Spectrum Of Elementary Particles Research Articles

Primal quantization postulate for quantum fields

We formulate a theory of quantum fields underpinned solely by the full geometric algebra structure generated by the vector space of spacetime. A modified dynamical equation of a field with associated background field potentials, distinct from Dirac’s equation, is developed and corrects the inertial potential that acts on the field. A discrete wavenumber spectrum with a possible correlation to the mass spectrum of elementary particles is obtained, and explicit expressions are derived. The formulation is mathematically driven and constitutes what we refer to as the primal field quantization postulate. While manifestly a relativistic quantum field theory, our formulation may provide a natural account of mass hierarchy and family generation. A fourth family of elementary particles is predicted, indicating that lepton and quark oscillations across generation members, as well as quantum decay processes and fluctuations, may need modifying.

The Standard Model and quantum state reduction from Heim’s field theory

Abstract Core parts of the Standard Model are derived from B. Heim’s quantum field theory, whose poly-metric describes spacetime and matter in a unified formalism. Its non-linear eigenvalue equation transforms into the Einstein field equation in the macroscopic limit. The 6-dimensional Heim space can be determined as locally isomorphic to a SU(2) ⊗ SU(2) ⊗ U(1) ⊗ U(1) symmetry and thus to the SU(3), which allows to connect to the local gauge symmetries and boson fields of the Standard Model. The Fermion and Higgs field and their coupling are deduced from Heim’s basic equations, providing new insight into possible correlations of these fields. Furthermore, the derivation yields an additional imaginary coupling term which seems to account for quantum mechanical state reduction in the non-relativistic limit. The recently performed calculation of the mass spectrum of elementary particles in a new approach based on Heim’s theory (with average error to the data < 1 % ${< } 1\%$ ) appears as even more relevant, having now shown that the theory can connect to the achievements of the Standard Model.

ON MASS QUANTIZATION

The problem of the mass spectrum of elementary particles is considered from the positions of reductionism and holism. It is shown that in the holistic description, the concept of substance (energy) is of paramount importance, and elementary particles are understood as emergent states that play a secondary role. A system of axioms is given that defines the basic definitions of the spectrum of matter. In this case, the spectrum of states (“elementary particles”) appears as a result of mass (energy) quantization. A mass formula is derived that depends on the quantum numbers defining the eigenvalues of the Casimir operators of the Lorentz group.

The Worlds on the Other Side of the Big Bang

Taking the Big Bang as an established fact, the question inevitably arises about what exactly caused it, in what environment could it have happened and what happened before it. The developed approach allows us to shed light on many raised questions and to establish what universal laws and structures formed what happened before the Big Bang, to understand its cause and the dynamic processes that led to it. This required a radical revision of many views, giving them a new meaning and content. This approach has led to a consistent and conceptually new understanding of these phenomena, which allowed correctly formulate questions to which there are still no clear answers. Based on this formulation of the problem, we came to new ideas about the nature of Dark energy, Dark matter and the region of their birth, formulated and described the mechanism of the formation of worlds and their hierarchy on the other side of the Big Bang and the mechanism of this explosion itself. The Primary Parent Particle was introduced into the concept, which was the basis of everything and is the carrier of the fundamental Primary space introduced by us, which had at least two phase states. This particle consists of Beginnings united in the form of Borromeo rings. This made it possible to calculate the structure and primary spectrum of elementary particles that arose on the other side of the Big Bang, the mechanisms of their formation and the resulting fundamental interactions that lead to the existence of vortices before the Big Bang; the mechanisms of the birth of multiple universes and much more are also considered. The concept of the “cosmic genetic code" is introduced, the characteristics and mechanism of its formation before the Big Bang are presented.

Mass spectrum of elementary particles

In this study, we discuss different methods for quantifying the mass of elementary particles. The Barut’s model approach gives us a more comprehensive understanding of elementary particles and their formation through magnetic interaction. Through this model, we can understand the mechanism of the formation of hundreds of unstable elementary particles whose components are interconnected through positive energy and thus quickly disintegrate into their basic components.

