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European Journal of Applied Sciences – Vol. 11, No. 1
Publication Date: February 25, 2023
DOI:10.14738/aivp.111.14114.
Fèvre, R. (2023). Elementary Particle Masses: Alternative Model to the BEH Mechanism. European Journal of Applied Sciences,
Vol - 11(1). 626-636.
Services for Science and Education – United Kingdom
Elementary Particle Masses: Alternative Model to the BEH
Mechanism
Raymond Fèvre
Abstract
In a first paper [1], we developed a model to calculate the masses of charged leptons
by quantifying the electrostatic field generated by these particles. In a second
article [2], we extended this model to weak and strong interactions in order to
calculate the masses of all elementary fermions. The present paper is a modified
version of the second article, adding a hypothesis on the mass of dark matter
particles. In this way, the model could be an alternative to the BEH mechanism of
the standard model.
INTRODUCTION
The BEH mechanism, called the "Higgs Field", was conceived in the 1960s to overcome
inconsistencies in the standard model. The standard model states that the masses of the
elementary particles are all null.
A quantum field was therefore introduced in order to impart a mass to the elementary particles,
first for the bosons W and Z, and then for the elementary fermions.
A particle must be associated with this quantum field. The particle theorists have thus assumed
the existence of a Higgs boson associated with the Higgs field. However, as the Higgs field is a
qualitative concept, it does not predict the mass of the boson and does not allow calculation of
the mass of elementary particles. Moreover, this theory postulates that the neutrino mass is
zero, which is false
The experimental discovery in 2012 at CERN of a boson with a mass close to 125 GeV was
presented almost unanimously as corresponding to the Higgs boson. But proof for this
identification was not provided. Now, the BEH model has been called into question by two
experimental results. The CMS and ATLAS detectors give two slightly different values (disjoint
error bars) for the H boson mass. The retroactive measurements of the W boson mass
(Fermilab) also give a different value from that measured so far.
The author of this article published a paper in JFAP on the subject in 2016, suggesting an
alternative for the Higgs boson: composite particles consisting of ultra-relativistic (UR)
interactions of tau leptons and /or bottom quarks [3]. A recent article [4] develops this subject
and shows that the W and Z bosons can also be the same type of composite particles
Furthermore, in 2014 we published an article in Physics Essays [1] suggesting an alternative to
the BEH mechanism in order to explain and calculate the mass of charged leptons. The model
infers the masses of these leptons from the quantification of the electrostatic field generated by
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Services for Science and Education – United Kingdom 628
European Journal of Applied Sciences (EJAS) Vol. 11, Issue 1, February-2023
rψ(r) ≺ exp (±
4πiθ
ħc
∫ Ed
(r)dr)
r
r0
(4)
We assume that the lower integration range is very small, of the order of magnitude of a Planck
length.
Considering the real wave function, the sum of the function written above and its complex
conjugate, we obtain:
rψ(r) ≺ cos [
4πθ
ħc
∫ Ed
(r)dr]
r
r0
(5)
The relation (3) shows that the derivative of the above function is zero when the total energy
defined in (1b) is zero, and therefore for the following value of the distance r to the particle:
rm =
αħ
2mc
(6)
For this value of r, called “classical radius of particle”, the electrostatic energy of particle
equals its mass energy, but it has not physical sense in classical physics.
The derivative of a function is null at its extrema, so the above value corresponds to an
extremum. Since the function defined in (eq.5) is a cosine function, this occurs when its
argument is a multiple of π and for the value of r given above, which defines a quantization
relation:
4πθ
ħc
∫ Ed
(r)dr = nπ
rm
r0
; n = integer (7)
Using (6) and (7), it becomes:
ln
rm
ro
=
na
2θ
+ 1 with a =
1
α
= 137.036 (8)
It is interesting to transform (8) by introducing the particle mass according to relation (6), the
Planck mass and the Planck radius:
rp = √
Għ
c
3 mpcrp = ħ
We obtain thus: