Self-consistent numerical approach to track particles in free electron laser interaction with electromagnetic field modes
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Theoretical & Experimental Research in Weak, Electromagnetic & Strong Interactions
The conducted research spans a wide range of topics in the theoretical, experimental and phenomenological aspects of elementary particle interactions. Theory projects involve topics in both the energy frontier and the intensity frontier. The experimental research involves energy frontier with the ATLAS Collaboration at the Large Hadron Collider (LHC). In theoretical research, novel ideas going beyond the Standard Model with strong theoretical motivations were proposed, and their experimental tests at the LHC and forthcoming neutrino facilities were outlined. These efforts fall into the following broad categories: (i) TeV scale new physics models for LHC Run 2, including left-right symmetry and trinification symmetry, (ii) unification of elementary particles and forces, including the unification of gauge and Yukawa interactions, (iii) supersummetry and mechanisms of supersymmetry breaking, (iv) superworld without supersymmetry, (v) general models of extra dimensions, (vi) comparing signals of extra dimensions with those of supersymmetry, (vii) models with mirror quarks and mirror leptons at the TeV scale, (viii) models with singlet quarks and singlet Higgs and their implications for Higgs physics at the LHC, (ix) new models for the dark matter of the universe, (x) lepton flavor violation in Higgs decays, (xi) leptogenesis in radiative models of neutrino masses, (xii) light mediator models of non-standard neutrino interactions, (xiii) anomalous muon decay and short baseline neutrino anomalies, (xiv) baryogenesis linked to nucleon decay, and (xv) a new model for recently observed diboson resonance at the LHC and its other phenomenological implications. The experimental High Energy Physics group has been, and continues to be, a successful and productive contributor to the ATLAS experiment at the LHC. Members of the group performed search for gluinos decaying to stop and top quarks, new heavy gauge bosons decaying to top and bottom quarks, and vector-like quarks produced in pairs and decaying to light quarks. Members of the OSU group played a leading role in the detailed optimization studies for the future ATLAS Inner Tracker (ITk), which will be installed during the Phase-II upgrade, replacing the current tracking system. The proposed studies aim to enhance the ATLAS discovery potential in the high-luminosity LHC era. The group members have contributed to the calibration of algorithms for identifying boosted vector bosons and b-jets, which will help expand the ATLAS reach in many searches for new physics.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Covariant Spectator Theory of np scattering: Isoscalar interaction currents
Using the Covariant Spectator Theory (CST), one boson exchange (OBE) models have been found that give precision fits to low energy $np$ scattering and the deuteron binding energy. The boson-nucleon vertices used in these models contain a momentum dependence that requires a new class of interaction currents for use with electromagnetic interactions. Current conservation requires that these new interaction currents satisfy a two-body Ward-Takahashi (WT), and using principals of {\it simplicity\/} and {\it picture independence\/}, these currents can be uniquely determined. The results lead to general formulae for a two-body current that can be expressed in terms of relativistic $np$ wave functions, ${\it \Psi}$, and two convenient truncated wave functions, ${\it \Psi}^{(2)}$ and $\widehat {\it \Psi}$, which contain all of the information needed for the explicit evaluation of the contributions from the interaction current. These three wave functions can be calculated from the CST bound or scattering state equations (and their off-shell extrapolations). A companion paper uses this formalism to evaluate the deuteron magnetic moment.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Elastic scattering of light nuclei through a simple potential model
The phase function method is adapted to deal with the scattering on our proposed interactions for α–α and α–{sup 3}He systems. The effect of the electromagnetic interaction is included in terms of a screened Coulomb potential. Based on our proposed potential models we present results for α–α and α–{sup 3}He elastic scattering phase shifts which compare well with more detailed calculations.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Zero-range effective field theory for resonant wino dark matter. Part II. Coulomb resummation
Near a critical value of the wino mass where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold, low-energy winos can be described by a zero-range effective field theory (ZREFT) in which the winos interact nonperturbatively through a contact interaction and charged winos also have electromagnetic interactions. At energies near the wino-pair thresholds, the Coulomb interaction from photon exchange between charged winos must also be treated nonperturbatively. The parameters of ZREFT can be determined by matching wino-wino scattering amplitudes calculated by solving the Schrödinger equation for winos interacting through a potential due to the exchange of electroweak gauge bosons. As a result with Coulomb resummation, ZREFT at leading order gives a good description of the low-energy two-body observables for winos.