The generation of mass in a non-linear field theory

Abstract The mass spectrum of elementary particles is calculated in a new approach, based on B. Heim’s quantum field theory, which manifests in a non-linear eigenvalue equation and merges into the Einstein field equation in the macroscopic limit. The poly-metric of the theory allows spacetime and matter to be described in a unified formalism, representing a radical geometrisation of physics. The calculated mass energies are in very good agreement with the empirical data (error < 1 % ${< }1\%$ on average) if the mass scale is gauged to the electron as lowest mass and the second main parameter, determining the strength of obtained mass hierarchy levels, is close to the half inverse of the fine structure constant, describing the difference in strength between the electromagnetic and the strong interaction. The obtained hierarchy levels are not identical to the particle generations of the Standard Model; however, show a self-similarity typical for non-linear theories. For higher values of the main quantum number N, the calculated mass formula becomes identical to the phenomenological formulae of Nambu, respectively, Mac Gregor.

On The Mass Spectrum of Elementary Particles

In the 50s of the last century, M.I. Danysh and J. Pniewski discovered the existence of hypernuclei. In them under the action of cosmic rays, one of nucleons was turned into an excited state. In this paper, it is shown that masses and magnetic moments of such excitations coincide with properties of some elementary particles. Based on this consent, a number of elementary particles should be considered as excited states of different combinations of electrons, positrons, and protons, rather than as composed from quarks with a fractional charge.

Influence of the magnetic interactions on the mass spectrum of elementary particles

Different approaches to the problem of mass quantization are discussed. The Barut ideas of crucial influence of magnetic forces for explaining the properties of the strong interaction are considered in details. It is shown that this approach gives the possibility to understand the enormous number of elementary particles (about 400) as the excited states of stable fundamental particles (e, p, v), bounded by magnetic interactions.

Exotic fermions in Kadyshevsky’s theory and the possibility to detect them

As it is known, the principal research interest of V.G. Kadyshevsky was the development of a geometric approach to quantum field theory with a constraint imposed on the mass spectrum of elementary particles. Non-Hermitian operators arising in this case seemed to be a major obstacle to the development of a consistent theory. These issues have been resolved recently, and the introduction of the pseudo-Hermitian algebraic approach to the construction of quantum theory was a major advance in this physical research. The central point of such theories is the construction of PT-symmetric non-Hermitian Hamiltonians with real eigenvalues. It is important to note that both purely theoretical and experimental studies (e.g., in non-Hermitian optics) are found among the many published papers on this subject. Therefore, we believe that the development of pseudo-Hermitian relativistic quantum theory with a maximal mass may provide favorable opportunities to discuss the possible experimental verification of theoretical results obtained in this field. Kadyshevsky himself regarded the hypothesis of existence of new particles, which he called exotic fermions, as an important prediction of his theory. The possibility of discovery of exotic neutrinos in precision experiments on the determination of the neutrino mass is discussed in the present study.

Statistical unfolding of elementary particle spectra: Empirical Bayes estimation and bias-corrected uncertainty quantification

We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse problem arising in data analysis at the Large Hadron Collider at CERN consists in estimating the intensity function of an indirectly observed Poisson point process. Unfolding typically proceeds in two steps: one first produces a regularized point estimate of the unknown intensity and then uses the variability of this estimator to form frequentist confidence intervals that quantify the uncertainty of the solution. In this paper, we propose forming the point estimate using empirical Bayes estimation which enables a data-driven choice of the regularization strength through marginal maximum likelihood estimation. Observing that neither Bayesian credible intervals nor standard bootstrap confidence intervals succeed in achieving good frequentist coverage in this problem due to the inherent bias of the regularized point estimate, we introduce an iteratively bias-corrected bootstrap technique for constructing improved confidence intervals. We show using simulations that this enables us to achieve nearly nominal frequentist coverage with only a modest increase in interval length. The proposed methodology is applied to unfolding the $Z$ boson invariant mass spectrum as measured in the CMS experiment at the Large Hadron Collider.

