scholarly journals Complex Limiting Velocity Expressions as Likely Characteristics of Dark Matter Particles

2020 ◽  
Vol 12 (4) ◽  
pp. 107
Author(s):  
Josip Soln
Keyword(s):  
Dark Matter ◽  
Particle Velocity ◽  
Dark Matter Particle ◽  
Model Description ◽  
Complex Conjugate ◽  
Beyond The Standard Model ◽  
Cosmological Observations ◽  
Angle Alpha ◽  
Limiting Velocity ◽  
The Universe

Many astrophysical and cosmological observations suggest that the matter in the universe is mostly of the dark matter type whose behavior goes beyond the Standard Model description. Hence it is justifiable to take a drastically different approach to the dark matter particles which is here done through the bicubic equation of limiting particle velocity formalism. The bicubic equation discriminant $D$ in this undertaking satisfy $D\succeq 0 $ determined by the congruent parameter $z$ satisfying $z^{2}\succeq 1$, where formally $z(m)=3\sqrt{3}mv^{2}/2E$, \ with $m$, $v$, and $E$ being respectively, particle mass, velocity and energy. Also nonlinearly related to the the particle congruent parameter $z$ is the particle congruent angle $% \alpha $ . These two dimensionless\ parameters $z$ \ and $\alpha $ simplify expressions in the bicubic equation limiting particle velocity formalism when evaluating the three particle limiting velocities, $c_{1},$ $c_{2}$\ and $c_{3},$ (primary, obscure and normal) in terms of the ordinary particle velocity, $v$. Corresponding to these limiting velocities \ one then deduces, with equal values, dark matter particle energies $E\left(c_{1}\right) $, $E\left( c_{2}\right) $ and $E\left( c_{3}\right) $. The exemplary values of the congruent parameters are in these regions, $1\preceq z\prec 3\sqrt{3}$ $/2$ and $\pi /2\succeq \alpha \succeq \pi /3$ . Already within these ranges of congruent parameters, the bicubic formalism yields for squares of particle limiting velocities that $c_{1}^{2}$ and $c_{2}^{2}$ are complex conjugate to each other, $c_{1}^{2\ast }=c_{2}^{2}$ ,and that $% c_{3\text{ }}^{2}$is real. The imaginary portions of $c_{1}^{2}$ and $% c_{2}^{2}$ do not change the realities of numerically equal to each other dark matter energies $E\left( c_{i}\right) ,i=1,2,3.$ In fact, real $E\left(c_{1,2}\right) $ energies can be equally evaluated with $c_{1,2}^{2}$ or $% \func{Re}$ $c_{1,2}^{2}$ or even with $\func{Im}c_{1,2}^{2}$ so that in new notation, $E\left( _{1,2}^{2}\right) =E\left( \func{Re}c_{1,2}^{2}\right) =E\left( \func{Im}c_{1,2}^{2}\right) $ $=E\left( c_{3}^{2}\right) $ all with the same real values. However, in these notations, the real particle momenta are $\overrightarrow{p}\left( (\func{Re}c_{1,2}^{2}\right) $ and $\\overrightarrow{p}\left( (c_{3}^{2}\right) $, defined with respective energies and, while in similar forms , numerically are different from each other.

scholarly journals Formation of Particle Real Energy in the Bicubic Equation Limiting Particle Velocity Formalism with Possible Applications to Light Dark Matter

2019 ◽  
Vol 11 (2) ◽  
pp. 92
Author(s):  
Josip Soln
Keyword(s):  
Dark Matter ◽  
Particle Velocity ◽  
Dark Matter Particle ◽  
Particle Energy ◽  
Physical Parameters ◽  
The Real ◽  
Complex Particle ◽  
Particle Parameters ◽  
Real Value ◽  
Limiting Velocity