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Binding the diproton in stars: anthropic limits on the strength of gravity
We calculate the properties and investigate the stability of stars that burn via strong (and electromagnetic) interactions, and compare their properties with those that, as in our Universe, include a rate-limiting weak interaction. It has been suggested that, if the diproton were bound, stars would burn ∼10{sup 18} times brighter and faster via strong interactions, resulting in a universe that would fail to support life. By considering the representative case of a star in our Universe with initially equal numbers of protons and deuterons, we find that stable, 'strong-burning' stars adjust their central densities and temperatures to have familiar surface temperatures, luminosities and lifetimes. There is no 'diproton disaster'. In addition, strong-burning stars are stable in a much larger region of the parameter space of fundamental constants, specifically the strength of electromagnetism and gravity. The strongest anthropic bound on stars in such universes is not their stability, as is the case for stars limited by the weak interaction, but rather their lifetime. Regardless of the strength of electromagnetism, all stars burn out in mere millions of years unless the gravitational coupling constant is extremely small, α{sub G}∼< 10{sup −30}.
79 ASTRONOMY AND ASTROPHYSICS↗
Quasilinear theory of general electromagnetic fluctuations including discrete particle effects for magnetized plasmas: General analysis
The general quasilinear Fokker–Planck kinetic equation for the gyrophase-averaged plasma particle distribution functions in magnetized plasmas is derived, making no restrictions on the energy of the particles and on the frequency of the electromagnetic fluctuations and avoiding the often made Coulomb approximation of the electromagnetic interactions. Here, the inclusion of discrete particle effects breaks the dichotomy of nonlinear kinetic plasma theory divided into the test particle and the test fluctuation approximation because it provides expression of both the non-collective and collective electromagnetic fluctuation spectra in terms of the plasma particle distribution functions. Within the validity of the quasilinear approach, the resulting full quasilinear transport equation can be regarded as a determining nonlinear equation for the time evolution of the plasma particle distribution functions.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Phenomenological description of relativistic-quark interaction on the basis of the Dirac equation with the Cornell potential
Relativistic-quark interaction is described phenomenologically on the basis of the Dirac equation with the Cornell potential. A general form of the initial equation involving the vector and scalar components of the Cornell potential is used for the case of an arbitrary relation between them. The Hamiltonian in the Foldy–Wouthuysen representation is derived in a general form with allowance for electromagnetic interaction. In contrast to earlier investigations, it is relativistic and exact for the zeroth- and first-order terms in the Planck constant and also for those second-order terms that describe contact interactions. General quantum-mechanical equations of motion for the momentum and spin are derived, and the classical limit of the Hamiltonian and for the equations of motion is found for the first time. A relation between the angular velocity of quark spin precession and the force acting on the quark is obtained. The energy of spin–orbit interaction is rather high (on the order of 100 MeV). Terms that describe spin–orbit and contact interactions have opposite signs for the vector and scalar components of the Cornell potential. The evolution of the quark helicity and the spin–spin interaction of the quarks are also calculated.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Electrodynamics of a generalized charged particle in doubly special relativity framework
In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative κ-Minkowski space–time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard–Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of κ-Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac framework of Hamiltonian constraint analysis.
