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13 pages, 4275 KB  
Article
Fluctuations of Temperature in the Polyakov Loop-Extended Nambu–Jona-Lasinio Model
by He Liu, Peng Wu, Hong-Ming Liu and Peng-Cheng Chu
Universe 2026, 12(2), 37; https://doi.org/10.3390/universe12020037 - 28 Jan 2026
Viewed by 87
Abstract
In this study, we investigate temperature fluctuations in hot QCD matter using a three-flavor Polyakov loop-extended Nambu–Jona-Lasinio (PNJL) model. The high-order cumulant ratios Rn2 (n>2) exhibit non-monotonic variations across the chiral phase transition, characterized by slight fluctuations [...] Read more.
In this study, we investigate temperature fluctuations in hot QCD matter using a three-flavor Polyakov loop-extended Nambu–Jona-Lasinio (PNJL) model. The high-order cumulant ratios Rn2 (n>2) exhibit non-monotonic variations across the chiral phase transition, characterized by slight fluctuations in the chiral crossover region and significant oscillations around the critical point. In contrast, distinct peak and dip structures are observed in the cumulant ratios at low-baryon chemical potential. These structures gradually weaken and eventually vanish at high chemical potential as they compete with the sharpening of the chiral phase transition, particularly near the critical point and the first-order phase transition. Our results indicate that these non-monotonic peak and dip structures in high-order cumulant ratios are associated with the deconfinement phase transition. This study quantitatively analyzes temperature fluctuation behavior across different phase transition regions, and the findings are expected to be observed and validated in heavy-ion collision experiments through measurements of event-by-event mean transverse momentum fluctuations. Full article
(This article belongs to the Special Issue Relativistic Heavy-Ion Collisions: Theory and Observation)
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49 pages, 1451 KB  
Review
Triply Heavy Ω Baryons with Jethad: A High-Energy Viewpoint
by Francesco Giovanni Celiberto
Symmetry 2026, 18(1), 29; https://doi.org/10.3390/sym18010029 - 23 Dec 2025
Cited by 1 | Viewed by 347
Abstract
We investigate the leading-power fragmentation of triply heavy Ω baryons in high-energy hadronic collisions. Extending our previous work on the Ω3c sector, we release the full OMG3Q1.0 family of collinear fragmentation functions by completing the description of the charm channel and [...] Read more.
We investigate the leading-power fragmentation of triply heavy Ω baryons in high-energy hadronic collisions. Extending our previous work on the Ω3c sector, we release the full OMG3Q1.0 family of collinear fragmentation functions by completing the description of the charm channel and delivering novel Ω3b functions. These hadron-structure-oriented functions are constructed from improved proxy-model calculations for heavy-quark and gluon fragmentation, matched to a flavor-aware DGLAP evolution based on the HF-NRevo scheme. For phenomenological applications, we employ the (sym)Jethad multimodular interface to compute and analyze NLL/NLO+ semi-inclusive Ω3Q plus jet distributions at the HL-LHC and FCC. This work consolidates the link between hadron structure, rare baryon production, and resummed QCD at the energy frontier. Full article
(This article belongs to the Special Issue Symmetry and Quantum Chromodynamics)
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10 pages, 1255 KB  
Article
Pion Production in an Extended Parity Doublet Model
by Jia Zhou, Kyungil Kim, Sangyong Jeon, Jun Xu and Youngman Kim
Symmetry 2025, 17(12), 2155; https://doi.org/10.3390/sym17122155 - 15 Dec 2025
Viewed by 174
Abstract
We study heavy-ion collisions with a focus on pion production using an extended parity doublet model implemented in the “DaeJeon Boltzmann–Uehling–Uhlenbeck” (DJBUU) code. We consider three different systems—108Sn + 112Sn, 112Sn + 124Sn, and 132Sn + 124 [...] Read more.
