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56 pages, 5180 KB  
Review
Ultracold Neutrons: From Production and Storage to Precision Tests of Fundamental Physics
by Abdurakhman Aldiyarov, Yevgeniy Korshikov, Ali Makhalov and Darkhan Yerezhep
Appl. Sci. 2026, 16(14), 7298; https://doi.org/10.3390/app16147298 - 21 Jul 2026
Viewed by 130
Abstract
Ultracold neutrons (UCNs) are free neutrons with kinetic energies so low that their equivalent thermal temperature lies below 3.5 mK (below 3 × 10−7 eV). At these extreme energies, neutrons exhibit de Broglie wavelengths on the order of hundreds of angstroms and [...] Read more.
Ultracold neutrons (UCNs) are free neutrons with kinetic energies so low that their equivalent thermal temperature lies below 3.5 mK (below 3 × 10−7 eV). At these extreme energies, neutrons exhibit de Broglie wavelengths on the order of hundreds of angstroms and move slowly enough to be confined in material, magnetic, and gravitational traps through total internal reflection. For context, this is about three orders of magnitude colder than the 1 K regime used in superfluid helium UCN sources, which underscores why these neutrons are called “ultracold”: their equivalent thermal energy is comparable to millikelvin physics, even though UCN sources themselves typically operate at 0.8–5 K and produce UCN through superthermal downscattering rather than thermal equilibrium. Over the past several decades, substantial progress in ultracold-neutron source technology has been achieved through the transition from mechanical neutron turbines to superthermal converters based on solid deuterium and superfluid helium. This review provides a comprehensive analysis of modern reactor-based (ILL, PNPI, TRIGA) and spallation-driven (PSI, TRIUMF, SNS, ESS) UCN sources, together with next-generation facilities targeting UCN densities of 103–104 cm−3. Particular attention is devoted to anomalous neutron losses during storage. It is shown that hydrogen-containing surface contaminants, inelastic scattering processes, and wall-induced depolarization contribute significantly to losses beyond those predicted for ideal materials. Current approaches for loss reduction are discussed, including diamond-like carbon coatings, magnetron sputtering techniques, optimization of the ortho–para ratio in neutron converters, and purification of superfluid 4He from trace concentrations of 3He impurities. The review further examines key precision experiments that drive advances in UCN technology, including investigations of the neutron lifetime discrepancy and searches for the neutron electric dipole moment at sensitivities approaching 10−27–10−28 e·cm as probes of CP violation and baryon asymmetry of the Universe. Finally, future directions for increasing UCN density, extending storage times, and enhancing the sensitivity of fundamental physics experiments are discussed. Full article
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29 pages, 2930 KB  
Article
The Pmmm QCD Condensate Lattice: Nominal Wyckoff Occupation as the Ground State and Topological Defects as the Geometric Origin of Particle Excitations
by Rami Rom
Symmetry 2026, 18(7), 1170; https://doi.org/10.3390/sym18071170 - 10 Jul 2026
Viewed by 192
Abstract
We propose a lattice structure and space group symmetry, Pmmm (No. 47), for the QCD condensate ground state, whose Wyckoff positions are occupied by the four light quarks and antiquarks u, d, u~, d~. These serve as [...] Read more.
We propose a lattice structure and space group symmetry, Pmmm (No. 47), for the QCD condensate ground state, whose Wyckoff positions are occupied by the four light quarks and antiquarks u, d, u~, d~. These serve as the fundamental building blocks of both the condensate lattice ground state and the baryonic and leptonic particle excitations embedded within it as topological defects of the nominal Wyckoff occupation, offering a more structured alternative to the QCD instanton liquid picture. Building on Bloch quark wave solutions of a tight-binding Hamiltonian defined on this lattice, we propose a generalization of Einstein’s Equivalence Principle: composite particles embedded in the lattice and propagating by tunnelling cannot distinguish acceleration by gravity, the strong, weak, or electromagnetic forces, or curvature of the lattice itself, arising from local variation in unit cell shape. We derive an eight-by-eight tight-binding Hamiltonian that decouples into two four-by-four blocks separating the quark and antiquark sectors. Electrons, positrons, protons, neutrons, deuterons, and α-particles are embedded in the lattice as defect-induced deviations from the nominal Wyckoff occupation, with their spin and helicity emerging structurally from this picture. We further propose that the lattice’s unit cells carry a small nonzero rest mass, whose collective gravitational effect across a galactic halo may account for the discrepancy between visible mass and rotation curves, identifying the Pmmm condensate as a dark matter candidate. Finally, we outline a mechanism near black hole horizons by which local melting of the condensate lattice followed by quark reactions that conserve the number and flavor of the quarks could yield a new route to baryon asymmetry. We propose a framework that goes several steps beyond the Standard Model by introducing a Pmmm space group unit cell for the QCD condensate ground state, built from the four light quarks and antiquarks u, d, u~, d~. We further propose that topological defects of the Pmmm condensate lattice are the geometric origin of particle excitations. Full article
(This article belongs to the Section C: Physics)
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36 pages, 1329 KB  
Article
Chiral Quark Soliton Model and Nucleon Parton Distribution Functions
by Masashi Wakamatsu
Symmetry 2026, 18(6), 892; https://doi.org/10.3390/sym18060892 - 24 May 2026
Viewed by 230
Abstract
The chiral quark soliton model (CQSM) is an effective quark model of baryons maximally taking account of the most important feature of low-energy QCD, i.e., the spontaneous chiral symmetry breaking of the QCD vacuum and the associated appearance of Nambu–Goldstone pions. It shares [...] Read more.
The chiral quark soliton model (CQSM) is an effective quark model of baryons maximally taking account of the most important feature of low-energy QCD, i.e., the spontaneous chiral symmetry breaking of the QCD vacuum and the associated appearance of Nambu–Goldstone pions. It shares many common features with the famous Skyrme model in that the baryons are viewed as rotating hedgehog objects in both models. Despite many similarities, it turned out that the CQSM can give more realistic predictions on most baryon observables. Above all, a decisive advantage of the CQSM over the Skyrme-like models is that it can handle non-local quark–quark correlations in baryons, which is absolutely impossible within the framework of effective meson theories. This feature is decisively important for making theoretical predictions on the quark distribution functions inside the nucleon, which are defined as nucleon matrix elements of bilinear quark operators with light-cone separation. In the present paper, we try to elucidate why and how the CQSM can give successful predictions for a variety of types of nucleon quark distribution functions, especially for the flavor asymmetry of the unpolarized and longitudinally polarized sea-quark (anti-quark) distribution functions in the nucleon. Full article
(This article belongs to the Special Issue Chiral Quark Models and Their Applications)
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26 pages, 2809 KB  
Review
Recent Advances in Charmed Baryon Measurements at Belle and Belle II
by Yuewen Zhong, Sen Jia and Chengping Shen
Symmetry 2026, 18(3), 490; https://doi.org/10.3390/sym18030490 - 13 Mar 2026
Viewed by 481
Abstract
We review recent experimental progress in charmed baryon physics achieved by the Belle and Belle II experiments, with an emphasis on measurements reported since 2022. Using large e+e data samples collected at or near the Υ(4S) [...] Read more.
We review recent experimental progress in charmed baryon physics achieved by the Belle and Belle II experiments, with an emphasis on measurements reported since 2022. Using large e+e data samples collected at or near the Υ(4S) resonance, Belle and Belle II have delivered a series of precision results on hadronic weak decays of anti-triplet charmed baryons, providing critical inputs for testing flavor-symmetry approaches and dynamical models. We summarize new and improved branching fraction determinations for Ξc0, Ξc+, and Λc+ decays, including channels with neutral hadrons in the final state and the first measurements of several singly Cabibbo-suppressed modes. We also highlight the first determination of the decay asymmetry parameter in Ξc0Ξ0π0. In addition, we review the first Belle II measurements of CP asymmetries in three-body singly Cabibbo-suppressed decays of Ξc+ and Λc+, and we discuss their implications for U-spin sum rules and searches for physics beyond the Standard Model. Finally, we look forward to exploiting the Belle II data set to perform more stringent tests of decay dynamics. Full article
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17 pages, 7025 KB  
Review
Dark Sector Searches at e+e Colliders
by Vindhyawasini Prasad
Universe 2026, 12(1), 20; https://doi.org/10.3390/universe12010020 - 12 Jan 2026
Viewed by 912
Abstract
The Standard Model (SM) of particle physics is one of the most successful frameworks in modern physics, yet it leaves several fundamental questions unanswered, including the nature of dark matter (DM). Precise knowledge of DM is crucial for testing astrophysical and cosmological observations [...] Read more.
