the region $33 \leq Z \leq 47$ of proton drip-line nuclei are presented. In addition, the proper inclusion of the angular momentum l of the emitted proton is essential for accurately calculating the proton emission energy from half-life.
2026, 50(8): 084102. doi: 10.1088/1674-1137/ae6631
Abstract:
We develop a framework for calculating nucleon-deuteron scattering using the Faddeev equations, employing strict perturbation theory to treat subleading interactions in chiral effective field theory (ChEFT). Rather than evaluating the distorted-wave expansion directly, our approach solves a hierarchy of integral equations to obtain subleading scattering amplitudes. We benchmark the method against the wave-packet continuum discretization. This framework benefits from the fact that renormalization-group-invariant chiral forces involve only a limited number of two-body partial waves at leading order. We use it to calculate differential cross sections and analyzing powers for nucleon-deuteron elastic scattering up to next-to-leading order.
We develop a framework for calculating nucleon-deuteron scattering using the Faddeev equations, employing strict perturbation theory to treat subleading interactions in chiral effective field theory (ChEFT). Rather than evaluating the distorted-wave expansion directly, our approach solves a hierarchy of integral equations to obtain subleading scattering amplitudes. We benchmark the method against the wave-packet continuum discretization. This framework benefits from the fact that renormalization-group-invariant chiral forces involve only a limited number of two-body partial waves at leading order. We use it to calculate differential cross sections and analyzing powers for nucleon-deuteron elastic scattering up to next-to-leading order.
2026, 50(7): 074104. doi: 10.1088/1674-1137/ae5ef5
Abstract:
Identifying the thermodynamic conditions marking the onset of fission cycling is crucial for modeling heavy-element production in the r-process. In this work, we develop a framework to determine this onset over the $ (T_9, n_n) $ plane. We define a heavy-region condition band near $ N \approx 184 $ and construct an equilibrium path band based on the effective neutron separation energy $ S_n^{0}(T_9, n_n) $. We then compare the lifetimes of neutron-induced fission and β-decay for nuclei with $ 94 \leqslant Z \leqslant 106 $. Within this framework, we construct a continuous map of actinide nuclei along the equilibrium path band, identifying where neutron-induced fission first overtakes β-decay. We find that, with increasing temperature and neutron density, the onset shifts toward nuclei with lower proton number (Z) and smaller mass number (A), transitioning from the Es-Cf region to the Am region. These results provide a quantitative benchmark for identifying the conditions under which fission cycling occurs in heavy r-process environments.
Identifying the thermodynamic conditions marking the onset of fission cycling is crucial for modeling heavy-element production in the r-process. In this work, we develop a framework to determine this onset over the $ (T_9, n_n) $ plane. We define a heavy-region condition band near $ N \approx 184 $ and construct an equilibrium path band based on the effective neutron separation energy $ S_n^{0}(T_9, n_n) $. We then compare the lifetimes of neutron-induced fission and β-decay for nuclei with $ 94 \leqslant Z \leqslant 106 $. Within this framework, we construct a continuous map of actinide nuclei along the equilibrium path band, identifying where neutron-induced fission first overtakes β-decay. We find that, with increasing temperature and neutron density, the onset shifts toward nuclei with lower proton number (Z) and smaller mass number (A), transitioning from the Es-Cf region to the Am region. These results provide a quantitative benchmark for identifying the conditions under which fission cycling occurs in heavy r-process environments.
2026, 50(7): 074001. doi: 10.1088/1674-1137/ae5dae
Abstract:
In the present study, new measurements of differential and angle-integrated cross sections for the 10B(n, α1)7Li*, 10B(n, α0)7Li, and 10B(n, α)7Li reactions were performed at the CSNS Back-n white neutron source. The Light-charged Particle Detector Array (LPDA) system was used to detect charged particles. The 6Li-Si monitor was employed to measure the neutron flux. The differential cross sections for the 10B(n, α)7Li reaction were obtained from 20.1° to 158.3° (13 angles) in the neutron energy region from 0.3 eV to 3.0 MeV (70 energy points). The differential cross sections for the 10B(n, α0)7Li and 10B(n, α1)7Li* reactions were also obtained at the same angular positions in the neutron energy region from 0.3 eV to 1.0 MeV (65 energy points). Fitting with the Legendre polynomial series, the angle-integrated cross sections of these three reactions were obtained through integration. The experimental data for these three reactions across such a wide neutron energy range are valuable references for future nuclear data evaluations.