The complex particle energy, appearing in this article, with the suggestive choices of physical parameters,is transformed simply into the real particle energy. Then with the bicubic equation limiting particle velocity formalism, one evaluates the three particle limiting velocities, $c_{1},$ $c_{2}$\ and $% c_{3},$ (primary, obscure and normal) in terms of the ordinary particle velocity, $v$, and derived positive $m_{+}=m\succ 0$ \ and negative \ $% m_{-}=-m\prec 0$ \ \ particle masses with $m_{+}^{2}=m_{-}^{2}=$ $m^{2}$. In general, the important quantity in solving this bicubic equation is the real square value $\ z^{2}(m)$ of the congruent parameter, $z(m)$, that connects real or complex value of particle energy, $E,$ and the real or complex value of particle velocity squared, $v^{2}$, $2Ez(m)=3\sqrt{3}mv^{2}$% . With real $z^{2}(m)$ one determines the real value of discriminant, $D,$ of the bicubic equation, and they together influence the connection between $% E$ and $v^{2}.$ Hence, when $z^{2}\prec 1$ and \ $D\prec 0$ one has simply that $E\gg mv^{2}$. However,with $D\succeq 0$ and $z^{2}\succeq 1$ , both $E$ and $v^{2}$ may become complex simultaneously through connecting relation $% E=3\sqrt{3}mv^{2}/2z(m)$, with their real values satisfying \ Re $E\succcurlyeq m\left( \func{Re}v^{2}\right) $, keeping, however $z^{2}$ the same and real. In this article, this new situation with $D\succeq 0$ is discussed in detail.by looking as how to adjust the particle\ parameters to have $\func{Im% }E=0$ with implication that automatically also Im$v^{2}=0.$.In fact, after having adjusted the particle\ parameters successfully this way, one simply writes Re$E=E$ and Re$v^{2}=v^{2}$. \ \ This way one arrives at that the limiting velocities satisfy $c_{1}=c_{2}$\ $\#$ $c_{3}$, which shows the degeneracy of $c_{1}$ and $c_{2}$ as the same numerical limiting velocity for two particles. This degeneracy $c_{1}$ =$c_{2}$ is simply due to the absence of $\func{Im}E$. It would start disappearing with just an infinitesimal $\func{Im}E$. Now,while $c_{1}=c_{2}$ is real, $c_{3}$ is imaginary and all of them associated with the same particle energy, $E$. With these velocity values the congruent parameter becomes quantized as $% z(m_{\pm })=3\sqrt{3}m_{\pm }v^{2}/2E=\pm 1$ which, with the bicubic discriminant $D=0$ value, implies the quantization also of the particle mass, $m,$ into $m_{\pm }=\pm m$ values . The numerically equal energies,from $E=\func{Re}E$ can be expressed as $\ \ \ \ \ \ \ \ \ \ \ $$E(c_{1,2}($ $m_{\pm }))=E(c_{3}(m_{\pm }))$ either directly in terms of $% c_{1}(m_{\pm })=c_{2}(m_{\pm })$ and $c_{3}(m_{\pm })$ or also indirectly in terms of particle velocity, $v$, as well as in the Lorentzian fixed forms with $v^{2}\#$ $c_{1}^{2},$ $c_{2}^{2}$\ or $c_{3}^{2}$ assuring different from zero mass, $m$ $\#$ $0$. At the end, with here developed formalism, one calculates for a light sterile neutrino dark matter particle, the energies associated with $m_{\pm} $ masses and $c_{1,2}$and $c_{3}$ limiting velocities.

scholarly journals Relativistic impulse approximation in the atomic ionization process induced by millicharged particles

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Chen-Kai Qiao ◽  
Shin-Ted Lin ◽  
Hsin-Chang Chi ◽  
Hai-Tao Jia
Keyword(s):  
Dark Matter ◽  
Cross Sections ◽  
Direct Detection ◽  
Impulse Approximation ◽  
Dark Matter Particle ◽  
Ionization Process ◽  
Beyond The Standard Model ◽  
Next Generation ◽  
Many Body ◽  
Atomic Ionization

