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European Journal of Applied Sciences – Vol. 10, No. 3

Publication Date: June 25, 2022

DOI:10.14738/aivp.103.12388. Fèvre, R. (2022). The W Boson Mass: 80.433 GeV: A Result of a Composite H, W, Z Bosons Model: Other Results: H, Z, Proton,

Neutron and Dark Matter Masses. European Journal of Applied Sciences, 10(3). 342-351.

Services for Science and Education – United Kingdom

The W Boson Mass: 80.433 GeV: A Result of a Composite H, W, Z

Bosons Model: Other Results: H, Z, Proton, Neutron and Dark

Matter Masses

Raymond Fèvre

ABSTRACT

The present article develops a model initially published in ref. [1] and completed in

ref. [2].This is a quasi-classical quantum model of composite particles with ultra- relativistic (UR) constituents (leptons and quarks). The model is used to calculate

the mass energy of three composite particles: an UR tauonium, an UR bottomonium

and an UR leptoquarkonium. The result is that these three hypothetic particles have

masses close to 125 GeV: the Higgs boson mass energy. These results are recalled in

the present article. Then the model is extended to calculate the mass energy of the

W and Z bosons assumed to be composite particles, as well as those of the proton

and the neutron. For the W boson, the model gives two values: one has a mass

strictly equal to that measured recently at Fermilab (80.433 GeV), higher than the

values measured so far. The other model value is according to the other

measurements of the W boson mass. Finally the model provides a hypothesis on

dark matter.

Key words: Higgs boson, W and Z bosons, Proton, Neutron, Dark matter, Composite

particles.

INTRODUCTION

The present article develops a model introduced in the article ref. [1] and completed in ref.[2].

This was a quasi-classical model quantizing the energy states of a pair of ultra-relativistic tau- antitau (UR tauonium). Then the model was extrapolated in an ultra-relativistic bottomonium

and a tau-bottom mixed particle. Quantization was achieved by applying the pre-quantum Bohr

rule to the particle vertices in a classical trajectory.

The model gives for these composite particles 3 different values for the mass energy close to

125 GeV, which is the mass energy of the Higgs boson (see ref. [3]). But the CMS detector at

CERN gives precisely 3 values for the H boson, with disjoint error bars, according to the boson

decay mode: 124.7 GeV for the 2-photon decay, 126 GeV for the 4-lepton decay and 125.35 for

the combined measures. The results of the model, according to the CMS measures, are recalled

in the present article. It therefore invites us to wonder if the H boson is really an elementary

particle.

The present article extends the model to all quarks interactions and shows that W and Z bosons

could be UR tau-bottomonia supporting some electron and quarks interactions. For the W

boson, we find 2 values, the second one having exactly the recent experimental mass given by

the Fermilab (80.433 5 GeV)

Developing results presented in ref. [4] we also extend the model in order:

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343

Fèvre, R. (2022). The W Boson Mass: 80.433 GeV: A Result of a Composite H, W, Z Bosons Model: Other Results: H, Z, Proton, Neutron and Dark

Matter Masses. European Journal of Applied Sciences, 10(3). 342-351.

URL: http://dx.doi.org/10.14738/aivp.103.12388

- To calculate the masse of proton, neutron and some other hadrons

- To show that dark matter could be an UR dark quarkonium.

MODELING LEPTONIUM WITH ULTRA-RELATIVISTIC CONSTITUENTS (UR LEPTONIUM)

Initially, we will consider the classical movement of a lepton and its antilepton bound by

electrostatic interaction within the framework of special relativity. We must consider the fact

that the moving charges create an electric field as a function of their speed. Here, both charges

are moving along symmetrical trajectories according to their common center of gravity (with

at all times opposite velocity vectors and equal in modulus), therefore the strength of their

interaction is a direct result of their speed.

For the quantum-setting equation, the situation is different than that of the electron movement

in the atom, because in this case the nucleus is assumed immobile; the electric field it generates

is derived from a Coulomb potential and therefore depends only on the distance to the center.

For the above reason, we cannot use the Dirac equation and the results it provides for

positronium here. It has not been studied for the present case, where the electrostatic bond

strength of the particles depends on their speed and does not derive from an electrostatic

Coulomb potential, which is based only on the distance to the center of gravity of the system.

We will simplify the problem by writing the equations of motion for the peak classical

trajectories of both particles and applying to these points the pre-quantum Bohr rule relating

to their kinetic momentum. We will see that this method allows calculation of the mass-energy

of the composite particle without requiring determination of the wave function.

The diagram below (figure 1) shows two leptons (one lepton and its anti-particle) moving

around their common center of gravity G to one of the peaks of their classical trajectory:

� ← ⊕ �!

Figure 1 ° G

�" ⊕ → �

Velocities v of both particles are equal and opposite in module, perpendicular to the radius

length r of their distance from the center of gravity G.

The attractive force acting between the two leptons is (ref. [5]):

� = − �ħ�

4�# / 1 − �#

�#

(1)

� = �#

ħ� = 1

137.036

e is the electric charge of the electron

Furthermore, the momentum of each lepton (where m is its mass) is:

� = ��

/1 − �#

�#

(2)