In the present study, new measurements of differential and angle-integrated cross sections for the 10B(n, α1)7Li*, 10B(n, α0)7Li, and 10B(n, α)7Li reactions were performed at the CSNS Back-n white neutron source. The Light-charged Particle Detector Array (LPDA) system was used to detect charged particles. The 6Li-Si monitor was employed to measure the neutron flux. The differential cross sections for the 10B(n, α)7Li reaction were obtained from 20.1° to 158.3° (13 angles) in the neutron energy region from 0.3 eV to 3.0 MeV (70 energy points). The differential cross sections for the 10B(n, α0)7Li and 10B(n, α1)7Li* reactions were also obtained at the same angular positions in the neutron energy region from 0.3 eV to 1.0 MeV (65 energy points). Fitting with the Legendre polynomial series, the angle-integrated cross sections of these three reactions were obtained through integration. The experimental data for these three reactions across such a wide neutron energy range are valuable references for future nuclear data evaluations.
2026, 50(7): 074101. doi: 10.1088/1674-1137/ae5807
Abstract:
Chromium (Cr) serves as an indispensable structural material in accelerator-driven systems (ADSs) and Generation IV reactors, where the precision of its neutron reaction data is important for ensuring reactor safety and operational reliability. However, significant discrepancies persist in both experimental data and evaluations for key reaction channels, such as $(n, p)$ and $(n, 2n)$, across the chromium isotopes ${}^{50,52,53,54}{\rm{Cr}}$. This paper presents a novel evaluation and validation of neutron reaction data for these isotopes at incident energies below 200 MeV, incorporating 571 experimental datasets from EXFOR covering cross sections, angular distributions, energy spectra, and double - differential cross sections. The newly evaluated data provide more reliable key cross sections: the ${}^{52}{\rm{Cr}}(n,2n)$ cross section resolves discrepancies and supports the data of Liskien et al.; the ${}^{52}{\rm{Cr}}(n, p)$ cross-section aligns well with natural chromium data across all energies and is validated by competition analysis. The results accurately replicate double differential cross sections and energy spectra, with neutron emission spectra matching experimental peaks and charged - particle spectra agreeing with measurements for ${}^{50,52}{\rm{Cr}}$. Moreover, the abundance - weighted sum of $(n, p)$ and $(n, 2n)$ cross sections for chromium isotopes agrees well with natural chromium data, confirming systematic consistency. All evaluations are validated using 62 ICSBEP 2014 benchmark facilities with $ k_{{\rm{eff}}}$ sensitivity to chromium neutron data > 1%. For the PMI002_01 experiment, the calculated $ k_{{\rm{eff}}}$ value decreased by $\sim 1000$ pcm relative to the CENDL - 3.2 results, improving agreement with the benchmark; in the OKTAVIAN shielding benchmark, the neutron leakage spectrum also reproduced experiments well.
Chromium (Cr) serves as an indispensable structural material in accelerator-driven systems (ADSs) and Generation IV reactors, where the precision of its neutron reaction data is important for ensuring reactor safety and operational reliability. However, significant discrepancies persist in both experimental data and evaluations for key reaction channels, such as $(n, p)$ and $(n, 2n)$, across the chromium isotopes ${}^{50,52,53,54}{\rm{Cr}}$. This paper presents a novel evaluation and validation of neutron reaction data for these isotopes at incident energies below 200 MeV, incorporating 571 experimental datasets from EXFOR covering cross sections, angular distributions, energy spectra, and double - differential cross sections. The newly evaluated data provide more reliable key cross sections: the ${}^{52}{\rm{Cr}}(n,2n)$ cross section resolves discrepancies and supports the data of Liskien et al.; the ${}^{52}{\rm{Cr}}(n, p)$ cross-section aligns well with natural chromium data across all energies and is validated by competition analysis. The results accurately replicate double differential cross sections and energy spectra, with neutron emission spectra matching experimental peaks and charged - particle spectra agreeing with measurements for ${}^{50,52}{\rm{Cr}}$. Moreover, the abundance - weighted sum of $(n, p)$ and $(n, 2n)$ cross sections for chromium isotopes agrees well with natural chromium data, confirming systematic consistency. All evaluations are validated using 62 ICSBEP 2014 benchmark facilities with $ k_{{\rm{eff}}}$ sensitivity to chromium neutron data > 1%. For the PMI002_01 experiment, the calculated $ k_{{\rm{eff}}}$ value decreased by $\sim 1000$ pcm relative to the CENDL - 3.2 results, improving agreement with the benchmark; in the OKTAVIAN shielding benchmark, the neutron leakage spectrum also reproduced experiments well.
