Particles

12 pages, 640 KB

Open AccessArticle

The Absolute Stability and Mass Constraints of Strange Stars in the MIT Bag Model

by Hasmik Shahinyan, Tigran Sargsyan and Arsen Babajanyan

Particles 2026, 9(2), 53; https://doi.org/10.3390/particles9020053 (registering DOI) - 12 May 2026

The primary objective of this study is a comprehensive investigation of the self-bound properties of strange quark matter (SQM), which is hypothesized to represent the absolute ground state of superdense strongly interacting matter. An analysis is performed within the framework of the MIT [...] Read more.

The primary objective of this study is a comprehensive investigation of the self-bound properties of strange quark matter (SQM), which is hypothesized to represent the absolute ground state of superdense strongly interacting matter. An analysis is performed within the framework of the MIT bag model, including first-order perturbative QCD corrections and the finite strange quark mass. By systematically varying the vacuum pressure (bag constant, B) and the strong coupling constant (α_c) over a broad parameter space, while assuming a finite strange quark mass (m_s ≠ 0), we explicitly compute the thermodynamic characteristics of the system including pressure, energy density, baryon number density, and the chemical potentials of quarks and charge-neutralizing electrons under conditions of β-equilibrium and global charge neutrality. Particular emphasis is placed on determining the minimum energy per baryon, which serves as the criterion for absolute stability. For parameter sets satisfying the self-binding condition, the integral properties of strange stars are derived via the numerical integration of the Tolman–Oppenheimer–Volkoff equations. The resulting mass–radius and mass–central density relations are analyzed, yielding the maximum stellar masses in the range (1.9 − 2.4)M_⊙. This study identifies the regions in the space of phenomenological parameters that allow for pure self-bound strange stars and demonstrates the sensitivity of stability and stellar properties to the underlying bag model parameters. Full article

(This article belongs to the Special Issue Selected Papers from “The Modern Physics of Compact Stars and Relativistic Gravity 2025”)

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24 pages, 2939 KB

Open AccessArticle

Getting a Handle on Correlation Functions

by Gernot Eichmann

Particles 2026, 9(2), 52; https://doi.org/10.3390/particles9020052 (registering DOI) - 12 May 2026

Abstract

The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions, the Lorentz-invariant coefficient functions of which encode the physics of the process. For growing [...] Read more.

The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions, the Lorentz-invariant coefficient functions of which encode the physics of the process. For growing n, the complexity of these objects may increase considerably and make it challenging to deal with them. Here, we give a pedagogical introduction to the topic and provide some tools to manage this complexity, and we will show how symmetries can be used as organizing principles. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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18 pages, 3587 KB

Open AccessArticle

Controlling Proton Acceleration with Advanced Gold Nanoantennas in a Kinetic Plasma Environment

by Konstantin Zsukovszki and Istvan Papp

Particles 2026, 9(2), 51; https://doi.org/10.3390/particles9020051 (registering DOI) - 11 May 2026

Abstract

Metallic nanoantennas are promising structures for enhancing energy transfer in high-intensity laser–matter interactions, especially in nanoplasmonic-assisted fusion. Under ultrashort laser pulses, they generate strong localized fields, modify ionization dynamics, and significantly affect charge acceleration in dense media. In this work, we present a [...] Read more.

Metallic nanoantennas are promising structures for enhancing energy transfer in high-intensity laser–matter interactions, especially in nanoplasmonic-assisted fusion. Under ultrashort laser pulses, they generate strong localized fields, modify ionization dynamics, and significantly affect charge acceleration in dense media. In this work, we present a comprehensive particle-in-cell (PIC) study of gold nanoantennas of various geometries—dipoles, planar crosses, three-dimensional crosses, and Yagi-inspired planar structures—irradiated by near-infrared femtosecond pulses at intensities at a range of ~4 × 10¹⁷–4 × 10¹⁸ W/cm². The antenna structures are embedded in a dense hydrogen-rich medium, allowing us to follow electron emission, gold ionization, and proton acceleration self-consistently. Crossed and Yagi-type geometries exhibit more robust resonant behavior than dipoles, with higher field localization and greatly reduced sensitivity to incident polarization. The proton energies increase to ~200 keV at 4 × 10¹⁷ W/cm², and saturate around ~300 keV at a higher intensity >~4 × 10¹⁸ W/cm², dependent on the geometry. This happens largely due to a rapid loss of conduction electrons from the gold structures. Our results highlight Yagi-based and cross-based nanoantennas as promising resonant dopes for laser-driven energy coupling and point toward optimized multi-arm architectures for future nanofusion-target engineering applications. Full article

