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2026 No.7
2026 No.6
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): 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): 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.
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(6): 065110. doi: 10.1088/1674-1137/ae50e5
Abstract:
In this study, we shed light on the unified approach to dark energy and dark matter via the generalized Chaplygin gas model in symmetric teleparallel gravity (STGR). We employ the equation of state provided by generalized Chaplygin gas, which naturally arises in string theory, tachyonic field theory, and Randall-Sundrum-type brane world solutions. Such a generalized Chaplygin gas not only provides a viable candidate for dark energy but also for dark matter via Bose-Einstein condensation (BEC). We also consider the interaction between dark matter and dark energy to provide a more realistic perspective. Moreover, we perform Markov Chain Monte Carlo (MCMC) analysis with the combined Hubble and Pantheon datasets, conduct Om diagnostics, and construct $ r-s $ plots to comment on the late behavior of our model. Through Om diagnostics, we find values located in phantom regions, as expected, owing to several physical reasons. Finally, we outline our future research directions.
In this study, we shed light on the unified approach to dark energy and dark matter via the generalized Chaplygin gas model in symmetric teleparallel gravity (STGR). We employ the equation of state provided by generalized Chaplygin gas, which naturally arises in string theory, tachyonic field theory, and Randall-Sundrum-type brane world solutions. Such a generalized Chaplygin gas not only provides a viable candidate for dark energy but also for dark matter via Bose-Einstein condensation (BEC). We also consider the interaction between dark matter and dark energy to provide a more realistic perspective. Moreover, we perform Markov Chain Monte Carlo (MCMC) analysis with the combined Hubble and Pantheon datasets, conduct Om diagnostics, and construct $ r-s $ plots to comment on the late behavior of our model. Through Om diagnostics, we find values located in phantom regions, as expected, owing to several physical reasons. Finally, we outline our future research directions.
2026, 50(6): 1-28.
Abstract:
Chromium (Cr) serves as an indispensable structural material in accelerator-driven systems (ADS) 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 study 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 H.,Liskien et al.'s data; 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, calculated $k_{{\rm{eff}}}$ decreased by $\sim 1000$ pcm relative to CENDL - 3.2, improving agreement with the benchmark; in the OKTAVIAN shielding benchmark, the neutron leakage spectrum also produces experiments well.
Chromium (Cr) serves as an indispensable structural material in accelerator-driven systems (ADS) 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 study 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 H.,Liskien et al.'s data; 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, calculated $k_{{\rm{eff}}}$ decreased by $\sim 1000$ pcm relative to CENDL - 3.2, improving agreement with the benchmark; in the OKTAVIAN shielding benchmark, the neutron leakage spectrum also produces experiments well.
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