We study heavy-ion collisions with a focus on pion production using an extended parity doublet model implemented in the “DaeJeon Boltzmann–Uehling–Uhlenbeck” (DJBUU) code. We consider three different systems—108Sn + 112Sn, 112Sn + 124Sn, and 132Sn + 124Sn—at a beam energy of Ebeam=270 A MeV, with an impact parameter of 3 fm, and compare our results with the SπRIT data. Since one of the key features of the parity doublet model is the existence of a chiral-invariant mass m0 that contributes to the nucleon mass, we investigate how pion production depends on the chiral-invariant mass in these heavy-ion collisions. We adopt the values of the chiral-invariant mass of 600, 700, and 800 MeV and find that the case with m0=800 MeV best reproduces the experimental data. We also observe that a larger m0 results in a higher maximum baryon density of nuclear matter produced during heavy-ion collisions. Full article
(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)
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12 pages, 384 KB  
Article
QCD Sum Rule Study of Topped Mesons Within Heavy Quark Effective Theory
by Shu-Wei Zhang, Xuan Luo, Hui-Min Yang and Hua-Xing Chen
Universe 2025, 11(10), 334; https://doi.org/10.3390/universe11100334 - 9 Oct 2025
Viewed by 508
Abstract
Motivated by the recent CMS observation of a near-threshold enhancement in top quark pair production, we investigate a novel class of hadronic systems containing a single top quark: the topped mesons (tq¯, with [...] Read more.
Motivated by the recent CMS observation of a near-threshold enhancement in top quark pair production, we investigate a novel class of hadronic systems containing a single top quark: the topped mesons (tq¯, with q¯=u¯,d¯,s¯). In contrast to the extensively studied toponium (tt¯) system—analyzed primarily within perturbative QCD—topped mesons offer a complementary nonperturbative probe of QCD dynamics in the heavy quark limit. These states are expected to exhibit longer lifetimes and narrower decay widths than toponium, as only a single top quark undergoes weak decay. We employ QCD sum rules within the framework of heavy quark effective theory to study the structure and mass spectrum of ground-state topped mesons. Our analysis predicts masses near 173.1 GeV, approximately 0.5–0.6 GeV above the top quark pole mass. Compared with singly topped baryons (tqq, with q=u,d,s), topped mesons have a simpler quark composition and more favorable decay channels (a topped meson is anticipated to decay weakly into a Υ meson and a charmed meson), enhancing their potential for both theoretical analysis and experimental discovery. Full article
(This article belongs to the Section High Energy Nuclear and Particle Physics)
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11 pages, 285 KB  
Article
Diquark Study in Quark Model
by Xinmei Zhu, Hongxia Huang and Jialun Ping
Particles 2025, 8(4), 83; https://doi.org/10.3390/particles8040083 - 2 Oct 2025
Viewed by 579
Abstract
To investigate diquark correlation in baryons, the baryon spectra with different light–heavy quark combinations are calculated using Gaussian expansion method within both the naive quark model and the chiral quark model. By computing the diquark energies and separations between any two quarks in [...] Read more.
To investigate diquark correlation in baryons, the baryon spectra with different light–heavy quark combinations are calculated using Gaussian expansion method within both the naive quark model and the chiral quark model. By computing the diquark energies and separations between any two quarks in baryons, we analyze the diquark effect in the ud-q/Q, us-Q, ss-q/Q, and QQ-q/Q systems (where q=u,d, or s; Q=c,b). The results show that diquark correlations exist in baryons. In particular, for qq-Q and QQ-q systems, the same type of diquark exhibits nearly identical energy and size across different baryons. In the orbital ground states of baryons, scalar–isoscalar diquarks have lower energy and a smaller size compared to vector–isovector diquark, which qualifies them as “good diquarks”. In QQ-q systems, a larger mass of Q leads to a smaller diquark separation and a more pronounced diquark effect. In qq-Q systems, the separation between the two light quarks remains larger than that between a light and a heavy quark, indicating that the internal structure of such diquarks must be taken into account. A comparison between the naive quark model and the chiral quark model reveals that the introduction of meson exchange slightly increases the diquark size in most systems. Full article
(This article belongs to the Special Issue Strong QCD and Hadron Structure)
32 pages, 1122 KB  
Article
Distribution of Heavy-Element Abundances Generated by Decay from a Quasi-Equilibrium State
by Gerd Röpke, David Blaschke and Friedrich K. Röpke
Universe 2025, 11(10), 323; https://doi.org/10.3390/universe11100323 - 23 Sep 2025
Cited by 1 | Viewed by 1045
Abstract
We present a freeze-out approach for describing the formation of heavy elements in expanding nuclear matter. Applying concepts used in modeling heavy-ion collisions or ternary fission, we determine the abundances of heavy elements taking into account in-medium effects such as Pauli blocking and [...] Read more.
We present a freeze-out approach for describing the formation of heavy elements in expanding nuclear matter. Applying concepts used in modeling heavy-ion collisions or ternary fission, we determine the abundances of heavy elements taking into account in-medium effects such as Pauli blocking and the Mott effect, which describes the dissolution of nuclei at high densities of nuclear matter. With this approach, we search for a universal initial distribution in a quasi-equilibrium state from which the coarse-grained pattern of the solar abundances of heavy elements freezes out and evolves by radioactive decay of the excited states. The universal initial state is characterized by the Lagrange parameters, which are related to temperature and chemical potentials of neutrons and protons. We show that such a state exists and determine a temperature of 5.266 MeV, a neutron chemical potential of 940.317 MeV and a proton chemical potential of 845.069 MeV, with a baryon number density of 0.013 fm−3 and a proton fraction of 0.13. Heavy neutron-rich nuclei such as the hypothetical double-magic nucleus 358Sn appear in the initial distribution and contribute to the observed abundances after fission. We discuss astrophysical scenarios for the realization of this universal initial distribution for heavy-element nucleosynthesis, including supernova explosions, neutron star mergers and the inhomogeneous Big Bang. The latter scenario may be of interest in the light of early massive objects observed with the James Webb Space Telescope and opens new perspectives on the universality of the observed r-process patterns and the lack of observations of population III stars. Full article
(This article belongs to the Section High Energy Nuclear and Particle Physics)
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46 pages, 1618 KB  
Review
Electroweak Form Factors of Baryons in Dense Nuclear Matter
by G. Ramalho, K. Tsushima and Myung-Ki Cheoun
Symmetry 2025, 17(5), 681; https://doi.org/10.3390/sym17050681 - 29 Apr 2025
Cited by 2 | Viewed by 1080
Abstract
There is evidence that the properties of hadrons are modified in a nuclear medium. Information about the medium modifications of the internal structure of hadrons is fundamental for the study of dense nuclear matter and high-energy processes, including heavy-ion and nucleus–nucleus collisions. At [...] Read more.
There is evidence that the properties of hadrons are modified in a nuclear medium. Information about the medium modifications of the internal structure of hadrons is fundamental for the study of dense nuclear matter and high-energy processes, including heavy-ion and nucleus–nucleus collisions. At the moment, however, empirical information about medium modifications of hadrons is limited; therefore, theoretical studies are essential for progress in the field. In the present work, we review theoretical studies of the electromagnetic and axial form factors of octet baryons in symmetric nuclear matter. The calculations are based on a model that takes into account the degrees of freedom revealed in experimental studies of low and intermediate square transfer momentum q2=Q2: valence quarks and meson cloud excitations of baryon cores. The formalism combines a covariant constituent quark model, developed for a free space (vacuum) with the quark–meson coupling model for extension to the nuclear medium. We conclude that the nuclear medium modifies the baryon properties differently according to the flavor content of the baryons and the medium density. The effects of the medium increase with density and are stronger (quenched or enhanced) for light baryons than for heavy baryons. In particular, the in-medium neutrino–nucleon and antineutrino–nucleon cross-sections are reduced compared to the values in free space. The proposed formalism can be extended to densities above the normal nuclear density and applied to neutrino–hyperon and antineutrino–hyperon scattering in dense nuclear matter. Full article
(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)
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12 pages, 551 KB  
Article
Deep-Learning-Based Optimization of the Signal/Background Ratio for Λ Particles in the CBM Experiment at FAIR
by Ivan Kisel, Robin Lakos and Gianna Zischka
Algorithms 2025, 18(4), 229; https://doi.org/10.3390/a18040229 - 16 Apr 2025
Viewed by 943
Abstract
Machine learning algorithms have become essential tools in modern physics experiments, enabling the precise and efficient analysis of large-scale experimental data. The Compressed Baryonic Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) demands innovative methods for processing the vast [...] Read more.