2026, 50(8): 085101. doi: 10.1088/1674-1137/ae662e
Abstract:
This paper primarily investigates the optical properties of two minimal deformations of the Schwarzschild black hole—the Kazakov-Solodukhin and Ghosh-Kumar black holes—under different accretion models. The event horizon, photon sphere, and critical impact parameter of the former increase relative to the Schwarzschild case, whereas those of the latter decrease. Data from the Event Horizon Telescope Collaboration are used to constrain the parameter ranges of the two black holes. Under spherical accretion, the quantum correction of the Kazakov-Solodukhin black hole enlarges the black hole shadow and reduces the integrated intensity, while the shadow of the magnetically charged Ghosh-Kumar black hole shrinks and the integrated intensity increases. The black hole’s shadow radius is independent of the choice of spherical accretion model. For an optically and geometrically thin accretion disk, the integrated intensity is dominated by direct emission, with photon-ring and lensed-ring contributions being negligible. In addition, the photon and lensed rings of the Kazakov-Solodukhin black hole are narrower, whereas those of the Ghosh-Kumar black hole are broader. Whereas the Kazakov-Solodukhin black hole is brighter, the Ghosh-Kumar black hole is dimmer. Additionally, bringing the disk closer to the black hole yields a smaller shadow radius. This paper proposes a method to distinguish different black holes within a specific thin-disk model.
This paper primarily investigates the optical properties of two minimal deformations of the Schwarzschild black hole—the Kazakov-Solodukhin and Ghosh-Kumar black holes—under different accretion models. The event horizon, photon sphere, and critical impact parameter of the former increase relative to the Schwarzschild case, whereas those of the latter decrease. Data from the Event Horizon Telescope Collaboration are used to constrain the parameter ranges of the two black holes. Under spherical accretion, the quantum correction of the Kazakov-Solodukhin black hole enlarges the black hole shadow and reduces the integrated intensity, while the shadow of the magnetically charged Ghosh-Kumar black hole shrinks and the integrated intensity increases. The black hole’s shadow radius is independent of the choice of spherical accretion model. For an optically and geometrically thin accretion disk, the integrated intensity is dominated by direct emission, with photon-ring and lensed-ring contributions being negligible. In addition, the photon and lensed rings of the Kazakov-Solodukhin black hole are narrower, whereas those of the Ghosh-Kumar black hole are broader. Whereas the Kazakov-Solodukhin black hole is brighter, the Ghosh-Kumar black hole is dimmer. Additionally, bringing the disk closer to the black hole yields a smaller shadow radius. This paper proposes a method to distinguish different black holes within a specific thin-disk model.
2026, 50(7): 075107. doi: 10.1088/1674-1137/ae66d2
Abstract:
This article delves into the observational properties of a Schwarzschild-like black hole (BH). Initially, the research provides a succinct examination of the spacetime geometry and the configuration of its horizon. Furthermore, we study the photon dynamics around the Schwarzschild-like BH in the presence of plasma using the Hamiltonian formalism. We found that the photon sphere radii increase under the influence of plasma frequency and vice versa for the spacetime parameters. Further exploration is dedicated to understanding how plasma affects the shadow of the BH, and we find that the radius of the BH shadow shrinks with the rise of the ξ parameter and plasma frequency. We then turn to constraining the spacetime parameters and the plasma frequency by using the observational data released by the Event Horizon Telescope (EHT) collaboration for M87* and Sgr A*. Additionally, the research scrutinizes the phenomenon of gravitational weak lensing in the vicinity of a Schwarzschild-like BH, considering both uniform and non-uniform plasma scenarios. The outcomes demonstrate that the angle of deflection increases under the influence of a uniform plasma frequency, whereas the opposite is true for non-uniform plasma. In both scenarios, a rise in the spacetime parameters results in a decrease in the deflection angle. Finally, we investigate the magnification of the gravitationally lensed image. The effect of the spacetime parameters and plasma frequencies on the total magnification is the same as in the deflection angles.
This article delves into the observational properties of a Schwarzschild-like black hole (BH). Initially, the research provides a succinct examination of the spacetime geometry and the configuration of its horizon. Furthermore, we study the photon dynamics around the Schwarzschild-like BH in the presence of plasma using the Hamiltonian formalism. We found that the photon sphere radii increase under the influence of plasma frequency and vice versa for the spacetime parameters. Further exploration is dedicated to understanding how plasma affects the shadow of the BH, and we find that the radius of the BH shadow shrinks with the rise of the ξ parameter and plasma frequency. We then turn to constraining the spacetime parameters and the plasma frequency by using the observational data released by the Event Horizon Telescope (EHT) collaboration for M87* and Sgr A*. Additionally, the research scrutinizes the phenomenon of gravitational weak lensing in the vicinity of a Schwarzschild-like BH, considering both uniform and non-uniform plasma scenarios. The outcomes demonstrate that the angle of deflection increases under the influence of a uniform plasma frequency, whereas the opposite is true for non-uniform plasma. In both scenarios, a rise in the spacetime parameters results in a decrease in the deflection angle. Finally, we investigate the magnification of the gravitationally lensed image. The effect of the spacetime parameters and plasma frequencies on the total magnification is the same as in the deflection angles.
2026, 50(7): 075106. doi: 10.1088/1674-1137/ae643d
Abstract:
We investigate the intrinsic distributions of key Gamma-Ray Burst (GRB) parameters that are essential to understanding the physics of their central engines, radiation mechanisms, and cosmological evolution. Using our independently developed GodEyes Monte Carlo framework, we generate synthetic long-GRB samples tailored to the Swift/BAT detector and explicitly incorporate instrumental selection effects. In particular, we account for the loss of low-peak-flux events due to the detector's sensitivity threshold, thereby enabling consistent comparisons between theoretical models and observations. Our results constrain the intrinsic distributions of several fundamental properties, including redshift, peak luminosity, isotropic energy, and related quantities. We find that the inferred intrinsic distribution of the spectral index $ \alpha^{\rm{PL}}$ deviates significantly from that derived from the observed sample. Moreover, we identify an excess of low-luminosity GRBs and show that a triple power-law luminosity function provides a substantially improved description of the data. By establishing a complete forward-modeling and validation pipeline, this work underscores the importance of accounting for observational biases and lays the groundwork for future tests with upcoming detections of faint and optically dark GRBs.
We investigate the intrinsic distributions of key Gamma-Ray Burst (GRB) parameters that are essential to understanding the physics of their central engines, radiation mechanisms, and cosmological evolution. Using our independently developed GodEyes Monte Carlo framework, we generate synthetic long-GRB samples tailored to the Swift/BAT detector and explicitly incorporate instrumental selection effects. In particular, we account for the loss of low-peak-flux events due to the detector's sensitivity threshold, thereby enabling consistent comparisons between theoretical models and observations. Our results constrain the intrinsic distributions of several fundamental properties, including redshift, peak luminosity, isotropic energy, and related quantities. We find that the inferred intrinsic distribution of the spectral index $ \alpha^{\rm{PL}}$ deviates significantly from that derived from the observed sample. Moreover, we identify an excess of low-luminosity GRBs and show that a triple power-law luminosity function provides a substantially improved description of the data. By establishing a complete forward-modeling and validation pipeline, this work underscores the importance of accounting for observational biases and lays the groundwork for future tests with upcoming detections of faint and optically dark GRBs.
2026, 50(7): 075104. doi: 10.1088/1674-1137/ae6630
Abstract:
Gravitational-wave astronomy offers a promising opportunity to directly observe scalar-induced gravitational waves originating from the early universe. Experiments—including ground-based interferometers such as LIGO and Virgo, and pulsar timing arrays (PTAs) based on facilities such as FAST and SKA—are poised to significantly enhance sensitivity to these signals. In this paper, we combine Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillation (BAO) datasets with upper or lower limits on the stochastic gravitational-wave background provided by FAST or SKA to constrain scalar-induced gravitational waves. To provide a comprehensive forecast, we consider two scenarios at a given frequency: one in which FAST or SKA does not detect scalar-induced gravitational waves, thereby setting an upper limit on the fractional energy density; and another in which these waves are detected, thus establishing a lower limit. In the ΛCDM+r model, the scalar spectral index of the power-law power spectrum is constrained to $ n_s=0.9598^{+0.0013}_{-0.0009} $ from the combination of CMB+BAO+SKA datasets in the upper-limit scenario where scalar-induced gravitational waves propagate at the speed of light. The constraint shifts to $ n_s = 0.9697\pm{0.0033} $ in the lower-limit scenario. Compared with the constraint from the combination of CMB+BAO datasets, the scalar spectral index $ n_s $ in the upper-limit scenario exhibits significant changes, which could serve as an indicator of scalar-induced gravitational waves. In the ΛCDM+$ \alpha_s $+r and ΛCDM+$ \alpha_s $+$ \beta_s $+r models, the running of the scalar spectral index $ \alpha_s $ and the running of the running $ \beta_s $ also show notable variations, suggesting potential indicators. The numerical findings clearly demonstrate the impact of the upper and lower limits provided by FAST or SKA.
Gravitational-wave astronomy offers a promising opportunity to directly observe scalar-induced gravitational waves originating from the early universe. Experiments—including ground-based interferometers such as LIGO and Virgo, and pulsar timing arrays (PTAs) based on facilities such as FAST and SKA—are poised to significantly enhance sensitivity to these signals. In this paper, we combine Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillation (BAO) datasets with upper or lower limits on the stochastic gravitational-wave background provided by FAST or SKA to constrain scalar-induced gravitational waves. To provide a comprehensive forecast, we consider two scenarios at a given frequency: one in which FAST or SKA does not detect scalar-induced gravitational waves, thereby setting an upper limit on the fractional energy density; and another in which these waves are detected, thus establishing a lower limit. In the ΛCDM+r model, the scalar spectral index of the power-law power spectrum is constrained to $ n_s=0.9598^{+0.0013}_{-0.0009} $ from the combination of CMB+BAO+SKA datasets in the upper-limit scenario where scalar-induced gravitational waves propagate at the speed of light. The constraint shifts to $ n_s = 0.9697\pm{0.0033} $ in the lower-limit scenario. Compared with the constraint from the combination of CMB+BAO datasets, the scalar spectral index $ n_s $ in the upper-limit scenario exhibits significant changes, which could serve as an indicator of scalar-induced gravitational waves. In the ΛCDM+$ \alpha_s $+r and ΛCDM+$ \alpha_s $+$ \beta_s $+r models, the running of the scalar spectral index $ \alpha_s $ and the running of the running $ \beta_s $ also show notable variations, suggesting potential indicators. The numerical findings clearly demonstrate the impact of the upper and lower limits provided by FAST or SKA.
2026, 50(7): 075105. doi: 10.1088/1674-1137/ae5ef3
Abstract:
Since the Event Horizon Telescope (EHT) collaboration released horizon-scale images of the supermassive black holes Sgr A* and M87*, a new observational window for probing black hole spacetimes in the strong-gravity regime has opened. As an important class of Kerr black hole mimickers, rotating Simpson-Visser (SV) black holes exhibit a degeneracy with Kerr black holes in terms of shadow size, making them difficult to distinguish using shadow observations alone. Motivated by this issue, we present a systematic investigation of the radiative properties and optical appearance of rotating SV black holes surrounded by a thin accretion disk, focusing on the influence of the regularization parameter g on the relevant observables. The results show that although the kinematic quantities and the location of the innermost stable circular orbit (ISCO) depend on the regularization parameter g, the radiative efficiency of the rotating SV black hole is the same as that of its Kerr counterpart. Within the Novikov-Thorne thin-disk model, we study the radiative flux, effective temperature, and spectral luminosity; adopting observational parameters relevant to Sgr A* and M87*, we compute concrete examples for rotating SV black holes and compare them with those for Kerr black holes. The results show that the parameter g suppresses the maximum values of these quantities. In addition, using a backward ray-tracing technique, we numerically simulate the optical appearance of rotating SV black holes and analyze the corresponding intensity images, redshift, and observed flux distributions. Our results indicate that these quantities are sensitive to g. In particular, as g increases, the observed intensity is significantly suppressed, and the photon ring region exhibits a remarkable increase in width. Our findings suggest that accretion-disk-related observables may provide important avenues to distinguish between rotating SV black holes and Kerr black holes, and offer theoretical guidance for future high-resolution observations.
Since the Event Horizon Telescope (EHT) collaboration released horizon-scale images of the supermassive black holes Sgr A* and M87*, a new observational window for probing black hole spacetimes in the strong-gravity regime has opened. As an important class of Kerr black hole mimickers, rotating Simpson-Visser (SV) black holes exhibit a degeneracy with Kerr black holes in terms of shadow size, making them difficult to distinguish using shadow observations alone. Motivated by this issue, we present a systematic investigation of the radiative properties and optical appearance of rotating SV black holes surrounded by a thin accretion disk, focusing on the influence of the regularization parameter g on the relevant observables. The results show that although the kinematic quantities and the location of the innermost stable circular orbit (ISCO) depend on the regularization parameter g, the radiative efficiency of the rotating SV black hole is the same as that of its Kerr counterpart. Within the Novikov-Thorne thin-disk model, we study the radiative flux, effective temperature, and spectral luminosity; adopting observational parameters relevant to Sgr A* and M87*, we compute concrete examples for rotating SV black holes and compare them with those for Kerr black holes. The results show that the parameter g suppresses the maximum values of these quantities. In addition, using a backward ray-tracing technique, we numerically simulate the optical appearance of rotating SV black holes and analyze the corresponding intensity images, redshift, and observed flux distributions. Our results indicate that these quantities are sensitive to g. In particular, as g increases, the observed intensity is significantly suppressed, and the photon ring region exhibits a remarkable increase in width. Our findings suggest that accretion-disk-related observables may provide important avenues to distinguish between rotating SV black holes and Kerr black holes, and offer theoretical guidance for future high-resolution observations.
2026, 50(7): 075102. doi: 10.1088/1674-1137/ae5ef2
Abstract:
The Kerr/CFT correspondence establishes a correspondence between extremal black holes in higher dimensions and a chiral conformal field theory (CFT) in their near-horizon limit. A generalization of this framework, known as the EVH/CFT correspondence, has been developed for four- and five-dimensional AdS black holes. It was further proposed in [1 ] that, for ${\rm{AdS}}_{D=6,7}$ black holes, a generalized duality between $(D-2)$-dimensional geometry and $(D-3)$-dimensional field theory may emerge in a suitably defined extremal vanishing horizon (EVH) limit. In this work, we show that, in the EVH limit, the near-EVH geometries of these ${\rm{AdS}}_{D=6,7}$ black holes reduce to lower-dimensional black holes whose metrics are conformally related to solutions of Einstein-Maxwell-Maxwell-dilaton (EMMD) gravity. This structural resemblance suggests a potential route toward the microscopic counting of non-AdS black hole entropy via higher-dimensional AdS/CFT techniques.
The Kerr/CFT correspondence establishes a correspondence between extremal black holes in higher dimensions and a chiral conformal field theory (CFT) in their near-horizon limit. A generalization of this framework, known as the EVH/CFT correspondence, has been developed for four- and five-dimensional AdS black holes. It was further proposed in [
2026, 50(7): 075101. doi: 10.1088/1674-1137/ae5c84
Abstract:
We study the pre-inflationary evolution of the universe within the framework of loop quantum cosmology for a scalar field with potential $ V(\phi)=M^{4}\frac{\phi^{2}}{M_{Pl}^{2}}\left(1+\alpha\frac{\phi^{2}}{M_{Pl}^{2}}\right) $, where α is a positive constant. In this framework, the classical initial singularity is resolved and replaced by a non-singular quantum bounce occurring at a critical energy density. Starting from the bounce, we analyze the background dynamics for both kinetic-energy-dominated and potential-energy-dominated initial conditions. Our results show that slow-roll inflation with a sufficient number of e-folds emerges generically over a wide range of initial inflaton values. We further examine the associated phase portrait and demonstrate the attractor behavior of the slow-roll inflationary solutions. Additionally, we study the spectral index $ n_s $ and the tensor-to-scalar ratio r for three limiting cases of α, finding that the model is observationally viable in the intermediate regime.