(This article belongs to the Special Issue Particles and Plasmas in Strong Fields)

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18 pages, 15573 KB

Open AccessReview

A Halo: Triggering a New Era of Nuclear Correlations

by Hiroyuki Sagawa, Xiao Lu and Shan-Gui Zhou

Particles 2026, 9(2), 50; https://doi.org/10.3390/particles9020050 (registering DOI) - 9 May 2026

Abstract

In this contribution to the Halo-40 Proceedings, we discuss two topics regarding halo phenomena. The first is the pairing anti-halo effect on the neutron radius of halo nuclei and the restoration of the halo due to the cancellation between the anti-halo effect and [...] Read more.

In this contribution to the Halo-40 Proceedings, we discuss two topics regarding halo phenomena. The first is the pairing anti-halo effect on the neutron radius of halo nuclei and the restoration of the halo due to the cancellation between the anti-halo effect and the continuum coupling; the second is the soft dipole excitation of deformed halo nuclei. We demonstrate the importance of Hartree–Fock–Bogoliubov and relativistic Hartree–Bogoliubov theory in a continuum for properly taking into account the halo nature of extended wave functions in the calculations of neutron radii as well as the soft dipole excitations of halo nuclei. It is shown that the anti-halo effect is very sensitive to the continuum coupling induced by Bogoliubov-type quasi-particles, which largely cancels the anti-halo effect on the neutron radius. The soft dipole excitations of deformed halo nuclei

^{31}

Ne and

^{37}

Mg are discussed within the deformed Woods–Saxon model. We point out that the sharp peak just above the threshold in the dipole response is created by the halo effect, and its strength can be used to identify the magnitude of deformation and the halo configuration in the Nilsson-level scheme. Full article

(This article belongs to the Special Issue Selected Papers from the International Symposium Commemorating the 40th Anniversary of Halo Nuclei)

17 pages, 1827 KB

Open AccessArticle

Beaming of Polarized Radiation in Subcritical X-Ray Pulsars

by Ivan D. Markozov, Alexander Y. Potekhin, Alexander D. Kaminker and Alexander A. Mushtukov

Particles 2026, 9(2), 49; https://doi.org/10.3390/particles9020049 - 5 May 2026

Abstract

Radiation of X-ray pulsars is powered by accretion on the neutron star surface from a binary companion under the influence of a strong magnetic field. We study the beaming of this radiation in the case of subcritical X-ray pulsars, where it is formed [...] Read more.

Radiation of X-ray pulsars is powered by accretion on the neutron star surface from a binary companion under the influence of a strong magnetic field. We study the beaming of this radiation in the case of subcritical X-ray pulsars, where it is formed in the accretion channel close to the neutron star surface. We solve equations of the hydrodynamics and radiative transfer of two coupled polarization modes in the accretion channel numerically, taking into account resonant Compton scattering and vacuum polarization. The beaming patterns are obtained for different accretion rates, photon energies, and polarizations, as well as for different models of the neutron star surface radiation. The calculated beaming patterns are converted into light curves for both the intensity and polarization, taking into account the effects of General Relativity. These beaming patterns and light curves are found to be strongly affected by the resonant Compton scattering for photon energies comparable with the electron cyclotron energy. In particular, the angular redistribution of radiation near the cyclotron resonance may reduce the light-curve modulation amplitude, which is consistent with observational indications of a suppressed pulsed fraction at these energies. Full article

(This article belongs to the Special Issue Selected Papers from “The Modern Physics of Compact Stars and Relativistic Gravity 2025”)

22 pages, 3907 KB

Open AccessReview

Nuclear Exotic Structures, Exotic Decays and Near-Barrier Reactions

by Cheng Yin, Chengjian Lin, Lei Yang, Feng Yang, Huiming Jia, Nanru Ma, Peiwei Wen and Tianpeng Luo

Particles 2026, 9(2), 48; https://doi.org/10.3390/particles9020048 - 1 May 2026

Abstract

The reaction dynamics of weakly-bound nuclear systems at near-barrier energies is a compelling topic in nuclear physics. This review summarizes decades of experimental work by the Nuclear Reaction Group at the China Institute of Atomic Energy. Using transfer reactions with the distorted wave [...] Read more.

The reaction dynamics of weakly-bound nuclear systems at near-barrier energies is a compelling topic in nuclear physics. This review summarizes decades of experimental work by the Nuclear Reaction Group at the China Institute of Atomic Energy. Using transfer reactions with the distorted wave born approximation and asymptotic normalization coefficient analyses, we confirm the first excited neutron halo (

^{13} C

) on the

β

-stability line and identified new halo states in

^{12} B

. Total reaction cross-section measurements revealed proton halo nuclei

^{27} P

and

^{29} S

, with core enlargement observed in

^{27} P

and

^{28} P

. We established conditions for halo formation and delineated the proton halo existence region. In two-proton emission studies, we observed

^{2} He

cluster emission from highly excited

^{17, 18} Ne

and

^{28, 29} S

, with

^{29} S

being the second such case internationally. In

β

-delayed decay, we discovered

β

2p emission in

^{22} Si

and determined its mass, observing isospin-symmetry breaking in

^{20} Mg

,

^{22} Si

, and

^{27} S

. Decay schemes for

^{27} S

and

^{26} P

addressed the

^{26} Al

abundance problem. For nuclear interactions, we investigated the

^{6} He

optical potential, finding the dispersion relation inapplicable for

^{6} He

+

^{209} Bi

, and developed notch and Bayesian methods to constrain uncertainties. For unstable nuclei, the proton drip-line systems

^{8}

B and

^{17}

F have been intensively studied via complete kinematics measurements of the

^{8}

B +

^{120}

Sn and

^{17}

F +

^{58}

Ni reactions, respectively. The results show that elastic breakup dominates for proton-halo

^{8} B

, while inelastic breakup prevails for

^{17} F

, with proton-rich nuclei exhibiting lower breakup probabilities than neutron-halo nuclei due to Coulomb effects. Fusion studies revealed sub-barrier enhancement in

^{17} F

+

^{58} Ni

from continuum couplings. We propose direct fusion–evaporation measurements with deflection systems integrated with breakup detection to disentangle complete and incomplete fusion channels. Full article

(This article belongs to the Special Issue Selected Papers from the International Symposium Commemorating the 40th Anniversary of Halo Nuclei)

13 pages, 1547 KB

Open AccessArticle

Lifetime Measurements—A Powerful Tool to Study Nuclear Structure

by Dimitar Tonev, Galina D. Dimitrova, Anguel Demerdjiev, Giovanni De Gregorio, Giacomo de Angelis, Elena Geleva, Nikolay Goutev, Nikolay N. Petrov, Ivaylo Pantaleev and Lilianna Panteleev-Simeonova

Particles 2026, 9(2), 47; https://doi.org/10.3390/particles9020047 - 1 May 2026

Abstract

Advanced Doppler-shift methods for the calculation of the γ-ray lineshape registered in recoil-distance Doppler-shift and Doppler-shift attenuation methods are presented, emphasizing the case using a gate set on the shifted part of a direct feeding transition. For the precise description of the γ-ray [...] Read more.

Advanced Doppler-shift methods for the calculation of the γ-ray lineshape registered in recoil-distance Doppler-shift and Doppler-shift attenuation methods are presented, emphasizing the case using a gate set on the shifted part of a direct feeding transition. For the precise description of the γ-ray lineshape, the process of evaporation of light particles from the compound nucleus has to be taken into account in the case of heavy ion-induced fusion-evaporation reactions. In addition, the impact of different approaches for calculating stopping powers is investigated in the process of the lifetime determinations. In the RDDS experiments, the γ-emission during the slowing down in the stopper is discussed in detail. Applications of the new procedures are demonstrated in two experiments: the first one is a plunger experiment performed in order to check for chirality in the ¹³⁴Pr nucleus and the second one is a DSAM experiment conducted to test the isospin symmetry in ³¹P and ³¹S mirror nuclei. Full article

(This article belongs to the Special Issue Selected Papers from the International Symposium Commemorating the 40th Anniversary of Halo Nuclei)

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16 pages, 644 KB

Open AccessReview

Radiative Decays of Hadronic Molecules: From Confusion to Inspiration

by Feng-Kun Guo, Christoph Hanhart and Alexey Nefediev

Particles 2026, 9(2), 46; https://doi.org/10.3390/particles9020046 - 28 Apr 2026

Abstract

Radiative decays of hadronic states provide an essential source of information that can facilitate deciphering their nature and properties. However, a lot of confusion concerning radiative decays of hadronic molecules and their interpretation can be found in the literature. In this paper, we [...] Read more.

