Electron-muon Mass Research Articles

On the lifetime of the muon state of the electron-muon mass doublet

In a previous paper the electron and muon masses were derived by combining the author’s general relativistic derivation of the inertial masses of spinor particles from the geometrical field and his model of the « physical vacuum » (from a self-consistent field theory of electrodynamics) in terms of an ideal gas of electron-positron pairs in a particular state that was derived from the theory. It was predicted earlier that in this field theory spinor particles occur in mass doublets. In the electron-muon case, the observation of the « heavy electron » (muon) is a consequence of quadrupolar excitation of the physical vacuum of pairs—correspondingly altering the geometrical field in the vicinity of the observed electron, thereby making it more inertial. In this paper, the lifetime of the heavy electron in this physical vacuum will be determined, de-excitation occurring by the transferral of electromagnetic energy from this heavy electron to the pairs of the physical vacuum by means of a quadrupolar transition. To facilitate the calculation with time-dependent perturbation theory, use is made of Fermi’s multiple-meson production theory, and the improvisation of his theory for break-up reactions by the author. In this way, the ensuing quantitative analysis yields a lifetime for the heavy electron that is of the order of 2.09·10-6 s, which is within 5% of the observed muon decay rate. It is then shown how the present theory, in which electromagnetic variables are in terms of 2-component spinor fields, explains the reaction Μ → e++Ν in terms of a process that is purely electromagnetic and does not entail neutrinos.

On the electron-muon mass doublet from general relativity

This paper examines a consequence of combining separate aspects of the author’s research program toward the development of a self-consistent field theory of a closed system. These were the separate studies that indicated that: 1) the inertial mass of matter is derivable from an explicit dynamical relation in terms of the geometrical field that describes a closed system in general relativity, and 2) the result of a self-consistent approach to electrodynamics that any region of spacetime must be populated with a countable and finite system of particleantiparticle pairs, each in its ground state of null energy and null momentum. The latter followed from an application of Noether’s theorem in a nonlinear field theory of electrodynamics. In this article, a linearized version of the theory that couples the matter and the metric field equations is studied. It is shown that the inertial mass field for spinor particles, being a 2-dimensional matrix field, has two distinct mass eigenvalues. From a study of the space-time curvature as due to the background gas of particle-antiparticle pairs, whenever the mass of an observed particle might be measured, semi-quantitative arguments are presented which imply that the ratio of these two eigenvalues for the electron mass doublet is the order of 3/2α ≅205 (α being the fine-structure constant)—a number that is quite close to the muon-electron mass ratio. The analysis implies that to be consistent with the magnitude of the electron mass, the specific volume of the background gas of pairs is the order of (10−15 cm)3. It is also noted that a further implication of this background gas of pairs should be the appearance of « electron jets » and the accompanying electromagnetic radiation, in those parts of the Universe where the temperatures of the ordinary mass distribution would reach values compatible with the dissociation energy of these pairs (corresponding toT ∼ 109 ‡K)—this provides a possible explanation for some of the observed characteristics of quasars.

Field Theory of Matter

A speculative field theory of matter is developed. Simple computational methods are used in a preliminary survey of its consequences. The theory exploits the known properties of leptons by means of a principle of symmetry between electrical and nucleonic charge. There are fundamental fields with spins 0, \textonehalf{}, 1. The spinless field is neutral. Spin \textonehalf{} and 1 fields can carry both electrical and nucleonic charge. The multiplicity of any nonzero charge is 3. Explicit dynamical mechanisms for the breakdown of unitary symmetry and for the muon-electron mass difference are given. A more general view of lepton properties is proposed. Mass relations for baryon and meson multiplets are derived, together with approximate couplings among the multiplets. The weakness of $\ensuremath{\varphi}$ production in $\ensuremath{\pi}\ensuremath{-}N$ collisions and the suppression of the $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\rho}+\ensuremath{\pi}$ decay is explained.

Dilatationally Invariant Quantum Electrodynamics of Electrons and Muons

The equation for a lepton propagator is studied in dilatationally invariant quantum electrodynamics and the possibility of an electrodynamic calculation of the electron-muon mass ratio is discussed. (auth)

An electrodynamic approach to the electron-muon mass ratio

By a mechanism well known from the theory of superconductivity the particles of an electrically charged massless fermion field may obtain a nonvanishing rest mass. If the mass renormalization in ordinary quantum electrodynamics is infinite, then it seems likely that a proper reformulation of the basic equations of quantum electrodynamics which eliminates the infinite constant δm will be a dilatationally-invariant theory corresponding to the model above. The dilatation invariance of the basic theory is not objectionable and opens on the contrary a natural possibility to understand how two leptons can have almost identical interactions but vastly different masses. The mass of a lepton is then determined by the nondilatationally-invariant perturbation caused by the other charged fields present in nature.

Schwinger's meson and the μ-mesic atom

The properties of Schwinger's meson (σ), which is supposed to interact with muons and cascade particles, have been estimated by calculating 1. (i) the muon self mass and comparing this with the muon-electron mass difference, 2. (ii) the anomalous effect of the bound state levels of μ-mesic atoms and comparing this with the experimental data. These and other results have been used to obtain values of the σ-meson mass and the strength of its coupling to muons and baryons.

On the electron-muon mass difference

On the basis of a previously developed formalism it is shown that a hypothetical (uncharged) boson isoscalar would remove the electron-muon mass degeneracy.