We study the pre-inflationary evolution of the universe within the framework of loop quantum cosmology for a scalar field with potential $ V(\phi)=M^{4}\frac{\phi^{2}}{M_{Pl}^{2}}\left(1+\alpha\frac{\phi^{2}}{M_{Pl}^{2}}\right) $, where α is a positive constant. In this framework, the classical initial singularity is resolved and replaced by a non-singular quantum bounce occurring at a critical energy density. Starting from the bounce, we analyze the background dynamics for both kinetic-energy-dominated and potential-energy-dominated initial conditions. Our results show that slow-roll inflation with a sufficient number of e-folds emerges generically over a wide range of initial inflaton values. We further examine the associated phase portrait and demonstrate the attractor behavior of the slow-roll inflationary solutions. Additionally, we study the spectral index $ n_s $ and the tensor-to-scalar ratio r for three limiting cases of α, finding that the model is observationally viable in the intermediate regime.
2026, 50(7): 075001. doi: 10.1088/1674-1137/ae5c6f
Abstract:
The Large Array of Imaging Atmospheric Cherenkov Telescopes (LACT) is a next-generation Cherenkov telescope array designed to study the morphology and energy spectra of ultra-high-energy gamma-ray sources in hybrid operation with the Large High Altitude Air Shower Observatory (LHAASO). With its excellent angular resolution, large effective area, and powerful gamma/hadron discrimination capabilities, LACT achieves outstanding sensitivity for observations of gamma-ray sources. In this paper, we present an optimized configuration for the LACT array, developed through comprehensive Monte Carlo simulations. Based on these simulations, we conducted on-site surveys at the LHAASO site and selected the most effective array layout. Detailed performance studies show that this optimized configuration delivers excellent sensitivity across various observational modes. Furthermore, we present a detailed outlook on LACT's potential observations of gamma-ray sources in the LHAASO catalog. By incorporating the measured energy spectra from LHAASO and accounting for LACT's detector response function at different zenith angles, we estimate the number of detectable events over a one-year observation period. This analysis provides a foundation for developing a preliminary observation strategy for LACT in the coming years.
The Large Array of Imaging Atmospheric Cherenkov Telescopes (LACT) is a next-generation Cherenkov telescope array designed to study the morphology and energy spectra of ultra-high-energy gamma-ray sources in hybrid operation with the Large High Altitude Air Shower Observatory (LHAASO). With its excellent angular resolution, large effective area, and powerful gamma/hadron discrimination capabilities, LACT achieves outstanding sensitivity for observations of gamma-ray sources. In this paper, we present an optimized configuration for the LACT array, developed through comprehensive Monte Carlo simulations. Based on these simulations, we conducted on-site surveys at the LHAASO site and selected the most effective array layout. Detailed performance studies show that this optimized configuration delivers excellent sensitivity across various observational modes. Furthermore, we present a detailed outlook on LACT's potential observations of gamma-ray sources in the LHAASO catalog. By incorporating the measured energy spectra from LHAASO and accounting for LACT's detector response function at different zenith angles, we estimate the number of detectable events over a one-year observation period. This analysis provides a foundation for developing a preliminary observation strategy for LACT in the coming years.