Radiative decays of hadronic states provide an essential source of information that can facilitate deciphering their nature and properties. However, a lot of confusion concerning radiative decays of hadronic molecules and their interpretation can be found in the literature. In this paper, we briefly review several types of such decays and pinpoint similarities and essential differences between them. In particular, we emphasise the crucial role played by the hierarchy of the scales relevant to the studied system and the resulting necessity of employing an approach that considers them appropriately. We illustrate the situation with several instructive examples. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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45 pages, 1772 KB

Open AccessReview

Symmetry- Preserving Contact Interaction Approaches: An Overview of Meson and Diquark Form Factors

by Laura Xiomara Gutiérrez-Guerrero and Roger José Hernández-Pinto

Particles 2026, 9(2), 45; https://doi.org/10.3390/particles9020045 - 24 Apr 2026

Abstract

We present an updated overview of the symmetry-preserving contact interaction model in hadronic physics, which was developed a little over a decade ago to describe the mass spectrum and internal structure of mesons and diquarks composed of light and heavy quarks. Over the [...] Read more.

We present an updated overview of the symmetry-preserving contact interaction model in hadronic physics, which was developed a little over a decade ago to describe the mass spectrum and internal structure of mesons and diquarks composed of light and heavy quarks. Over the years, the contact interaction model has evolved into a framework capable of treating both ground and excited states, providing a simple yet consistent approach to nonperturbative QCD. In this review, we examine the mass spectrum and elastic form factors of forty mesons with different spins and parities, together with their corresponding diquark partners. Importantly, we update the comparison of contact interaction predictions using recent results from the literature, offering a fresh perspective on the model’s performance, strengths, and limitations. The analysis presented here refines previous conclusions and supports the contact interaction model as a practical tool for hadron structure studies, with potential applications to baryons and multiquark states. We also present comparisons with other theoretical models and approaches, including lattice quantum chromodynamics, and comment on future prospects in view of ongoing and planned experimental programs regarding hadron structure. In particular, forthcoming measurements at FAIR together with future studies at Jefferson Lab and the Electron Ion Collider are expected to provide key insights into hadron structure, with FAIR offering indirect constraints via hadron spectroscopy, hadronic interactions, and in-medium properties; high-precision data on meson structure and form factors from Jefferson Lab and the Electron Ion Collider will provide valuable benchmarks with which to confront predictions based on the contact interaction model. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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17 pages, 450 KB

Open AccessReview

A Solution of the Scalar Nonet Mass Puzzle

by Mihail Chizhov, Emanuil Chizhov, Daniela Kirilova and Momchil Naydenov

Particles 2026, 9(2), 44; https://doi.org/10.3390/particles9020044 - 23 Apr 2026

Abstract

We present a short review dedicated to low-lying meson states. We present all meson nonets, which consist from up, down and strange light quarks. We consider the scalar nonet as a basic nonet. We work in the framework of the massless Nambu–Jona-Lasinio [...] Read more.

We present a short review dedicated to low-lying meson states. We present all meson nonets, which consist from up, down and strange light quarks. We consider the scalar nonet as a basic nonet. We work in the framework of the massless Nambu–Jona-Lasinio

U_{R} (3) \times U_{L} (3)

quark model. The collective meson states are described through initially bare quark–antiquark pairs, whose condensates lead simultaneously to spontaneous breaking of the chiral and the flavour symmetry. After quantisation and the spontaneous breaking of the chiral symmetry, when quarks obtain constituent nonzero masses, they become dressed. We present an explanation of the inverse mass hierarchy of the low-lying nonet of the scalar mesons. The proposed explanation is based on symmetry principles. It is shown that, due to the flavour symmetry breaking, two isodoublets of

K_{0}^{*} (700)

mesons play the role of Goldstone bosons. It is also proven that there exists a solution with almost degenerate masses of the

a_{0} (980)

and

f_{0} (980)

mesons and a zero mass of the

f_{0} (500)

meson. Short description of the physical properties of other meson nonets is provided. In particular unique mass relations among the different nonets, which are experimentally confirmed, are presented. Full article