Elementary particles, the concept of mass, and emergent spacetime

It is argued that the problem of space quantization should be considered in close connection with the problem of mass quantization. First, the nonlocality of quantum physics suggests that if spacetime emerges from the underlying quantum layer, this emergence should occur simultaneously at all distance and momentum scales, and not just at the Planck scale. Second, the spectrum of elementary particles provides us with a lot of important information, experimentally inaccessible at the Planck scale, that could be crucial in unravelling the mechanism of emergence. Accordingly, we start with a brief review of some fundamental issues appearing both in the spectroscopy of excited baryons and in connection with the concept of quark mass. It is pointed out that experiment suggests the inadequacy of the description of baryonic interior in terms of ordinary spacetime background. Thus, it is argued that one should be able to learn about the emergence of space from the studies of the quark/hadron transition. The problem of mass is then discussed from the point of view of nonrelativistic phase space and its Clifford algebra, which proved promising in the past. Connection with the Harari-Shupe explanation of the pattern of a single Standard Model generation is briefly reviewed and a proposal for the reintroduction of relativistic covariance into the phase-space scheme is presented.

Spinor Structure and Internal Symmetries

Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries $P$, $T$ and their combination $PT$ are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation $C$ is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation $C$ allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincar\'{e} group and $SU(3)$-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of $SU(3)$). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of $SU(3)$-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann--Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.

Avoiding Death by Vacuum

The two-Higgs doublet model (2HDM) can have two electroweak breaking, CP-conserving, minima. The possibility arises that the minimum which corresponds to the known elementary particle spectrum is metastable, a possibility we call the "panic vacuum". We present analytical bounds on the parameters of the softly broken Peccei-Quinn 2HDM which are necessary and sufficient conditions to avoid this possibility. We also show that, for this particular model, the current LHC data already tell us that we are necessarily in the global minimum of the theory, regardless of any cosmological considerations about the lifetime of the false vacua.

The Oscillating Universe Theory (To the Unified Field Theory)

This paper represents model of oscillating universe theory. We try to realize model of both electromagnetic waves and spectrum of elementary particles from the unified point of view. Consideration of problems of the gravitational optics and dark matter is developing from the solid crystal model for the vacuum. The vacuum is represented as a three-dimensional crystal lattice matter with a very small lattice period, much less than 10-26 cm. The oscillators are located at the nodes of an infinite lattice. It is shown that an infinite set of equations to describe the coupled oscillations of moving oscillators converges to a system of twelve equations. We have obtained the combined equations for a multicomponent order parameter in the form of the electric and magnetic vacuum polarization, which defines the spectrum and symmetry of normal oscillations in the form of elementary particles. Two order parameters—a polar vector and an axial vector— had to be introduced as electrical and magnetic polarization, correspondingly, in order to describe dynamic properties of vacuum. Vacuum susceptibility has been determined to be equal to the fine structure constant a. Unified interaction constant g for all particles equal to the double charge of Dirac monopole has been found (g = e/a, where e—electron charge). The fundamental vacuum constants are: g, a, parameters of length and parameters of time for electron and nucleon oscillations, correspondingly. Energy of elementary particles has been expressed in terms of the fundamental vacuum parameters, light velocity being equal to . The term mass of particle has been shown to have no independent meaning. Particle energy does have physical sense as wave packet energy related to vacuum excitation. Exact equation for particle movement in the gravitational field has been derived, the equation being applied to any relatively compact object: planet, satellite, electron, proton, photon and neutrino. The situation has been examined according to the cosmological principle when galaxies are distributed around an infinite space. In this case the recession of galaxies is impossible, so the red shift of far galaxies’ radiation has to be interpreted as the blue time shift of atomic spectra; it follows that zero-energy, and consequently electron mass are being increased at the time. Since physical vacuum has existed eternally, vacuum parameters can be either constant, or oscillating with time. It is the time oscillation of the parameters that leads to the growth of electron mass within the last 15 billion years and that is displayed in the red shift; the proton mass being decreased that is displayed in planet radiation.

A possible model for the mass spectrum of elementary particles

A conjecture on the origin of elementary particle masses is discussed, based on the “microuniverse” and quantum state reduction concepts. The reduction of the quantum state of a real particle is understood to take place objectively; in every interaction event with other real particles, the quantum state of the particle is annihilated and a new one is created. In these events, the particle is localised in time and in space, with a maximum precision established by the uncertainty principle. The minimum energy required for this localisation constitutes the chief contribution to the particle’s mass. A further contribution is provided by the self-interaction of the particle during localisation, which occurs within a finite duration. Some algorithms for estimating these two contributions are presented and discussed.