Machine learning algorithms have become essential tools in modern physics experiments, enabling the precise and efficient analysis of large-scale experimental data. The Compressed Baryonic Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) demands innovative methods for processing the vast data volumes generated at high collision rates of up to 10 MHz. This study presents a deep-learning-based approach to enhance the signal/background (S/B) ratio for Λ particles within the Kalman Filter (KF) Particle Finder framework. Using the Artificial Neural Networks for First Level Event Selection (ANN4FLES) package of CBM, a multi-layer perceptron model was designed and trained on simulated data to classify Λ particle candidates as signal or background. The model achieved over 98% classification accuracy, enabling significant reductions in background—in particular, a strong suppression of the combinatorial background that lacks physical meaning—while preserving almost the whole Λ particle signal. This approach improved the S/B ratio by a factor of 10.97, demonstrating the potential of deep learning to complement existing particle reconstruction techniques and contribute to the advancement of data analysis methods in heavy-ion physics. Full article
(This article belongs to the Special Issue 2024 and 2025 Selected Papers from Algorithms Editorial Board Members)
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10 pages, 320 KB  
Article
Elliptic and Quadrangular Flow of Protons in the High-Baryon-Density Region
by Shaowei Lan, Zuowen Liu, Like Liu and Shusu Shi
Universe 2025, 11(1), 27; https://doi.org/10.3390/universe11010027 - 17 Jan 2025
Cited by 1 | Viewed by 1022
Abstract
The collective flow provides valuable insights into the anisotropic expansion of particles produced in heavy-ion collisions and is sensitive to the equation of the state of nuclear matter in high-baryon-density regions. In this paper, we use the hadronic transport model SMASH to investigate [...] Read more.
The collective flow provides valuable insights into the anisotropic expansion of particles produced in heavy-ion collisions and is sensitive to the equation of the state of nuclear matter in high-baryon-density regions. In this paper, we use the hadronic transport model SMASH to investigate the elliptic flow (v2), quadrangular flow (v4), and their ratio (v4/v22) in Au+Au collisions at high baryon density. Our results show that the inclusion of baryonic mean-field potential in the model successfully reproduces experimental data from the HADES experiment, indicating that baryonic interactions play an important role in shaping anisotropic flow. In addition to comparing the transverse momentum (pT), rapidity, and centrality dependence of v4/v22 between HADES data and model calculations, we also explore its time evolution and energy dependence across sNN= 2.4 to 4.5 GeV. While the ratio v4/v22 for high-pT particles approaches 0.5, which aligns with expectations from hydrodynamic behavior, we emphasize that this result primarily reflects agreement with the HADES measurements rather than a definitive indication of ideal fluid behavior. These findings contribute to understanding the early-stage dynamics in heavy-ion collisions at high baryon density. Full article
(This article belongs to the Section High Energy Nuclear and Particle Physics)
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8 pages, 345 KB  
Article
CP Violation: Differing Binding Energy Levels of Quarks and Antiquarks, and Their Transitions in Λ-Baryons and B-Mesons
by Dimitris M. Christodoulou and Demosthenes Kazanas
Foundations 2024, 4(4), 552-559; https://doi.org/10.3390/foundations4040036 - 15 Oct 2024
Viewed by 1784
Abstract
We consider spontaneous quark transitions between the Λ0 baryon and its resonant states, and (anti)quark transitions between the neutral kaon K0 and the two heavy ηq-mesons (q = c, b). The measured differences in mass deficits are used to [...] Read more.
