On the mass spectrum of elementary particles

A simple theory of the elementary particle mass spectrum is proposed. It originates from the Dirac idea of the free electron motion and from the transformed Klein-Gordon equation. The theory is based on an equation that includes the squared mass operator having an infinite sequence of orthogonal eigenfunctions and a discrete spectrum of eigenvalues. A discrete mass formula is derived. It yields values of mass that are in agreement with present-day empiric data for elementary particles.     

The substructure of the weak bosons and the weak mixing angle

In models in which the weak intermediate bosons are bound states consisting of spin $\text{1}\text{2}$ constituents the effective neutral current mixing angle sin²θ_W is related to the W wave function at the origin. Dynamical constraints for the bound state structure of the W-boson follow. Although the observed value of sin²θ_W is rather large, it seems possible to obtain the observed value in a dynamical mixing scheme. The weak bosons are extended objects, whose sizes are of the order of 10^?16 cm.     

Rest mass quantisation of elementary particles and possible existence of hitherto unknown particles

A general mass formula, based on the principle of quantisation of rest mass, gives accurate mass ratios for many of the known elementary particles, predicting the muon mass to within 1 part in 10,000 of the experimental value and indicates the possibility for the existence of a number of particles which have not yet been identified experimentally.     

An electromagnetic inertial mass theory applied to elementary particles

A definition of inertial mass is advanced which views this mass property as being due to intrinsic periodic electromagnetic processes characterized by an amplitudeR and an angular frequencyω. The existence of a stableE/M composite mass unit, called a hylon, is then postulated composed of two or more of these primitive processes. Selected space-time coherence relations are then imposed onω andR through ad hoc quantizations based on notions borrowed from historical physical theories. Elementary particles are then investigated to test the efficacy of the mass definition and coherence relations. It is found that by equating the postulated hylon mass with the experimental pion masses, a mass spectrum emerges which has a close correspondence with many of the more stable particles and resonances. A case is then made for considering these particles as being primarily electromagnetic in nature and exhibiting an underlying space-time structure in terms of the theory advanced.     

Electroproduction of supersymmetric particles and gauge bosons

The electroproduction of scalar leptons and gauginos at HERA and at supercollider energies is studied. In particular, the channel $\text{ep}\text{→}\text{e}\text{(→}\text{e}\text{+}\text{γ}\text{)}\text{γ}\text{X}$ is analyzed in full detail. The exa analytic expressions for the cross section and the spectrum of the final electron are derived and evaluated for $\text{√s ? 0.15?3}\text{TeV}$ and different values of the scalar electron and photino masses. Since the exact formulae are relatively complicated, simplified expressions in the Weizsäcker-Williams approximation are also given and their accuracy is discussed by comparison with the exact formulae. The standard processes $\text{ep}\text{→}\text{Z}\text{(→ v}\text{v}\text{)}\text{eX and ep}\text{→}\text{W}\text{(→}\text{e}\text{v}\text{)v}\text{X}$ which also lead to one final electron and two invisible particles are considered in parallel. The corresponding cross sections and distributions are discussed in comparison with the supersymmetric signal. The Z⁰ cross section is found to be quite smaller than was reported previously. To clarify this point the Z⁰ production at the leptonic vertex was computed both exactly and in the Weizsäcker-Williams approximation with quite consistent results.     

Quark mass and the masses of Goldstone bosons

Based on the Dyson-Schwinger Equations (DSEs) of QCD in the “rainbow” approximation, the fully dressed quark propagator S _f (p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solution of the equations. The dressed quark amplitudes A _f and B _f which built up the fully dressed quark propagator, and the dynamical running masses M _f , which is defined by A _f and B _f for light quarks u, d and s, are calculated, respectively. Using the predicted current masses m _f , quark local vacuum condensates, and our predicted value of pion decay constant, the masses of Goldstone bosons K, π and η and their in-medium values are also evaluated. Our predictions fit to data and to many other different calculations quite well. The numerical results show that the mass of quark is dependent of its momentum p ². The fully dressed quark amplitudes A _f and B _f have correct behaviors and can be used for many purposes in our future researches on non-perturbative QCD.      

Thermodynamical proof of the Gibbs formula for elementary quantum systems

An elementary derivation is given of the formula for the thermal equilibrium states of quantum systems that can be described in finite-dimensional Hilbert spaces. The three assumptions made, Passivity, Structural Stability, and Consistency, have phenomenological interpretations. Except at zero temperature, Structural Stability follows already from Passivity and a weak form of Consistency.     

Unity of elementary particles and forces for the third family

We propose a non-supersymmetric SU(5)$\mathit{SU}(5)$ model in which only the third family of fermions are unified. The model remedies the non-unification of the three Standard Model couplings in non-supersymmetric SU(5)$\mathit{SU}(5)$. It also provides a mechanism for baryon number violation which is needed for the baryon asymmetry of the Universe and is not present in the Standard Model. Current experimental constraints on the leptoquark gauge bosons, mediating such baryon and lepton violating interactions in our model, allow their masses to be at the TeV scale. These can be searched for as a (bτ) or (tt) resonance at the Large Hadron Collider as predicted in our model.     