Abstract The millicharged particle has become an attractive topic to probe physics beyond the Standard Model. In direct detection experiments, the parameter space of millicharged particles can be constrained from the atomic ionization process. In this work, we develop the relativistic impulse approximation (RIA) approach, which can duel with atomic many-body effects effectively, in the atomic ionization process induced by millicharged particles. The formulation of RIA in the atomic ionization induced by millicharged particles is derived, and the numerical calculations are obtained and compared with those from free electron approximation and equivalent photon approximation. Concretely, the atomic ionizations induced by mllicharged dark matter particles and millicharged neutrinos in high-purity germanium (HPGe) and liquid xenon (LXe) detectors are carefully studied in this work. The differential cross sections, reaction event rates in HPGe and LXe detectors, and detecting sensitivities on dark matter particle and neutrino millicharge in next-generation HPGe and LXe based experiments are estimated and calculated to give a comprehensive study. Our results suggested that the next-generation experiments would improve 2-3 orders of magnitude on dark matter particle millicharge δχ than the current best experimental bounds in direct detection experiments. Furthermore, the next-generation experiments would also improve 2-3 times on neutrino millicharge δν than the current experimental bounds.

scholarly journals Beyond the Standard Model at LEP

1991 ◽  
Vol 336 (1642) ◽  
pp. 247-259 ◽  
Keyword(s):  
Dark Matter ◽  
Standard Model ◽  
Beyond The Standard Model ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Massive Neutrinos ◽  
Supersymmetric Particles ◽  
The Universe

LEP data constrain severely many proposed extensions of the Standard Model. These include: massive neutrinos, which are now largely excluded as candidates for the dark matter of the Universe; supersymmetric particles, the lightest of which would still constitute detectable dark matter; technicolour, of which many favoured versions are now excluded by precision electroweak measurements; and grand unified theories, of which LEP data favour supersymmetric versions.

THE LHC AND THE UNIVERSE AT LARGE

2009 ◽  
Vol 24 (04) ◽  
pp. 657-669 ◽  
Author(s):  
PIERRE BINÉTRUY
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Dark Matter ◽  
Extra Dimensions ◽  
Beyond The Standard Model ◽  
Electroweak Phase Transition ◽  
Primordial Gravitational Waves ◽  
The Standard Model ◽  
Particle Astrophysics ◽  
The Universe

I discuss here some of the deeper connections between the physics studied at the LHC (electroweak phase transition, physics beyond the Standard Model, extra dimensions) and some of the most important issues in the field of particle astrophysics and cosmology (dark matter, primordial gravitational waves, black holes,…).

scholarly journals Observational Role of Dark Matter in f(R) Models for Structure Formation

2018 ◽  
Vol 46 ◽  
pp. 1860045
Author(s):  
Murli Manohar Verma ◽  
Bal Krishna Yadav
Keyword(s):  
Dynamical System ◽  
Dark Matter ◽  
Fixed Points ◽  
Gravity Models ◽  
Stability Conditions ◽  
Cosmological Observations ◽  
General Relativistic ◽  
The Stability ◽  
The Universe

The fixed points for the dynamical system in the phase space have been calculated with dark matter in the [Formula: see text] gravity models. The stability conditions of these fixed points are obtained in the ongoing accelerated phase of the universe, and the values of the Hubble parameter and Ricci scalar are obtained for various evolutionary stages of the universe. We present a range of some modifications of general relativistic action consistent with the [Formula: see text]CDM model. We elaborate upon the fact that the upcoming cosmological observations would further constrain the bounds on the possible forms of [Formula: see text] with greater precision that could in turn constrain the search for dark matter in colliders.