We consider spontaneous quark transitions between the Λ0 baryon and its resonant states, and (anti)quark transitions between the neutral kaon K0 and the two heavy ηq-mesons (q = c, b). The measured differences in mass deficits are used to calculate the binding energy levels of valence c and b (anti)quarks in these transitions. The method takes into account the isospin energy release in K0 transitions and the work conducted by the strong force in suppressing internal Coulomb repulsions that develop in the charged Λc+-baryon. We find that the flips sc and s¯c¯ both release energy back to the strong field and that the overall range of quark energy levels above their u-ground is 100-MeV wider than that of antiquark energy levels above their d¯-ground. The wider quark range stems from the flip sb, which costs 283 MeV more (or 3× more) than the corresponding antiquark flip s¯b¯. At the same time, transitions from the respective ground states to the s and s¯ states (or the c and c¯ states) point to a clear origin of the elusive charge-parity (CP) violation. The determined binding energy levels of (anti)quarks allow us to analyze in depth the (anti)quark transitions in Λ-baryons and B-mesons. Full article
(This article belongs to the Section Physical Sciences)
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14 pages, 305 KB  
Article
Gravitational Particle Production and the Hubble Tension
by Recai Erdem
Universe 2024, 10(9), 338; https://doi.org/10.3390/universe10090338 - 23 Aug 2024
Cited by 10 | Viewed by 1370
Abstract
The effect of gravitational particle production of scalar particles on the total effective cosmic energy density (in the era after photon decoupling till the present) is considered. The effect is significant for heavy particles. It is found that gravitational particle production results in [...] Read more.
The effect of gravitational particle production of scalar particles on the total effective cosmic energy density (in the era after photon decoupling till the present) is considered. The effect is significant for heavy particles. It is found that gravitational particle production results in an effective increase in the directly measured value of the Hubble constant H0, while it does not affect the value of the Hubble constant in the calculation of the number density of baryons at the present time that is used to calculate recombination redshift. This may explain why the Hubble constants determined by local measurements and non-local measurements (such as CMB) are different. This suggests that gravitational particle production may have a non-negligible impact on H0 tension. Full article
(This article belongs to the Special Issue Current Status of the Hubble Tension)
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 2 | Viewed by 2415
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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23 pages, 549 KB  
Article
Quark Clusters, QCD Vacuum and the Cosmological 7Li, Dark Matter and Dark Energy Problems
by Rachid Ouyed, Denis Leahy, Nico Koning and Prashanth Jaikumar
Universe 2024, 10(3), 115; https://doi.org/10.3390/universe10030115 - 1 Mar 2024
Cited by 2 | Viewed by 1921
Abstract
We propose a non-exotic electromagnetic solution (within the standard model of particle physics) to the cosmological 7Li problem based upon a narrow 2 MeV photo-emission line from the decay of light glueballs (LGBs). These LGBs form within color superconducting quark clusters (SQCs), [...] Read more.