Critical exponents and elementary particles

Particles are shown to exist for a.e. value of the mass in single phase ⁴ lattice and continuum field theories and nearest neighbor Ising models. The particles occur in the form of poles at imaginary (Minkowski) momenta of the Fourier transformed two point function. The new inequalitydm ²/dZ, where =m ₀ ² is a bare mass² andZ is the strength of the particle pole, is basic to our method. This inequality implies inequalities for critical exponents.Supported in part by the National Science Foundation under grant PHY 76-17191Supported in part by the National Science Foundation under grant MPS 75-21212     

On the masses of elementary particles

We make an attempt to describe the spectrum of masses of elementary particles, as it comes out empirically in six distinct scales. We argue for some rather well defined mass scales, like the electron mass; we elaborate on the assumption that there is a minimum mass associated to any electric charge. Another natural mass scale is Λ = Λ _QCD coming arbitrarily at quantizing a classically conformal SU(3) _c theory. Indeed, some scales of masses will cover also masses of composite particles or mass differences. We extend some plausible arguments for other scales, as binding or self-energy effects of the microscopic forces, plus some speculative uses, here and there, of gravitation. We also consider briefly exotics like supersymmetry and extra dimensions in relation to the mass scale problem, including some mathematical arguments (e.g. triality), which might throw light on the three-generation problem. We also address briefly the issues of dark matter and dark energy.     

The Planck Aether model for a unified theory of elementary particles

A dense assembly of an equal number of two kinds of Planck masses, one having positive and the other one negative kinetic energy, described by a nonrelativistic nonlinear Heisenberg equation with pointlike interactions, is proposed as a model for a unified theory of elementary particles. The dense assembly of Planck masses leads to a vortex field below the Planck scale having the form of a vortex lattice, which can propagate two types of waves, one having the property of Maxwell's electromagnetic and the other one the property of Einstein's gravitational waves. The waves have a cutoff at a wavelength equal to the vortex lattice constant about 10³ times larger than the Planck length, reproducing the GUT scale of elementary particle physics. The vortex lattice has a resonance energy leading to two kinds of quasiparticles, both of which have the property of Dirac spinors. Depending on the resonance energy, estimated to be 10⁷ times smaller than the Planck energy, the mass of one of these quasiparticles is about equal to the electron mass. The mass of the other particle is much smaller, making it a likely candidate for the much smaller neutrino mass. Larger spinor masses occur as internal excitations, with a maximum of four such excitations corresponding to a maximum of four particle families. Other vortex solutions may describe the quark-lepton symmetries of the standard model. All masses, with the exception of the Planck mass particles, are quasiparticles for which Lorentz invariance holds, with the Galilei invariance at the Planck scale dynamically broken into Lorentz invariance below this scale. The assumed equal number of Planck masses with positive and negative kinetic energy makes the cosmological constant exactly equal to zero.     

On-shell renormalization for particles with mixing

The subject of our discussion are the on mass-shell renormalization conditions in any order of the perturbative calculations with particle mixing. The imaginary parts of the propagators which are connected with the particle decay width are taken into account. The phenomenological LSZ relation for unstable particles is discussed. The on-shell renormalization condition for the mixing of particles with spins 0+0, 0+1. and 1+1 is presented.     

On the electromagnetic structure of elementary particles

Using modern similarity and dimensionality methods, criteria of similarity are derived and used as transformations, which effect the conversion from one natural system of units to another. The exclusion principles thus defined are used to determine the powers of the similarity criteria in quantitative relations.Systems of units of the fermion and boson types are used in the simplest identification of the parameters corresponding to elementary particles.A set of electric and magnetic physical constants with dimensionality length, area, and volume, is obtained and successfully unified within the limits of a vortex ring, the maximum dimensions of which are defined by the Compton wavelength, and the minimum by the classical radius of the particle. The vortex ring model is in accordance with the latest experimental data, and it enables the behavior of the incident and target particles in the scattering process to be predicted.In modern theoretical physics the elementary particles are still considered as essentially structureless point formations, and hence it is impossible to give a purely theoretical treatment of the structure of the particles. Thus the various attempts in this direction (Hofstadter, Blokhintsev) have a polyphenomenological character and are internally inconsistent. (The search for the structure of an elementary particle is carried out on the assumption that it is not elementary, since truly elementary particles are defined as point size.) The author recognizes the need for an original approach to the structure of elementary particles, based on a method of study adequate for the problem. Such a method is the theory of dimensionality and similarity (Sedov, Gukhman, and Kirpichev), which serves as a scientific basis of a physical experiment (Kirpichev), or as the scientific basis for a model of the phenomena, insofar as the criteria of similarity are a reflection of the physical model of the process (Gukhman).It is a pleasure to thank Academician L. I. Sedov and Professor K. A. Putilov for valuable criticism and advice, and Professor A. S. Irisov and V. V. Lokhin for useful discussions.     

A spin-asymmetry term for the mass formula

From the shell model the number of nucleons with total angular momentum $\text{j = l+}\text{1}\text{2}$ in an average nucleus exceeds that of nucleons with $\text{j = l?}\text{1}\text{2}$. The spin-orbit and the spin-asymmetry energy brought about by this polarisation are shown to contribute on the average ?1.5 MeV to the surface energy coefficient. The fluctuating difference between the polarisation energy and its smooth approximation is argued to be an important component of the microscopic shell term in actual mass formulae.     

On the gravitational structure of elementary particles

Gravitational Bags are spherically symmetric solutions of higher dimensional Kaluza-Klein (K-K) theories, where the compact dimensions become very large near the center of the geometry, although they are small elsewhere. K-K excitations become therefore very light when located near the center of this geometry and this appears to affect drastically the naive tower of masses spectrum of K-K theories. In the context of string theories, string excitations can be enclosed by Gravitational Bags, making them not only lighter, but also localized as observed by somebody who does not probe the central regions. Strings however can still have divergent sizes, as quantum mechanics seems to demand, since the extra dimensions blow up at the center of the geometry.This essay received the second award from the Gravity Research Foundation for the year 1989-Ed.