The Standard Model (SM) of particle physics is one of the most successful frameworks in modern physics, yet it leaves several fundamental questions unanswered, including the nature of dark matter (DM). Precise knowledge of DM is crucial for testing astrophysical and cosmological observations and for determining the matter density of our Universe. Many hidden dark sector models beyond the SM open the possibility of coupling between DM and SM particles via various portals. The corresponding new physics particles include light Higgs bosons, dark photons, axion-like particle, and spin-1/2 fermions. Furthermore, the introduction of a dark baryon could simultaneously explain the origin of DM and the observed matter–antimatter asymmetry in the Universe. If these hypothetical particles have masses of a few GeV, they can be explored at high-intensity e+e colliders, such as in the BaBar, Belle/Belle II, and BESIII experiments. This report reviews the current status of DM searches at e+e colliders, with a focus on portal-based scenarios. Full article
(This article belongs to the Special Issue Modified Gravity and Dark Energy Theories)
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30 pages, 665 KB  
Article
Top-Down Analysis of Leptogenesis and Dirac Neutrino Masses in an Extended CP-Violating Standard Model
by Chilong Lin
Symmetry 2025, 17(11), 1888; https://doi.org/10.3390/sym17111888 - 6 Nov 2025
Viewed by 872
Abstract
We analytically investigate the charge parity (CP) violation, neutrino masses, and leptogenesis in the Standard Model (SM) with an extension to Dirac neutrinos, building on our previous quark sector analysis. Using systematic top-down diagonalization of fermion mass matrices and experimental neutrino mass-squared differences, [...] Read more.
We analytically investigate the charge parity (CP) violation, neutrino masses, and leptogenesis in the Standard Model (SM) with an extension to Dirac neutrinos, building on our previous quark sector analysis. Using systematic top-down diagonalization of fermion mass matrices and experimental neutrino mass-squared differences, we predict the complete neutrino mass spectrum and assess leptogenesis viability. We find that our analysis yields specific mass predictions: mh5.01×102 eV, ml6.09×103 eV, and a bimodal middle mass (mm4.97×102 eV for inverted ordering, mm1.05×102 eV for normal ordering). Four viable scenarios emerge with parameter constraints ranging from highly restrictive (1<g<1.01512) to moderately broad (1<g<5.9). Crucially, Dirac neutrino leptogenesis is about 71 orders of magnitude weaker than baryogenesis, indicating that Standard Model leptogenesis is negligible and Beyond Standard Model physics is needed for significant leptogenesis contributions. CP violation emerges through SN symmetry breaking, with mass degeneracies controlled by model parameters. Remarkably, while mass-squared differences are small, individual neutrino masses can be significantly larger, potentially addressing dark matter mass requirements and enhancing cosmological significance. This work provides testable predictions for neutrino experiments and establishes a unified analytical approach to CP violation across fermion sectors. Full article
(This article belongs to the Special Issue Neutrinos and Symmetry: Theoretical Developments and New Directions)
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24 pages, 576 KB  
Article
Asymmetry in the Mean Free Path of Neutrinos in Hot Neutron Matter Under Strong Magnetic Fields
by Eduardo Bauer and Vanesa D. Olivera
Symmetry 2025, 17(6), 896; https://doi.org/10.3390/sym17060896 - 6 Jun 2025
Viewed by 1267
Abstract
We investigate the asymmetry in the mean free path of massive neutrinos propagating through hot neutron matter under strong magnetic fields. The system is studied at temperatures up to 30 MeV and baryon densities up to ρ/ρ0 = 2.5, where [...] Read more.