(This article belongs to the Special Issue Selected Papers from the 14th International Conference on New Frontiers in Physics (ICNFP 2025))

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16 pages, 1112 KB

Open AccessArticle

Nuclear Binding Energies from Composite-Knot Ropelength: A Topological Model That Mirrors Quantum-Mechanical Phenomenology

by Thomas Riedel

Particles 2026, 9(2), 43; https://doi.org/10.3390/particles9020043 - 22 Apr 2026

Abstract

We report a curious numerical observation: If atomic nuclei are modelled as connect-sums of threefoil knots with alternating chirality, the ropelength of the composite knot—a purely geometric quantity requiring no quantum mechanics—tracks the experimental binding-energy curve from hydrogen to uranium. A two-parameter fit [...] Read more.

We report a curious numerical observation: If atomic nuclei are modelled as connect-sums of threefoil knots with alternating chirality, the ropelength of the composite knot—a purely geometric quantity requiring no quantum mechanics—tracks the experimental binding-energy curve from hydrogen to uranium. A two-parameter fit to 50 nuclei gives

R^{2} = 0.9998

(coefficient of determination; 1 = perfect fit) and

RMS = 6.9 MeV

(root-mean-square deviation between model and experiment), comparable to the five-parameter Bethe–Weizsäcker formula (

RMS = 8.3 MeV

) at less than half the parameter count. Out-of-sample predictions for

{}^{244}{Pu}

and

{}^{252}{Cf}

, not used in the fit, are accurate to

0.4 MeV

and

8.4 MeV

, respectively. What makes the observation worth reporting is not the fit itself, but the range of nuclear phenomenology that emerges uninstructed from the topology: saturation, surface energy, isospin pairing, odd-even staggering, and geometric analogues of nuclear isomers all appear as consequences of the connect-sum construction, without additional assumptions. We catalogue these correspondences, assess which are structural and which may be coincidental, and identify concrete numerical tests that would distinguish the two possibilities. Full article

(This article belongs to the Section Nuclear and Hadronic Theory)

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21 pages, 6527 KB

Open AccessArticle

Poincaré Invariance and the Unruh Effect

by Alexandre Deur, Stanley J. Brodsky, Craig D. Roberts and Balša Terzić

Particles 2026, 9(2), 42; https://doi.org/10.3390/particles9020042 - 22 Apr 2026

Abstract

In quantum field theory, the vacuum is popularly considered to be a complex medium populated with virtual particle + antiparticle pairs. To an observer experiencing uniform acceleration, it is generally held that these virtual particles become real, appearing as a gas at a [...] Read more.

In quantum field theory, the vacuum is popularly considered to be a complex medium populated with virtual particle + antiparticle pairs. To an observer experiencing uniform acceleration, it is generally held that these virtual particles become real, appearing as a gas at a temperature that grows with the acceleration. This is the Unruh effect. However, it has been shown that vacuum complexity is an artifact produced by treating quantum field theory in a manner that does not manifestly enforce causality. Choosing a quantization approach that patently enforces causality, the quantum field theory vacuum is barren, bereft even of virtual particles. We show that acceleration has no effect on a trivial vacuum; hence, there is no Unruh effect in such a treatment of quantum field theory. Since the standard calculations suggesting an Unruh effect are formally consistent, insofar as they have been completed, there must be a canceling contribution that is omitted in the usual analyses. We argue that it is the dynamical action of conventional Lorentz transformations on the structure of an Unruh detector. Full article

(This article belongs to the Section Quantum Field Theory and Quantum Gravity)

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25 pages, 639 KB

Open AccessArticle

Observational Diagnostics of a Parametrized Deceleration Parameter in FLRW Cosmology

by Bhupendra Kumar Shukla, Deger Sofuoğlu, Aroonkumar Beesham, Rishi Kumar Tiwari and Mfanafuthi Siyabonga Msweli

Particles 2026, 9(2), 41; https://doi.org/10.3390/particles9020041 - 20 Apr 2026

Abstract

The evolution of the deceleration parameter

q (z)

plays a crucial role in understanding the dynamics of dark energy within the framework of modern cosmology. In this study, we perform a parametric reconstruction of

q (z)

in a spatially [...] Read more.

