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2026 No.8
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(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(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(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(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.
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- Cosmology
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- Cover Story (Issue 1, 2026) A focused review of quintom cosmology: from quintom dark energy to quintom bounce
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