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26 pages, 441 KiB

Open AccessArticle

Neutrino Oscillations in the Model of Interaction of Spinor Fields with Zero-Range Potential Concentrated on a Plane

by Yury Pismak and Olga Shakhova

Symmetry 2021, 13(11), 2180; https://doi.org/10.3390/sym13112180 - 15 Nov 2021

Viewed by 1725

Abstract

Symanzik’s approach to the description of quantum field systems in an inhomogeneous space-time is used to construct a model for the interaction of neutrino fields with matter. In this way, the problem of the influence of strong inhomogeneities of the medium on the [...] Read more.

Symanzik’s approach to the description of quantum field systems in an inhomogeneous space-time is used to construct a model for the interaction of neutrino fields with matter. In this way, the problem of the influence of strong inhomogeneities of the medium on the processes of oscillations is considered. As a simple example, a model of neutrino scattering on a material plane is investigated. Within this model, in the collisions of particles with planes, a special filtration mechanism can be formed. It has a significant impact on the dynamics of subsequent neutrino oscillations which are analogous to the Mikheev-Smirnov-Wolfenstein effect at propagation of these particles in an adiabatic medium. Taking into account the possibility of the filtration process in a highly inhomogeneous environment can be useful in planning and carrying out experimental studies of neutrino physics. It can also be considered by investigations of the role of neutrino in astrophysical processes by means of numerical simulations methods. Full article

(This article belongs to the Special Issue Symmetry in Particle Physics II)

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28 pages, 1148 KiB

Open AccessArticle

Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment

by Ashot S. Gevorkyan, Alexander V. Bogdanov and Vladimir V. Mareev

Symmetry 2021, 13(8), 1546; https://doi.org/10.3390/sym13081546 - 23 Aug 2021

Cited by 3 | Viewed by 2145

Abstract

Evolution of a self-consistent joint system (JS), i.e., a quantum system (QS) + thermal bath (TB), is considered within the framework of the Langevin–Schrödinger (L-Sch) type equation. As a tested QS, we considered two linearly coupled quantum oscillators that interact with TB. The [...] Read more.

Evolution of a self-consistent joint system (JS), i.e., a quantum system (QS) + thermal bath (TB), is considered within the framework of the Langevin–Schrödinger (L-Sch) type equation. As a tested QS, we considered two linearly coupled quantum oscillators that interact with TB. The influence of TB on QS is described by the white noise type autocorrelation function. Using the reference differential equation, the original L-Sch equation is reduced to an autonomous form on a random space–time continuum, which reflects the fact of the existence of a hidden symmetry of JS. It is proven that, as a result of JS relaxation, a two-dimensional quantized small environment is formed, which is an integral part of QS. The possibility of constructing quantum thermodynamics from the first principles of non-Hermitian quantum mechanics without using any additional axioms has been proven. A numerical algorithm has been developed for modeling various properties and parameters of the QS and its environment. Full article

(This article belongs to the Special Issue Symmetry in Particle Physics II)

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14 pages, 332 KiB

Open AccessArticle

Electroweak Effects in e⁺e⁻→ZH Process

by Andrej Arbuzov, Serge Bondarenko, Lidia Kalinovskaya, Renat Sadykov and Vitaly Yermolchyk

Symmetry 2021, 13(7), 1256; https://doi.org/10.3390/sym13071256 - 13 Jul 2021

Cited by 4 | Viewed by 1735

Abstract

Electroweak radiative corrections to the cross-section of the process

e^{+} e^{-} \to Z H

are considered. The complete one-loop electroweak radiative corrections are evaluated with the help of the SANC system. Higher-order contributions of the initial-state radiation are computed in the [...] Read more.

Electroweak radiative corrections to the cross-section of the process

e^{+} e^{-} \to Z H

are considered. The complete one-loop electroweak radiative corrections are evaluated with the help of the SANC system. Higher-order contributions of the initial-state radiation are computed in the QED structure function formalism. Numerical results are produced by a new version of the ReneSANCe event generator and MCSANCee integrator for the conditions of future electron-positron colliders. The resulting theoretical uncertainty in the description of this process is estimated. Full article

(This article belongs to the Special Issue Symmetry in Particle Physics II)

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11 pages, 346 KiB

Open AccessArticle

Split Casimir Operator and Universal Formulation of the Simple Lie Algebras

by Alexey Isaev and Sergey Krivonos

Symmetry 2021, 13(6), 1046; https://doi.org/10.3390/sym13061046 - 9 Jun 2021

Cited by 3 | Viewed by 1879

Abstract

We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in adjoint representation. By means of these characteristic identities, for all simple Lie algebras we derive explicit formulae for invariant projectors onto irreducible subrepresentations in

T^{\otimes 2}

[...] Read more.