The evolution of the deceleration parameter

q (z)

plays a crucial role in understanding the dynamics of dark energy within the framework of modern cosmology. In this study, we perform a parametric reconstruction of

q (z)

in a spatially flat Friedmann–Robertson–Walker (FLRW) Universe composed of radiation, pressureless dark matter, and dark energy. We consider a physically motivated form of

q (z)

that effectively describes the transition of the Universe from a decelerating to an accelerating expansion phase. This parametrization is incorporated into the Friedmann equations to derive the corresponding Hubble parameter, which is then confronted with a comprehensive set of observational data, including Hubble parameter measurements

H (z)

, Type Ia supernovae (SNIa), and Baryon Acoustic Oscillations (BAO) data. Employing the Markov Chain Monte Carlo (MCMC) approach, we constrain the model parameters using the combined

H (z) + S N I a + B A O

dataset. The best-fit parameters are subsequently used to reconstruct the cosmographic quantities, such as the deceleration, jerk, and snap parameters, which provide deeper insight into the expansion history of the Universe. Finally, a comparative analysis with the standard

Λ

CDM model is carried out to assess the compatibility and effectiveness of the proposed parametrization. Full article

(This article belongs to the Section Astroparticle Physics and Cosmology)

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15 pages, 972 KB

Open AccessArticle

β Decay of ²⁰Na

by Qiang Wang, You-Bao Wang, Jun Su, Zhi-Yu Han, B. Alex Brown, Li-Hua Chen, Zi-Qiang Chen, Bao-Qun Cui, Bo Dai, Tao Ge, Xin-Yue Li, Yun-Ju Li, Zhi-Hong Li, Gang Lian, Yin-Long Lyu, Rui-Gang Ma, Tian-Li Ma, Xie Ma, Ying-Jun Ma, Yi Su, Bing Tang, Chun-Guang Wang, Hong-Yi Wu, Fu-Rong Xu, Sheng-Quan Yan, Sheng Zeng, Hao Zhang, Yun Zheng, Chao Zhou, Yang-Ping Shen, Bing Guo, Tian-Jue Zhang and Wei-Ping Liu Show full author list Hide full author list

Particles 2026, 9(2), 40; https://doi.org/10.3390/particles9020040 - 17 Apr 2026

Abstract

²⁰Na is a well-known

β

-delayed

α

emitter, owing to the large decay energy of ²⁰Na above the α + ¹⁶O threshold in the

A = 5 α

daughter nucleus ²⁰Ne. In this work, the decay property of ²⁰ [...] Read more.

²⁰Na is a well-known

β

-delayed

α

emitter, owing to the large decay energy of ²⁰Na above the α + ¹⁶O threshold in the

A = 5 α

daughter nucleus ²⁰Ne. In this work, the decay property of ²⁰Na is investigated in detail via the β-γ β-α and β-γ-α coincidence spectroscopy. As the day-one experiment of the Beijing Rare Isotope Facility (BRIF), the intense ²⁰Na beam was produced using the Isotope Separator On Line (ISOL) technique through the 100 MeV proton bombarding a stack of MgO as a thick target. Specific interest was focused on the exotic decay mode of ²⁰Na; the previously reported low-energy α lines at 713 and 846 keV were confirmed, and several weak β-γ-α decay sequences were clearly identified for the first time, thanks to the strong resolving power of α-γ coincidence spectroscopy. The decay properties of ²⁰Na are compared to the shell model calculation, which agree reasonably well with the allowed β transition strengths and subsequent electro-magnetic transitions with the use of the sd shell-model space with the USDB interaction. Full article

(This article belongs to the Special Issue Selected Papers from the International Symposium Commemorating the 40th Anniversary of Halo Nuclei)

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10 pages, 321 KB

Open AccessArticle

Leading Low-Temperature Correction to the Heisenberg–Euler Lagrangian

by Felix Karbstein

Particles 2026, 9(2), 39; https://doi.org/10.3390/particles9020039 - 15 Apr 2026

Abstract

In this article, we show that the well-known leading low-temperature correction to the Heisenberg–Euler Lagrangian in a constant electromagnetic field arising at two loops can be efficiently extracted from its one-loop zero-temperature analogue. Resorting to the real-time formalism of equilibrium quantum field theory [...] Read more.