2026, 50(8): 081001. doi: 10.1088/1674-1137/ae6310
Abstract:
Hadron-hadron interactions, being nonperturbative in nature, play a significant role in addressing phenomenological questions in particle physics. Femtoscopy is a powerful tool in heavy-ion collision experiments, enabling the extraction of hadron-hadron interactions via momentum-correlation functions (CFs). These CFs are typically expressed as a convolution of source functions and hadron-hadron wave functions, with the latter encoding information about the interactions. However, source functions remain poorly constrained and are commonly approximated by a Gaussian form. Reconstructing source functions from experimental correlation data constitutes an "inverse problem." To address this, we propose a toy model based on Tikhonov regularization. Using a square-well potential with four distinct strengths, we calculate the CFs for inputs of single Gaussian source functions and mixed Gaussian source functions. The resulting CFs are then used to reconstruct the source functions via Tikhonov regularization. Our results show that the Gaussian source function can be successfully reconstructed, highlighting the potential of this approach for extracting realistic source functions from hadron pairs of interest.
Hadron-hadron interactions, being nonperturbative in nature, play a significant role in addressing phenomenological questions in particle physics. Femtoscopy is a powerful tool in heavy-ion collision experiments, enabling the extraction of hadron-hadron interactions via momentum-correlation functions (CFs). These CFs are typically expressed as a convolution of source functions and hadron-hadron wave functions, with the latter encoding information about the interactions. However, source functions remain poorly constrained and are commonly approximated by a Gaussian form. Reconstructing source functions from experimental correlation data constitutes an "inverse problem." To address this, we propose a toy model based on Tikhonov regularization. Using a square-well potential with four distinct strengths, we calculate the CFs for inputs of single Gaussian source functions and mixed Gaussian source functions. The resulting CFs are then used to reconstruct the source functions via Tikhonov regularization. Our results show that the Gaussian source function can be successfully reconstructed, highlighting the potential of this approach for extracting realistic source functions from hadron pairs of interest.
2026, 50(7): 074105. doi: 10.1088/1674-1137/ae5ef6
Abstract:
The atomic nucleus, viewed as a system of bound quarks, should, in principle, be described within an effective theory of low-energy quantum chromodynamics. This paper provides an overview of recently developed models that embody essential features of the desired effective theory. The Fermi gas model helps explain why the number of d quarks is approximately equal to that of u quarks in stable light nuclei up to $ {}^{40}_{20}{\rm Ca} $. A modified bag model accounts for the deviation from this rule in heavier nuclei. With this model, the static properties of a wide range of stable nuclei can be described with reasonable accuracy. To make the most of the modified bag model, it is useful to invoke gauge/gravity duality. A refined version of duality states: "The dynamics inside an extremal black hole in $ {{\rm{AdS}}}_5 $ is mapped onto the corresponding dynamics of a stable subnuclear system in $ {\mathbb R}_{1,3} $". This version of duality allows one to predict the primary decay channel of the lightest glueball. Another implication is that this framework explains why the periodic table contains a finite number of stable elements. Duality makes it possible to calculate the maximum allowed charge $ Z_{{\rm{max}}} $ of stable heavy nuclei: $ Z_{{\rm{max}}}\approx 82 $, which is the charge of the $ {}^{208}_{\phantom{2}82}{\rm Pb} $ nucleus.
The atomic nucleus, viewed as a system of bound quarks, should, in principle, be described within an effective theory of low-energy quantum chromodynamics. This paper provides an overview of recently developed models that embody essential features of the desired effective theory. The Fermi gas model helps explain why the number of d quarks is approximately equal to that of u quarks in stable light nuclei up to $ {}^{40}_{20}{\rm Ca} $. A modified bag model accounts for the deviation from this rule in heavier nuclei. With this model, the static properties of a wide range of stable nuclei can be described with reasonable accuracy. To make the most of the modified bag model, it is useful to invoke gauge/gravity duality. A refined version of duality states: "The dynamics inside an extremal black hole in $ {{\rm{AdS}}}_5 $ is mapped onto the corresponding dynamics of a stable subnuclear system in $ {\mathbb R}_{1,3} $". This version of duality allows one to predict the primary decay channel of the lightest glueball. Another implication is that this framework explains why the periodic table contains a finite number of stable elements. Duality makes it possible to calculate the maximum allowed charge $ Z_{{\rm{max}}} $ of stable heavy nuclei: $ Z_{{\rm{max}}}\approx 82 $, which is the charge of the $ {}^{208}_{\phantom{2}82}{\rm Pb} $ nucleus.
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