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STARlight: A Monte Carlo simulation program for ultra-peripheral collisions of relativistic ions
© 2016 Elsevier B.V. Ultra-peripheral collisions (UPCs) have been a significant source of study at RHIC and the LHC. In these collisions, the two colliding nuclei interact electromagnetically, via two-photon or photonuclear interactions, but not hadronically; they effectively miss each other. Photonuclear interactions produce vector meson states or more general photonuclear final states, while two-photon interactions can produce lepton or meson pairs, or single mesons. In these interactions, the collision geometry plays a major role. We present a program, STARlight, that calculates the cross-sections for a variety of UPC final states and also creates, via Monte Carlo simulation, events for use in determining detector efficiency. Program summary Program Title: STARlight (v2.2) Program Files doi: http://dx.doi.org/10.17632/xjpf4rxtbj.1 Licensing provisions: GNU GPLv3 Programming Language: C++ External Routines: PYTHIA 8.2 and DPMJET 3.0 are needed for some final states. Nature of problem: The cross-section for ultra-peripheral collisions is obtained by integrating the photon fluxes in transverse impact parameter space, subject to the requirement (which is also impact parameter dependent) that the colliding nuclei do not interact hadronically. The program is a two step process. First, it calculates the cross-sections for the reaction of interest, as a function of W (photon–Pomeron or two-photon center of mass energy), Y (final state rapidity) and pT (final state transverse momentum). Second, STARlight generates Monte Carlo events which can be used to determine cross-sections within specific kinematic constraints or for studies of detector efficiencies. The second step includes the decay of any unstable particles produced in the reaction, with appropriate consideration of particle spins and parity. It outputs these events in ASCII format. Solution method: The program generates a two dimensional look-up table of the production cross-section as a function of final state rapidity and mass. The dimensions of the table are selectable, allowing the user to choose the desired accuracy. For certain final states, a second two-dimensional look-up table, giving the transverse momentum distribution, as a function of rapidity, is also used. With these look-up tables, the program generates final states. Particle decays and the final angular distributions are calculated for each event. Restrictions: The program is focused on ultra-relativistic collisions at Brookhaven's RHIC (Relativistic Heavy Ion Collider) and CERN's LHC (Large Hadron Collider), with final states that are visible in a central detector. At lower energies (i.e., at the CERN SPS), caution should be exercised because STARlight does not account for the longitudinal momentum transfer to the nucleus; this is larger at low beam energies. References: http://starlight.hepforge.org and references in this article.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Analysis of the static magnetic field-dependent optical transmission of Ni nanorod colloidal suspensions
The magnetic field-dependent optical transmission of dilute Ni nanorod aqueous suspensions was investigated. A series of four samples of nanorods were synthesized using the AAO template method and processed to stable colloids. The distributions of their length and diameter were characterized by analysis of TEM images and revealed average diameters of ∼25 nm and different lengths in the range of 60 nm–1100 nm. The collinear magnetic and optical anisotropy was studied by static field-dependent transmission measurements of linearly polarized light parallel and perpendicular to the magnetic field direction. The experimental results were modelled assuming the field-dependent orientation distribution function of a superparamagnetic ensemble for the uniaxial ferromagnetic nanorods in liquid dispersion and extinction cross sections for longitudinal and transversal optical polarization derived from different approaches, including the electrostatic approximation and the separation of variables method, both applied to spheroidal particles, as well as finite element method simulations of spheroids and capped cylindrical particles. The extinction cross sections were compared to reveal the differences associated with the approximations of homogeneous polarization and/or particle shape. The consequences of these approximations for the quantitative analysis of magnetic field-dependent optical transmission measurements were investigated and a reliable protocol derived. Furthermore, the changes in optical cross sections induced by electromagnetic interaction between two nanorods in parallel end-to-end and side-by-side configuration as a function of their separation were studied.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Topics in Theoretical Physics