In this article, we show that the well-known leading low-temperature correction to the Heisenberg–Euler Lagrangian in a constant electromagnetic field arising at two loops can be efficiently extracted from its one-loop zero-temperature analogue. Resorting to the real-time formalism of equilibrium quantum field theory that explicitly separates out the zero-temperature contribution from the finite-temperature corrections, the determination becomes essentially trivial. In essence, it only requires taking derivatives of the Heisenberg–Euler Lagrangian at one loop and zero temperature for the field strength. As a bonus, we then effectively dress the low-temperature contribution at two loops by one-particle reducible tadpole structures. This generates a subset of higher-loop contributions to the Heisenberg–Euler Lagrangian in the limit of low temperatures. We extract their leading strong-field behavior at a given loop order, and finally resum these to all loop orders. Full article

(This article belongs to the Special Issue Particles and Plasmas in Strong Fields)

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23 pages, 14334 KB

Open AccessReview

Recent Developments in and Applications of the Relativistic Chiral Nuclear Force

by Li-Sheng Geng, Jun-Xu Lu, Qing-Yu Zhai, Zhi-Wei Liu and Shi-Hang Shen

Particles 2026, 9(2), 38; https://doi.org/10.3390/particles9020038 - 4 Apr 2026

Abstract

The nuclear force is central to our understanding of complex nuclear phenomena and to the applications of nuclear techniques. The non-perturbative nature of low-energy strong interaction and color confinement have provided an ab initio understanding of nuclear force, a challenge for almost a [...] Read more.

The nuclear force is central to our understanding of complex nuclear phenomena and to the applications of nuclear techniques. The non-perturbative nature of low-energy strong interaction and color confinement have provided an ab initio understanding of nuclear force, a challenge for almost a century, since the pioneering work of Yukawa. Since 1990, chiral effective field theory (ChEFT) has become the de facto standard for describing nuclear interactions; most prior studies employed heavy-baryon chiral perturbation theory. Only recently, there have been successful attempts to construct a chiral nuclear force employing covariant baryon chiral perturbation theory. In this work, we review recent developments and applications of relativistic chiral nuclear forces. We first elaborate on the necessity of relativistic/covariant theories, then present the construction of the first high-precision relativistic chiral nuclear force up to next-to-next-to-leading order (NNLO), and discuss the ongoing progress in higher-order nucleon–nucleon (NN) and n-d scattering, as well as their applications in nuclear matter, finite nuclei, and hypernuclear systems. Finally, we summarize the achievements and outline the future outlook of this research field. Full article

(This article belongs to the Special Issue Selected Papers from the International Symposium Commemorating the 40th Anniversary of Halo Nuclei)

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28 pages, 794 KB

Open AccessArticle

Emergent Higgs Field and the Schwarzschild Black Hole

by Dragana Pilipović

Particles 2026, 9(2), 37; https://doi.org/10.3390/particles9020037 - 3 Apr 2026

Abstract

The derivations presented in this paper suggest an intimate relationship between geometry and the electroweak sector at the Planck scale. A Lorentz-invariant maximally symmetric stochastically perturbed spacetime transformed to spherical coordinates reveals an emergent Schwarzschild metric, entirely a statistical structure of stochastic spacetime. [...] Read more.

The derivations presented in this paper suggest an intimate relationship between geometry and the electroweak sector at the Planck scale. A Lorentz-invariant maximally symmetric stochastically perturbed spacetime transformed to spherical coordinates reveals an emergent Schwarzschild metric, entirely a statistical structure of stochastic spacetime. Similarly, the transition from a maximally symmetric universe with a complex

S U (2)

scalar doublet

ϕ

, comprising four independent real scalar fields with a zero vacuum expectation value (VEV), to spherical coordinates at the Planck scale reveals the spontaneously broken electroweak (EW) sector. Working in the unitarity gauge, the resulting EW potential can be simultaneously mapped in space at the Planck scale and across the EW sector. In space, the resulting EW potential includes a deep well within the Schwarzschild sphere and a shallow well just outside corresponding to an accretion disk. The same potential mapped in the EW space provides an entire family of possible sombrero hat potentials with fourth-order coupling specific to a point in space. At the minimum points of the potential in space, inside the Schwarzschild sphere and at the accretion disk, the

λ

corresponding to the Standard Model (SM) fourth-order coupling is instead derived as

\frac{λ}{5}

. The factor of

\frac{1}{5}

is a simple consequence of the conservation of the EW VEV and the fact that the SM formulation of the EW potential does not account for situations where the perturbations in