We investigate the asymmetry in the mean free path of massive neutrinos propagating through hot neutron matter under strong magnetic fields. The system is studied at temperatures up to 30 MeV and baryon densities up to ρ/ρ0 = 2.5, where ρ0 is the nuclear saturation density. Magnetic field strengths up to B = 1018 G are considered. We analyze three different equations of state: one corresponding to a non-interacting Fermi gas and two derived from Skyrme-type interactions. The impact of a finite neutrino mass is assessed and found to be negligible within the energy range considered. The neutrino mean free path is computed for various angles of incidence with respect to the magnetic field direction, revealing a clear angular asymmetry. We show that quantum interference terms contribute significantly to this asymmetry, enhancing neutrino emission in directions perpendicular to the magnetic field at high densities. This result contrasts with previous expectations and suggests a revised interpretation of neutrino transport in magnetized nuclear matter. Full article
(This article belongs to the Special Issue Neutrino Physics and Symmetries)
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13 pages, 1143 KB  
Review
Reflections on Chiral Symmetry Within QCD
by Anthony Thomas
Symmetry 2025, 17(4), 512; https://doi.org/10.3390/sym17040512 - 28 Mar 2025
Cited by 2 | Viewed by 1814
Abstract
The fact that chiral symmetry is a crucial feature of the strong force was realized before the discovery of quantum chromodynamics. However, the full power it exerts on the structure of the nucleon only became apparent afterwards. We present a high-level and somewhat [...] Read more.
The fact that chiral symmetry is a crucial feature of the strong force was realized before the discovery of quantum chromodynamics. However, the full power it exerts on the structure of the nucleon only became apparent afterwards. We present a high-level and somewhat personal overview of its role in almost every aspect of the proton structure, from its mass and spin to the asymmetry of its antimatter content and its strange quark content. The lessons learned from studying the proton are also vital with respect to the modern challenge of the nature of baryon-excited states. Full article
(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)
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21 pages, 601 KB  
Article
Quantum Entanglement Asymmetry and the Cosmic Matter–Antimatter Imbalance: A Theoretical and Observational Analysis
by Florian Neukart
Entropy 2025, 27(2), 103; https://doi.org/10.3390/e27020103 - 22 Jan 2025
Cited by 4 | Viewed by 3555
Abstract
We propose a distinct mechanism to explain the matter–antimatter imbalance observed in the universe, rooted in quantum entanglement asymmetry (QEA). Our concept of QEA differs from its usage in the recent literature, where it typically measures how much symmetry is broken within a [...] Read more.
We propose a distinct mechanism to explain the matter–antimatter imbalance observed in the universe, rooted in quantum entanglement asymmetry (QEA). Our concept of QEA differs from its usage in the recent literature, where it typically measures how much symmetry is broken within a subsystem of a larger quantum system. Here, we define QEA as an intrinsic asymmetry in the entanglement properties of particle–antiparticle pairs in the early universe, leading to a preferential survival of matter over antimatter. We develop a theoretical framework incorporating QEA into the standard cosmological model, providing clear justification for the asymmetry in entangled states and corresponding modifications to the Hamiltonian. Numerical simulations using lattice Quantum Chromodynamics (QCD) demonstrate that QEA can produce a net baryon asymmetry consistent with observations. We also predict specific signatures in Cosmic Microwave Background (CMB) anisotropies and large-scale structure formation, offering potential avenues for empirical verification. This work aims to deepen the understanding of cosmological asymmetries and highlight the significance of quantum entanglement in the universe’s evolution. Full article
(This article belongs to the Section Astrophysics, Cosmology, and Black Holes)
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6 pages, 4345 KB  
Article
The HIBEAM Experiment
by Alexander Burgman
Particles 2025, 8(1), 6; https://doi.org/10.3390/particles8010006 - 16 Jan 2025
Cited by 1 | Viewed by 1852
Abstract
The violation of baryon number is an essential ingredient for baryogenesis—the preferential creation of matter over antimatter—needed to account for the observed baryon asymmetry in the universe. However, such a process has yet to be experimentally observed. The HIBEAM/NNBAR program is a proposed [...] Read more.
The violation of baryon number is an essential ingredient for baryogenesis—the preferential creation of matter over antimatter—needed to account for the observed baryon asymmetry in the universe. However, such a process has yet to be experimentally observed. The HIBEAM/NNBAR program is a proposed two-stage experiment at the European Spallation Source to search for baryon number violation. The program will include high-sensitivity searches for processes that violate baryon number by one or two units as follows: free neutron–antineutron oscillation via mixing, neutron–antineutron oscillation via regeneration from a sterile neutron state, and neutron disappearance; the effective process of neutron regeneration is also possible. The program can be used to discover and characterize mixing in the neutron, antineutron, and sterile neutron sectors. The experiment addresses topical open questions such as the origins of baryogenesis and the nature of dark matter, and it is sensitive to scales of new physics that substantially exceed those available at colliders. A goal of the program is to open a discovery window to neutron conversion probabilities (sensitivities) by up to three orders of magnitude compared with previous searches, which is a rare opportunity. A conceptual design report for NNBAR has recently been published. Full article
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15 pages, 463 KB  
Review
Lepton Asymmetries in Cosmology
by Massimiliano Lattanzi and Mauro Moretti
Symmetry 2024, 16(12), 1657; https://doi.org/10.3390/sym16121657 - 15 Dec 2024
Cited by 9 | Viewed by 3407
Abstract
The cosmological lepton asymmetry, i.e., an excess of leptons over antileptons, is still only loosely constrained, and might be much larger than its tiny baryonic counterpart. If this is the case, charge neutrality requires the lepton asymmetries to be confined in the neutrino [...] Read more.
The cosmological lepton asymmetry, i.e., an excess of leptons over antileptons, is still only loosely constrained, and might be much larger than its tiny baryonic counterpart. If this is the case, charge neutrality requires the lepton asymmetries to be confined in the neutrino sector. We recall the observational effects of neutrino asymmetries on the abundance of light elements produced during Big Bang Nucleosynthesis and on the pattern of cosmic microwave background anisotropies. We point to the necessity of solving the neutrino transport equations, taking into account the effect of flavour oscillation, to derive general and robust constraints on lepton asymmetries. We review the current bounds and briefly discuss prospects for next-generation CMB experiments. Full article
(This article belongs to the Special Issue Symmetry in Cosmological Theories and Observations)
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11 pages, 245 KB  
Review
Application of Clifford’s Algebra to Describe the Early Universe
by Bohdan Lev
Mathematics 2024, 12(21), 3396; https://doi.org/10.3390/math12213396 - 30 Oct 2024
Cited by 1 | Viewed by 2589
Abstract
This article is a shortened review of previous results obtained by the author. The advantages of describing the geometric nature of the physical properties of the early universe using the Clifford algebra approach are demonstrated. A geometric representation of the wave function of [...] Read more.
This article is a shortened review of previous results obtained by the author. The advantages of describing the geometric nature of the physical properties of the early universe using the Clifford algebra approach are demonstrated. A geometric representation of the wave function of the early universe is used, and a new mechanism of spontaneous symmetry breaking with different degrees of freedom is proposed. A possible supersymmetry is revealed, and it is shown that the energy of the initial vacuum can be considered equal to zero. The origin of baryonic asymmetry and the nature of dark matter can be explained using a geometric representation of the wave function of the early universe. Full article
(This article belongs to the Section B: Geometry and Topology)
50 pages, 3558 KB  
Article
Dark Atoms of Nuclear Interacting Dark Matter
by Vitaly A. Beylin, Timur E. Bikbaev, Maxim Yu. Khlopov, Andrey G. Mayorov and Danila O. Sopin
Universe 2024, 10(9), 368; https://doi.org/10.3390/universe10090368 - 11 Sep 2024
Cited by 8 | Viewed by 2721
Abstract
The lack of positive evidence for Weakly Interacting Massive Particles (WIMPs) as well as the lack of discovery of supersymmetric (SUSY) particles at the LHC may appeal to a non-supersymmetric solution for the Standard Model problem of the Higgs boson mass divergence, the [...] Read more.