This award supported a broadly based research effort in theoretical particle physics, including research aimed at uncovering the laws of nature at short (subatomic) and long (cosmological) distances. These theoretical developments apply to experiments in laboratories such as CERN, the facility that operates the Large Hadron Collider outside Geneva, as well as to cosmological investigations done using telescopes and satellites. The results reported here apply to physics beyond the so-called Standard Model of particle physics; physics of high energy collisions such as those observed at the Large Hadron Collider; theoretical and mathematical tools and frameworks for describing the laws of nature at short distances; cosmology and astrophysics; and analytic and computational methods to solve theories of short distance physics. Some specific research accomplishments include + Theories of the electroweak interactions, the forces that give rise to many forms of radioactive decay; + Physics of the recently discovered Higgs boson. + Models and phenomenology of dark matter, the mysterious component of the universe, that has so far been detected only by its gravitational effects. + High energy particles in astrophysics and cosmology. + Algorithmic research and Computational methods for physics of and beyond the Standard Model. + Theory and applications of relativity and its possible limitations. + Topological effects in field theory and cosmology. + Conformally invariant systems and AdS/CFT. This award also supported significant training of students and postdoctoral fellows to lead the research effort in particle theory for the coming decades. These students and fellows worked closely with other members of the group as well as theoretical and experimental colleagues throughout the physics community. Many of the research projects funded by this grant arose in response to recently obtained experimental results in the areas of particle physics and cosmology. We describe a few of these below. Relativity is founded on a symmetry property of nature called "Lorentz Invariance". Like all symmetry properties, it is essential to determine precisely how symmetric nature actually is; that is, do the laws of nature fully respect the symmetry or is there room for tiny symmetry violating effects? An important consequence of Lorentz invariance is the existence of a universal limiting velocity for all physical particles. Light travels at this limiting velocity so it is frequently referred to as simply "the speed of light", but relativity requires that ALL particles travel more slowly than this speed. Once the Higgs particle was discovered in 2012 a natural question was whether or not this particle's speed was consistent with relativity. Although the speed of the Higgs particle is not measurable directly, Cohen has shown that, if the maximal speed of the Higgs particle was not precisely the same as the speed of light, then the Higgs would have some unusual properties. In some cases the Higgs would be unstable to some unusual decay modes; in other cases the interactions of the Higgs with other particles would change the properties of these other particles in ways that could be observed in so-called cosmic rays, very energetic particles (such as photons, protons and other atomic nuclei) coming from space. Once these particles hit the upper atmosphere they produce a "shower" of particles that can be seen by ground-based instruments. If the Higgs has a maximal speed that differs even a tiny bit from the speed of light these showers would look quite different from what is observed. In this way Cohen was able to establish that the Higgs travels with a maximal speed that cannot differ from the speed of light by more than one part in a thousand-trillion. This is by far the most precisely determined property of the Higgs particle. Cohen and Schmaltz reviewed evidence from the Large Hadron Collider (LHC), a particle physics experiment operating at the CERN laboratory near Geneva, for a new particle sometimes called a W'. This evidence included certain unexpected by-products in collisions of protons at very high energy. While the evidence was not significant enough to claim a discovery, it was sufficiently intriguing that many particle theorists worked to construct explanations for this signal. Cohen and Schmaltz were able to determine that such explanations are highly constrained by previous experiments involving collisions of very energetic particles. Nevertheless they were able to construct a theory that adequately explains the LHC data and remain consistent with prior experiments. Their explanation predicts the existence of yet another new particle, called a Z', with a mass slightly greater than that of the W'. This additional particle, if it exists, should be seen as more data is collected from the LHC. Amusingly, there is one collision by-product that has already been seen by the CMS experiment at the LHC that supports the existence of this new particle; however, it is not unlikely that this single event is a so-called "background" event, that is a somewhat atypical by-product of a conventional Standard Model process. This theory for the anomalous LHC data will either be confirmed or excluded with further data-taking at the LHC. The ratio of the number of electrons produced in bottom quark decays over the number of muons produced has been measured at the LHC. This ratio is interesting because it can be predicted very precisely from a basic property of the Standard Model: lepton universality. If lepton universality is correct, the ratio of electrons to muons is predicted to be equal to 1. The first measurements of this ratio find a value different from 1 with a statistical significance of about 3 standard deviations. Schmaltz and collaborator proposed a new extension of the Standard Model which can explain the new data. In