ϕ

dominate. A more general formulation of the EW potential restores the SM quartic coupling and preserves

λ

in space. An emergent Higgs field inside the Schwarzschild black hole is found to directly relate to the stochastic spacetime fields normalized by the Schwarzschild radius. The corresponding Higgs vacuum has both a ground and excited state and the possibility of both positive and negative vacuum entropy. Finally, the scalar-field VEV degeneracy in EW space of the metastable Higgs vacuum appears instead differentiated in space with possible probability, tunneling, and entropy implications. Full article

(This article belongs to the Section Phenomenology and Physics Beyond the Standard Model)

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12 pages, 14870 KB

Open AccessArticle

Description of ²⁹F and ³¹F Within the Deformed Relativistic Hartree–Bogoliubov Theory in Continuum

by Kaiyuan Zhang, Ling Li, Jie Yan, Guixiang Ye, Xinhui Wu, Jia-Lin An, Shi-Sheng Zhang, Cong Pan and Xiang-Xiang Sun

Particles 2026, 9(2), 36; https://doi.org/10.3390/particles9020036 - 2 Apr 2026

Cited by 1

Abstract

The experimental exploration of halo nuclei over the past four decades has established ground-state halo phenomena in about twenty nuclei, providing important benchmarks for modern nuclear theories. The deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc) has been successfully applied to describe known halo [...] Read more.

The experimental exploration of halo nuclei over the past four decades has established ground-state halo phenomena in about twenty nuclei, providing important benchmarks for modern nuclear theories. The deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc) has been successfully applied to describe known halo nuclei and to predict new candidates during the last dozen years. In this work, the possible two-neutron halo nuclei

{}^{29}F

and

{}^{31}F

are investigated within the DRHBc framework. In the spherical limit, an inversion between the

2 p_{3 / 2}

and

1 f_{7 / 2}

orbitals is obtained relative to the conventional single-particle ordering, which plays a crucial role in the formation of deformed halos in these nuclei. Assuming a prolate deformation with

β_{2} \approx 0.4

, as suggested in previous studies, a deformed two-neutron halo in

{}^{29}F

is reproduced. For

{}^{31}F

, a well-deformed ground state with

β_{2} \approx 0.24

and a more pronounced two-neutron halo emerge self-consistently. Full article

(This article belongs to the Special Issue Selected Papers from the International Symposium Commemorating the 40th Anniversary of Halo Nuclei)

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13 pages, 8112 KB

Open AccessArticle

Searching for Stable States in the T_DD1 Systems Based on a Chiral Quark Model

by Yuheng Wu, Linkai Li, Yuheng Xing, Xinxing Wu and Yue Tan

Particles 2026, 9(2), 35; https://doi.org/10.3390/particles9020035 - 2 Apr 2026

Abstract

Experimentally, the

1^{+}

state

X (3872)

was first discovered, and subsequently, its partner state

Y (4260)

, with the same quark content

(c \bar{q} q \bar{c})

and quantum number

1^{-}

was also observed. [...] Read more.

Experimentally, the

1^{+}

state

X (3872)

was first discovered, and subsequently, its partner state

Y (4260)

, with the same quark content

(c \bar{q} q \bar{c})

and quantum number

1^{-}

was also observed. Inspired by this pattern, we systematically investigate the newly discovered

1^{+}

state

T_{c c}

and its possible

1^{-}

partner, the

T_{D D_{1}}

system with the same quark content

(c \bar{q} c \bar{q})

. Within the framework of the chiral quark model, we perform a comprehensive study of the bound and resonance states of

T_{D D_{1}}

using the Gaussian expansion method (GEM). Two quark configurations, the molecular structure and the diquark structure, are considered in our calculations. Our results indicate the existence of a shallow bound state dominated by the

D D_{1}^{*}

channel, which is analogous to the experimentally observed

T_{c c}

, as well as two compact resonant states with narrow widths around 4.5 GeV. To avoid the influence of model parameters on the results, we additionally fitted a new set of parameters and obtained consistent conclusions. According to our calculation results, although the color-octet and diquark configurations have relatively high energies, the channel-coupling effects induced by them play a crucial role in the formation of these stable states. We strongly encourage experimental efforts to search for the stable states predicted in the

T_{D D_{1}}

system. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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