Particle physics today, tomorrow and beyond

2018 ◽  
Vol 33 (02) ◽  
pp. 1830003 ◽  
Author(s):  
John Ellis
Keyword(s):  
Dark Matter ◽  
Standard Model ◽  
Particle Physics ◽  
Beyond The Standard Model ◽  
Visible Matter ◽  
The Standard Model ◽  
Cosmological Inflation ◽  
The Stability ◽  
The Universe ◽  
Lhc I

The most important discovery in particle physics in recent years was that of the Higgs boson, and much effort is continuing to measure its properties, which agree obstinately with the Standard Model, so far. However, there are many reasons to expect physics beyond the Standard Model, motivated by the stability of the electroweak vacuum, the existence of dark matter and the origin of the visible matter in the Universe, neutrino physics, the hierarchy of mass scales in physics, cosmological inflation and the need for a quantum theory for gravity. Most of these issues are being addressed by the experiments during Run 2 of the LHC, and supersymmetry could help resolve many of them. In addition to the prospects for the LHC, I also review briefly those for direct searches for dark matter and possible future colliders.

scholarly journals Neutron to dark matter decay in neutron stars

2018 ◽  
Vol 33 (31) ◽  
pp. 1844020 ◽  
Author(s):  
T. F. Motta ◽  
P. A. M. Guichon ◽  
A. W. Thomas
Keyword(s):  
Dark Matter ◽  
Neutron Star ◽  
Neutron Stars ◽  
Decay Width ◽  
Decay Mode ◽  
Measurement Problem ◽  
Dark Matter Particle ◽  
Neutron Decay ◽  
Astrophysical Data ◽  
The Universe

Recent proposals have suggested that a previously unknown decay mode of the neutron into a dark matter particle could solve the long lasting measurement problem of the neutron decay width. We show that, if the dark particle in neutron decay is the major component of the dark matter in the universe, this proposal is in disagreement with modern astrophysical data concerning neutron star masses.

scholarly journals Exploring Properties of Dark and Visible Mass Distribution on Different Scales in the Universe

2005 ◽  
Vol 20 (14) ◽  
pp. 3124-3127
Author(s):  
Yuriy Mishchenko ◽  
Chueng-Ryong Ji
Keyword(s):  
Dark Matter ◽  
Galaxy Clusters ◽  
Mass Distribution ◽  
Linear Correlation ◽  
Spiral Galaxies ◽  
Recent Observation ◽  
Short Note ◽  
Dark Matter Particle ◽  
The Universe

In this short note we discuss recent observation of linear correlation on log-log scale between distribution of dark and visible mass in gravitationally bound systems. The coefficient of such correlation appears to be essentially the same for various systems of dramatically different scales such as spiral galaxies of different luminosities and galaxy clusters. We briefly touch possible interpretations of this observation and implications for the mass of dark matter particle.

scholarly journals DES map shows a smoother distribution of matter than expected: a possible explanation

2021 ◽  
Vol 21 (10) ◽  
pp. 241
Author(s):  
Eugene Oks
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Beyond The Standard Model ◽  
Hydrogen Atoms ◽  
Standard Quantum ◽  
Dark Energy Survey ◽  
Multipole Radiation ◽  
Physical Laws ◽  
Energy Survey ◽  
The Universe

Abstract The largest and most detailed map of the distribution of dark matter in the Universe has been recently created by the Dark Energy Survey (DES) team. The distribution was found to be slightly (by a few percent) smoother and less clumpy than predicted by general relativity. This result was considered as a hint of some new physical laws. In the present paper we offer a relatively simple model that could explain the above result without resorting to any new physical laws. The model deals with the dynamics of a system consisting of a large number of gravitating neutral particles, whose mass is equal to the mass of hydrogen atoms. The central point of the model is a partial inhibition of the gravitation for a relatively small subsystem of the entire system. It would be sufficient for this subsystem to constitute just about a few percent of the total ensemble of particles for explaining the few percent more smooth distribution of dark matter (observed by the DES team) compared to the prediction of general relativity. The most viable candidate for the dark matter particles in this model is the second flavor of hydrogen atoms (SFHA) that has only S-states and therefore does not couple to the electric dipole radiation or even to higher multipole radiation, so that the SFHA is practically dark. The SFHA has experimental confirmation from atomic experiments, it does not go beyond the Standard Model, it is based on standard quantum mechanics and it explains puzzling astrophysical observations of the redshifted line 21 cm from the early Universe. Thus, our model explaining the DES result of a little too smooth distribution of dark matter without resorting to any new physical laws seems to be self-consistent.

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