We propose a non-exotic electromagnetic solution (within the standard model of particle physics) to the cosmological 7Li problem based upon a narrow 2 MeV photo-emission line from the decay of light glueballs (LGBs). These LGBs form within color superconducting quark clusters (SQCs), which are tens of Fermi in size, in the radiation-dominated post-BBN epoch. The mono-chromatic line from the LGBγ+γ decay reduces Big Bang nucleosynthesis (BBN) 7Be by 2/3 without affecting other abundances or the cosmic microwave background (CMB) physics, provided the combined mass of the SQCs is greater than the total baryonic mass in the universe. Following the LGB emission, the in-SQC Quantum ChromoDynamics (QCD) vacuum becomes unstable and “leaks” (via quantum tunneling) into the external space-time (trivial) vacuum, inducing a decoupling of SQCs from hadrons. In seeking a solution to the 7Li problem, we uncovered a solution that also addresses the Dark Energy (DE) and dark matter (DM) problem, making these critical problems intertwined in our model. Being colorless, charge-neutral, optically thin, and transparent to hadrons, SQCs interact only gravitationally, making them a viable cold DM (CDM) candidate. The leakage (i.e., quantum tunneling) of the in-SQC QCD vacuum to the trivial vacuum offers an explanation of DE in our model and allows for a cosmology that evolves into a ΛCDM universe at a low redshift with a possible resolution of the Hubble tension. Our model distinguishes itself by proposing that the QCD vacuum within SQCs possesses the ability to tunnel into the exterior trivial vacuum, resulting in the generation of DE. This implies the possibility that DM and hadrons might represent distinct phases of quark matter within the framework of QCD, characterized by different vacuum properties. We discuss SQC formation in heavy-ion collision experiments at moderate temperatures and the possibility of detection of MeV photons from the LGBγ+γ decay. Full article
(This article belongs to the Section Cosmology)
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5 pages, 225 KB  
Article
Understanding the Effect of Conserved Charges on the Coalescence Sum Rule of Directed Flow
by Kishora Nayak, Shu-Su Shi and Zi-Wei Lin
Universe 2024, 10(3), 112; https://doi.org/10.3390/universe10030112 - 1 Mar 2024
Cited by 2 | Viewed by 1692
Abstract
Recently, the rapidity-odd directed flow (v1) of produced hadrons (K, ϕ, p¯, Λ¯, Ξ¯+, Ω, and Ω¯+) has been studied. Several combinations of these [...] Read more.
Recently, the rapidity-odd directed flow (v1) of produced hadrons (K, ϕ, p¯, Λ¯, Ξ¯+, Ω, and Ω¯+) has been studied. Several combinations of these produced hadrons, with very small mass differences but differences in the net electric charge (Δq) and net strangeness (ΔS) on the two sides, have been considered. A difference in v1 between the two sides of these combinations (Δv1) has been proposed as a consequence of the electromagnetic field produced in relativistic heavy-ion collisions, especially if Δv1 increases with Δq. Our study is performed to understand the effect of the coalescence sum rule (CSR) on Δv1. We point out that the CSR leads to Δv1=cqΔq+cSΔS, where the coefficients cq and cS reflect the Δv1 of produced quarks. Equivalently, one can write Δv1=cqΔq+cBΔB, involving the difference in the net baryon number ΔB, where the CSR gives cB=3cS. We then propose two methods to extract the coefficients for the Δq and ΔS dependences of Δv1. Full article
(This article belongs to the Special Issue Multiparticle Dynamics)
10 pages, 453 KB  
Article
How Long Does the Hydrogen Atom Live?
by David McKeen and Maxim Pospelov
Universe 2023, 9(11), 473; https://doi.org/10.3390/universe9110473 - 4 Nov 2023
Cited by 5 | Viewed by 3100
Abstract
It is possible that the proton is stable while atomic hydrogen is not. This is the case in models with new particles carrying baryon number which are light enough to be stable themselves, but heavy enough so that proton decay is kinematically blocked. [...] Read more.
It is possible that the proton is stable while atomic hydrogen is not. This is the case in models with new particles carrying baryon number which are light enough to be stable themselves, but heavy enough so that proton decay is kinematically blocked. Models of new physics that explain the neutron lifetime anomaly generically have this feature, allowing for atomic hydrogen to decay through electron capture on a proton. We calculate the radiative hydrogen decay rate involving the emission of a few hundred keV photon, which makes this process experimentally detectable. In particular, we show that the low energy part of the Borexino spectrum is sensitive to radiative hydrogen decay, and turn this into a limit on the hydrogen lifetime of order 1030s or stronger. For models where the neutron mixes with a dark baryon, χ, this limits the mixing angle to roughly 1011, restricting the nχγ branching to 104, over a wide range of parameter space. Full article
(This article belongs to the Special Issue Neutron Lifetime)
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