THE PION MODEL

We revisit the problem of a mechanism that generates the mass spectrum of elementary particles. This has vexed physicists for several decades now. In this connection, we deduce a formula that gives the masses of all known elementary particles, even though other quantum numbers are suppressed. These considerations become important in view of the Large Hadron Collider which is expected to attain 14 TeV by 2013.

New Theoretical Results about the Mass Spectrum of Elementary Particles

The particle is represented by the wave packet in nonlinear space-time continuum. Because of dispersion, thepacket periodically appears and disappears in movement and the envelope of the process coincides with the wavefunction. There was considered the partial differential equation of telegraph-type describing the motion of suchwave packet in spherical coordinate space (r,θ ,?) . There was constructed also the analytical solution u(r,θ ,?)of this equation and the integral over all space of 2 2 gradu was supposed being equal to the mass of the particleidentified with the wave packet. As the solution u(r,θ ,?) depends on two parameter L,m being positiveinteger, it was possible to calculate our theoretical particle masses MLm for different L,m. So, we haveobtained the theoretical mass spectrum of elementary particles. The comparison with known experimental massspectrum shows our calculated theoretical mass spectrum is sufficiently verisimilar.

New Consideration of Problems of Gravitational Optics and Dark Matter Based on Crystal Model of Vacuum

In presented paper we try to consider problems of the gravitational optics and dark matter developing from the crystal model for the vacuum. How it is follows from consideration it enables to describe both electromagnetic waves and spectrum of elementary particles from the unified point of view. Two order parameters – a polar vector and an axial vector - had to be introduced as electrical and magnetic polarization, correspondingly, in order to describe dynamic properties of vacuum. Vacuum susceptibility has been determined to be equal to the fine structure constant . Unified interaction constant g for all particles equal to the double charge of Dirac monopole has been found (g = e/, where e charge electron). The fundamental vacuum constants are: g, , parameters of length and parameters of ti- me for electron and nucleon oscillations, correspondingly. Energy of elementary particles has been expressed in terms of the fundamental vacuum parameters, light velocity being equal to . The term mass of particle has been shown to have no independent meaning. Particle energy does have physical sense as wave packet energy related to vacuum excitation. Exact equation for particle movement in the gravitational field has been derived, the equation being applied to any relatively compact object: planet, satellite, electron, proton, photon and neutrino. The situation has been examined according to the cosmological principle when galaxies are distributed around an infinite space. In this case the recession of galaxies is impossible, so the red shift of far galaxies’ radiation has to be interpreted as the blue time shift of atomic spectra; it follows that zero-energy, and consequently electron mass are being increased at the time. Since physical vacuum has been existed eternally, vacuum parameters can be either constant, or oscillating with time. It is the time oscillation of the parameters that leads to the growth of electron mass within the last 15 billion years and that is displayed in the red shift; the proton mass being decreased that is displayed in planet radiation.

On the Mass Spectrum of Elementary Particles in Unitary Quantum Theory

The particle is represented by the wave packet in nonlinear space-time continuum. Because of dispersion, the packet periodically appears and disappears in movement and the envelope of the process coincides with the wave function. There was considered the partial dierential equation of telegraphtype describing the motion of such wave packet in spherical coordinate space(r,,’ ). There was constructed also the analytical solution u(r,,’ ) of this equation and the integral of

Relativistic Quantum Mechanics as a Consequence of the Planck Mass Plasma Conjecture

The Planck mass plasma conjecture is the hypothesis that the vacuum of space is a kind of plasma composed of positive and negative Planck mass particles interacting by the Planck force over a Planck length, repulsive for equal and attractive for unequal Planck masses. The hypothesis permits to derive quantum mechanics and Lorentz invariance as asymptotic approximations for energies small compared to the Planck energy. Besides a spectrum of elementary particles greatly resembling the particles of the standard model, the hypothesis gives a value of the fine structure constant at the energy where the strong, the weak, and electromagnetic interaction become equal.