We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in adjoint representation. By means of these characteristic identities, for all simple Lie algebras we derive explicit formulae for invariant projectors onto irreducible subrepresentations in

T^{\otimes 2}

in the case when T is the adjoint representation. These projectors and characteristic identities are considered from the viewpoint of the universal description of the simple Lie algebras in terms of the Vogel parameters. Full article

(This article belongs to the Special Issue Symmetry in Particle Physics II)

22 pages, 9711 KiB

Open AccessFeature PaperArticle

Chains of Interacting Solitons

by Yakov M. Shnir

Symmetry 2021, 13(2), 284; https://doi.org/10.3390/sym13020284 - 7 Feb 2021

Cited by 6 | Viewed by 2239

Abstract

We present an overview of multisoliton chains arising in various non-integrable field theories and discuss different mechanisms which may lead to the occurrence of such axially-symmetric classical solutions. We explain the pattern of interactions between different solitons, in particular Q-balls, Skyrmions, and monopoles, [...] Read more.

We present an overview of multisoliton chains arising in various non-integrable field theories and discuss different mechanisms which may lead to the occurrence of such axially-symmetric classical solutions. We explain the pattern of interactions between different solitons, in particular Q-balls, Skyrmions, and monopoles, and show how chains of interacting non-BPS solitons may form in a dynamic equilibrium between repulsive and attractive forces. Full article

(This article belongs to the Special Issue Symmetry in Particle Physics II)

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14 pages, 1023 KiB

Open AccessArticle

Flavour Anomalies in a U(1) SUSY Extension of the SM

by Alexander Bednyakov and Alfiia Mukhaeva

Symmetry 2021, 13(2), 191; https://doi.org/10.3390/sym13020191 - 26 Jan 2021

Cited by 6 | Viewed by 1590

Abstract

Flavour anomalies have attracted a lot of attention over recent years as they provide unique hints for possible New Physics. Here, we consider a supersymmetric (SUSY) extension of the Standard Model (SM) with an additional anomaly-free gauge

U (1)

group. The [...] Read more.

Flavour anomalies have attracted a lot of attention over recent years as they provide unique hints for possible New Physics. Here, we consider a supersymmetric (SUSY) extension of the Standard Model (SM) with an additional anomaly-free gauge

U (1)

group. The key feature of our model is the particular choice of non-universal charges to the gauge boson

Z^{'}

, which not only allows a relaxation of the flavour discrepancies but, contrary to previous studies, can reproduce the SM mixing matrices both in the quark and lepton sectors. We pay special attention to the latter and explicitly enumerate all parameters relevant for our calculation in the low-energy effective theory. We find regions in the parameter space that satisfy experimental constraints on meson mixing and LHC

Z^{'}

searches and can alleviate the flavour anomalies. In addition, we also discuss the predictions for lepton-flavour violating decays

B^{+} \to K^{+} μ τ

and

B^{+} \to K^{+} e τ

. Full article

(This article belongs to the Special Issue Symmetry in Particle Physics II)

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11 pages, 322 KiB

Open AccessFeature PaperArticle

On ξ-Process for DVCS-Amplitude

by Igor V. Anikin

Symmetry 2020, 12(12), 1996; https://doi.org/10.3390/sym12121996 - 3 Dec 2020

Cited by 3 | Viewed by 1418

Abstract

In this note, we demonstrate in detail the

ξ

-process implementation applied to the deeply virtual Compton scattering amplitude to ensure both the QCD and QED gauge invariance. The presented details are also important for the understanding of the contour gauge used in [...] Read more.

In this note, we demonstrate in detail the

ξ

-process implementation applied to the deeply virtual Compton scattering amplitude to ensure both the QCD and QED gauge invariance. The presented details are also important for the understanding of the contour gauge used in different processes. Full article

(This article belongs to the Special Issue Symmetry in Particle Physics II)

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Review

Jump to: Research

43 pages, 1277 KiB

Open AccessReview

R²-Cosmology and New Windows for Superheavy Dark Matter

by Elena Arbuzova, Alexander Dolgov and Rajnish Singh

Symmetry 2021, 13(5), 877; https://doi.org/10.3390/sym13050877 - 14 May 2021

Cited by 10 | Viewed by 2067

Abstract

Evolution and heating of the universe in

R^{2}

-modified gravity are considered. It is shown that the universe’s history can be separated into four different epochs: (1) inflation, (2) heating due to curvature oscillations (scalaron decay), (3) transition to matter dominated period, [...] Read more.

Evolution and heating of the universe in

R^{2}

-modified gravity are considered. It is shown that the universe’s history can be separated into four different epochs: (1) inflation, (2) heating due to curvature oscillations (scalaron decay), (3) transition to matter dominated period, and (4) conventional cosmology governed by General Relativity. Cosmological density of dark matter (DM) particles for different decay channels of the scalaron is calculated. The bounds on the masses of DM particles are derived for the following dominant decay modes: to minimally coupled scalars, to massive fermions, and to gauge bosons. Full article

(This article belongs to the Special Issue Symmetry in Particle Physics II)

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