addition, Schmaltz and collaborators proposed several new measurements of ratios of decay rates which can confirm or rule out the surprising results from the earlier LHC data. The most recent and precise measurements of the cosmic microwave background from the Planck satellite, from a combination of measurements of the dark matter distribution in the universe, and from a measurement of the expansion rate of the universe today show some disagreement when interpreted in terms of the so-called LambdaCDM model. Schmaltz and collaborators proposed an alternative model to LambdaCDM in which the usual cold dark matter is replaced by a new ``dark sector". This sector consists of a cold dark matter particle which interacts with a newly postulated dark radiation component of the universe. The dark radiation can help explain the discrepancy in measurements of the expansion rate, and the dark matter interactions subtly modify the clumping of dark matter at large scales, thus potentially explaining both kinds of tensions in the data. In two publications Schmaltz described the new model and then performed a precision comparison of the predictions of the model with all currently available cosmological data. The results favor the new model at the level of three standard deviations with current data. Quantum Field Theory (QFT) is the language we use to describe quantum systems which are consistent with Einstein’s theory of Special Relativity. In particular, the requirement of Einstein’s theory that signals not travel faster than the speed of light constrains the types of interactions which particles can engage in. One consequence of relativity is that these interactions cannot preserve particle number. The stronger the interactions, the more severe the particle number violation in a given Relativistic QFT. When particle number violation is strong, it becomes very difficult to adequately parameterize the quantum wave function (which characterizes the state of a quantum system). For example, though we can formulate the QFT which describes the strong force as a set of interactions between quark and gluon particles, we have no clear idea how to express the proton state in terms of these quarks and gluons. This is because the proton, though a bound state of quarks and gluons, is not a state of a fixed number of particles due to strong interactions. Yet, understanding the proton state is very important in order to theoretically predict the reaction rates observed at the LHC in Geneva, which is a proton-proton collider. Katz has formulated a new approach to QFT, which among other things offers a way to adequately approximate the quantum wave function of a bound state at strong coupling. The approximation scheme is related to the fact that any sensible QFT (including that of the strong interactions) is at short distances approximately self-similar upon rescaling of space and time. It turns out that keeping track of the response upon this rescaling is important in efficiently parameterizing the state. Katz and collaborators have used this observation to approximate the state of the proton in toy versions of the strong force. In the late 60s Sheldon Glashow, Abdus Salam and Steven Weinberg (1979 Nobel Prize awardees) proposed a theory unifying weak and electromagnetic interaction which assumed the existence of new particles, the W and Z bosons. The W and Z bosons were eventually detected in high-energy collision in a particle accelerator at CERN, and the recent discovery of the Higgs meson at the Large Hadron Collider (LHC), always at CERN, completed the picture. However, deep theoretical considerations indicate that the theory by Glashow, Weinberg and Salam, often referred to as "the standard model" cannot be the whole story: the existence of new particles and new interactions at yet higher energies is widely anticipated. The experiments at the LHC are looking for these, while theorists, like Brower, Rebbi and collaborators, are investigating models for these new interactions. Working in a large national collaboration with access to the most powerful DOE computers Brower, Rebbi and colleagues have been using calculational techniques, similar to those successfully employed for many years to investigate the interactions among quarks in nucleons, to study theories that can describe the expected "beyond the standard model" (BSM) interactions. Their results, which include also a model for dark matter, have been published in several refereed papers in prestigious journals. Various ideas in topologically interesting field theories predict hypothetical objects such as fractional charges and Majorana excitations. However, such fascinating objects have not been seen in particle physics. Nevertheless, these objects demonstrate possible phenomena that quantum field theory can support. Pi used condensed matter physics as a laboratory to study possible realizations and observable effects of these objects predicted by quantum field theory. In recent times there has developed considerable interest among condensed matter field theorists in precisely the same geometrical and topological structures, which were first discovered in particle physics field theories. From particle physicists' point of view, this is an interesting development, since condensed matter provides an arena in which one can concretely realize particle physics ideas. Moreover, particle physicists can learn new ideas from condensed matter physics. Higgs phenomenon is precisely an important particle physics realization of condensed matter ideas. In contrast to the small distance characterizing condensed matter systems, field theory also describes large distance physics characterizing cosmology. Pi worked on various geometrical effects in the standard theory of cosmology, viz general relativity.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Neutrino Masses from the Point of View of Economy and Simplicity