The lack of positive evidence for Weakly Interacting Massive Particles (WIMPs) as well as the lack of discovery of supersymmetric (SUSY) particles at the LHC may appeal to a non-supersymmetric solution for the Standard Model problem of the Higgs boson mass divergence, the origin of the electroweak energy scale and the physical nature of the cosmological dark matter in the approach of composite Higgs boson. If the Higgs boson consists of charged constituents, their binding can lead to stable particles with electroweak charges. Such particles can take part in sphaleron transitions in the early Universe, which balance their excess with baryon asymmetry. Constraints on exotic charged species leave only stable particles with charge 2n possible, which can bind with n nuclei of primordial helium in neutral dark atoms. The predicted ratio of densities of dark atoms and baryonic matter determines the condition for dark atoms to dominate in the cosmological dark matter. To satisfy this condition of the dark-atom nature of the observed dark matter, the mass of new stable 2n charged particles should be within reach of the LHC for their searches. We discuss the possibilities of dark-atom binding in multi-atom systems and present state-of-the-art quantum mechanical descriptions of dark-atom interactions with nuclei. Annual modulations in such interactions with nuclei of underground detectors can explain the positive results of DAMA/NaI and DAMA/LIBRA experiments and the negative results of the underground WIMP searches. Full article
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19 pages, 2294 KB  
Review
Neutrino at Different Epochs of the Friedmann Universe
by Alexandre V. Ivanchik, Oleg A. Kurichin and Vlad Yu. Yurchenko
Universe 2024, 10(4), 169; https://doi.org/10.3390/universe10040169 - 2 Apr 2024
Cited by 10 | Viewed by 2991
Abstract
At least two relics of the Big Bang have survived: the cosmological microwave background (CMB) and the cosmological neutrino background (CνB). Being the second most abundant particle in the universe, the neutrino has a significant impact on its evolution from the [...] Read more.
At least two relics of the Big Bang have survived: the cosmological microwave background (CMB) and the cosmological neutrino background (CνB). Being the second most abundant particle in the universe, the neutrino has a significant impact on its evolution from the Big Bang to the present day. Neutrinos affect the following cosmological processes: the expansion rate of the universe, its chemical and isotopic composition, the CMB anisotropy and the formation of the large-scale structure of the universe. Another relic neutrino background is theoretically predicted, it consists of non-equilibrium antineutrinos of Primordial Nucleosynthesis arising as a result of the decay of neutrons and tritium nuclei. Such antineutrinos are an indicator of the baryon asymmetry of the universe. In addition to experimentally detectable active neutrinos, the existence of sterile neutrinos is theoretically predicted to generate neutrino masses and explain their oscillations. Sterile neutrinos can also solve such cosmological problems as the baryonic asymmetry of the universe and the nature of dark matter. The recent results of several independent experiments point to the possibility of the existence of a light sterile neutrino. However, the existence of such a neutrino is inconsistent with the predictions of the Standard Cosmological Model. The inclusion of a non-zero lepton asymmetry of the universe and/or increasing the energy density of active neutrinos can eliminate these contradictions and reconcile the possible existence of sterile neutrinos with Primordial Nucleosynthesis, the CMB anisotropy, and also reduce the H0-tension. In this brief review, we discuss the influence of the physical properties of active and sterile neutrinos on the evolution of the universe from the Big Bang to the present day. Full article
(This article belongs to the Special Issue The Friedmann Cosmology: A Century Later)
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26 pages, 2095 KB  
Article
Asymmetric Dark Matter in Baryon Asymmetrical Universe
by Vitaly A. Beylin, Maxim Yu. Khlopov and Danila O. Sopin
Symmetry 2024, 16(3), 311; https://doi.org/10.3390/sym16030311 - 6 Mar 2024
Cited by 3 | Viewed by 2998
Abstract
New heavy particles with electroweak charges arise in extensions of the standard model. They should take part in sphaleron transitions in the early Universe, which balance baryon asymmetry with the excess of new charged particles. If electrically charged with charge 2n [...] Read more.
New heavy particles with electroweak charges arise in extensions of the standard model. They should take part in sphaleron transitions in the early Universe, which balance baryon asymmetry with the excess of new charged particles. If electrically charged with charge 2n, they bind with n nuclei of primordial helium in dark atoms of dark matter. This makes it possible to find the ratio of densities of asymmetric dark matter and baryonic matter. Examples of the model with new, successive, and stable generation of quarks and leptons and the minimal walking technicolor model are considered. Full article
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