In the framework of such basic principles as local gauge invariance, unification of the weak and electromagnetic interactions and spontaneous symmetry breaking in the Standard Model the most economical and simplest possibilities are realized. We discuss the problem of neutrino masses from the point of view of economy and simplicity. It is unlikely that neutrino masses are of the same SM origin as masses of leptons and quarks. The Weinberg effective Lagrangian is the simplest and the most economical, beyond the Standard Model mechanism of the generation of small Majorana neutrino masses. The resolution of the sterile neutrino anomaly and observation of the neutrinoless double β-decay would be crucial tests of this mechanism.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Spatially and spectrally resolved orbital angular momentum interactions in plasmonic vortex generators
Abstract Understanding the near-field electromagnetic interactions that produce optical orbital angular momentum (OAM) is crucial for integrating twisted light into nanotechnology. Here, we examine the cathodoluminescence (CL) of plasmonic vortices carrying OAM generated in spiral nanostructures. The nanospiral geometry defines a photonic local density of states that is sampled by the electron probe in a scanning transmission electron microscope (STEM), thus accessing the optical response of the plasmonic vortex with high spatial and spectral resolution. We map the full spectral dispersion of the plasmonic vortex in spiral structures designed to yield increasing topological charge. Additionally, we fabricate nested nanospirals and demonstrate that OAM from one nanospiral can be coupled to the nested nanospiral, resulting in enhanced luminescence in concentric spirals of like handedness with respect to concentric spirals of opposite handedness. The results illustrate the potential for generating and coupling plasmonic vortices in chiral nanostructures for sensitive detection and manipulation of optical OAM.
36 MATERIALS SCIENCE↗
Topological phases reviewed: The Aharonov Bohm, Aharonov Casher, and He McKellar Wilkens phases
There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of 'an electric dipole encircles magnetic charges' was realised experimentally, and discuss possible future experimental realisations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Decoupling antennas in printed technology using elliptical metasurface cloaks
In this paper, we extend the idea of reducing the electromagnetic interactions between transmitting radiators to the case of widely used planar antennas in printed technology based on the concept of mantle cloaking. Here, we show that how lightweight elliptical metasurface cloaks can be engineered to restore the intrinsic properties of printed antennas with strip inclusions. In order to present the novel approach, we consider two microstrip-fed monopole antennas resonating at slightly different frequencies cloaked by confocal elliptical metasurfaces formed by arrays of sub-wavelength periodic elements, partially embedded in the substrate. The presence of the metasurfaces leads to the drastic suppression of mutual near-field and far-field couplings between the antennas, and thus, their radiation patterns are restored as if they were isolated. Moreover, it is worth noting that this approach is not limited to printed radiators and can be applied to other planar structures as well.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Neutrino in standard model and beyond
After discovery of the Higgs boson at CERN the Standard Model acquired a status of the theory of the elementary particles in the electroweak range (up to about 300 GeV). What general conclusions can be inferred from the Standard Model? It looks that the Standard Model teaches us that in the framework of such general principles as local gauge symmetry, unification of weak and electromagnetic interactions and Brout-Englert-Higgs spontaneous breaking of the electroweak symmetry nature chooses the simplest possibilities. Two-component left-handed massless neutrino fields play crucial role in the determination of the charged current structure of the Standard Model. The absence of the right-handed neutrino fields in the Standard Model is the simplest, most economical possibility. In such a scenario Majorana mass term is the only possibility for neutrinos to be massive and mixed. Such mass term is generated by the lepton-number violating Weinberg effective Lagrangian. In this approach three Majorana neutrino masses are suppressed with respect to the masses of other fundamental fermions by the ratio of the electroweak scale and a scale of a lepton-number violating physics. The discovery of the neutrinoless double β-decay and absence of transitions of flavor neutrinos into sterile states would be evidence in favor of the minimal scenario we advocate here.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