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European Journal of Applied Sciences – Vol. 11, No. 6
Publication Date: December 25, 2023
DOI:10.14738/aivp.116.16092
Fèvre, R. (2023). Composite H, W, Z Bosons: A Model Explaining the Different Experimental Values of their Masses Other Results:
Pi-Meson, Nucleons, Heavy bosons, Dark Matter Masses. European Journal of Applied Sciences, Vol - 11(6). 317-330.
Services for Science and Education – United Kingdom
Composite H, W, Z Bosons: A Model Explaining the Different
Experimental Values of their Masses Other Results: Pi-Meson,
Nucleons, Heavy bosons, Dark Matter Masses
Raymond Fèvre
Dijon, France
ABSTRACT
The present article is the second version of an article published on June 2022 by
“European Journal of Applied Sciences”. It 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 bosons: 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, the neutron, the pi-mesons and the
composite bosons with a top quark constituent. For the W boson, the model gives
two values: one has a mass 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.
INTRODUCTION
The present article is the second version of an article published by “European Journal of Applied
Sciences” on June 2022. This version gives a more rigorous calculation of the Z and W composite
bosons masses, then adds the calculation of the pi-mesons masses
The article content develops a model introduced in the article ref. [1] and completed in ref. [2].
This is a quasi-classical model quantizing the energy states of the interaction of an ultra- relativistic tau-antitau pair (UR tauonium). Then the model is extrapolated in ultra-relativistic
bottomonium and taubottomonium (where the constituents are tau-bottom mixed particles).
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 three different values for the mass energy, close
to 125 GeV, which is the mass energy of the Higgs boson (see ref. [3]). These values correspond
precisely to the measurements carried out by the CERN ATLAS detector (Run 1only: 7TeV) for
the H boson, according to the boson decay mode:
• 126.02 GeV for the 2-photons decay: UR bottomonium mass.
• 124.51 GeV for the 4-leptons decay: UR taubottomonim mass.
• 125.38 GeV for the combined measures: UR tauonium mass.
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The results of the model, according to the CERN detectors measures, are recalled in the present
article with a commentary on the more precise recent measures. 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 taubottomonia supporting some electron and quarks interactions. For the W
boson, we find two 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:
• To calculate the masses of proton, neutron, pi-mesons and composite bosons with a top
quark constituent.
• 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 the peak (with maximal v) of their classical trajectory:
v ← ⊕ l
+
G °
l
− ⊕ → v
(Figure 1)
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.
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Fèvre, R. (2023). Composite H, W, Z Bosons: A Model Explaining the Different Experimental Values of their Masses Other Results: Pi-Meson, Nucleons,
Heavy bosons, Dark Matter Masses. European Journal of Applied Sciences, Vol - 11(6). 317-330.
URL: http://dx.doi.org/10.14738/aivp.116.16092
The attractive force acting between the two leptons is (ref. [5]):
f = −
αħc
4r
2 √1−
v
2
c
2
(1)
α =
e
2
ħc
=
1
137.036
e is the electric charge of the electron
Furthermore, the momentum of each lepton (where m is its mass) is:
p =
mv
√1−
v
2
c
2
(2)
p and v are collinear vectors tangent to the trajectory of the lepton, and therefore perpendicular
to the attractive force f. In this case, the derivative of the momentum vector:
dp
dt
= m
dv
dt
√1−
v
2
c
2
(3)
is radial; the expression of this component is, by introducing the radius of curvature ρ of the
path:
mv
2
ρ√1−
v
2
c
2
=
pv
ρ
(4)
Here, p and v represent the modules of the momentum and speed at that point.
Equating (1) and (4) we have:
pvr
2
ρ
=
αħc
4√1−
v
2
c
2
(5)
We now introduce Bohr's quantization rule, applied to both lepton systems, as follows:
2pρ = nħ (6)
n: integer
which consists of taking as principle the quantization of angular momentum. The relation (5)
becomes:
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vr
2
cρ2 =
α
2n√1−
v
2
c
2
(7)
Let:
s =
ρ
2
r
2
It is possible to fix the value of the relationship between the radius of curvature and the distance
to the center of gravity by referring to the classical movement. The simplest case is that of a
circular path for which we have s = 1. In general, the standard trajectory is not an ellipse but a
rosette, because the issue is dealt with in the relativistic framework. However, at the vertices
of this trajectory, the curve traced by each lepton is very close to an ellipse, as the equations of
motion at these points are identical to those that result in an ellipse in non-relativistic
mechanics.
In the case of an ellipse with high eccentricity, the ratio ρ / r is near 2 for the vertex close to the
foci coinciding with the center of gravity, so s≃4.
Equation (7) is in fact an equation v (velocity at the peak trajectory of each lepton), which can
be put as follows:
v
2
c
2
(1 −
v
2
c
2
) =
s
2α
2
4n2
(8)
That simple equation has the following solutions:
Solution 1:
v
2
c
2 =
1
2
(1 − √ 1 − 4
s
2α2
4n2
) ≅
s
2α
2
4n2
(9)
Solution 2:
v
2
c
2 =
1
2
(1 + √ 1 − 4
s
2α2
4n2
) ≅ 1 −
s
2α
2
4n2 ≅ 1 (10)
DISCUSSION
The First Solution (9) is weakly relativistic, v is greatly inferior to c. In this case, using the
classical expression of the kinetic energy for the system of two tau leptons, we obtain the energy
levels:
|En| ≃
s
2α
2mc2
4n2
(11)
Assuming that the classical trajectory is a circle or s = 1, we find the inferred relations for the
positronium by quantum theory, (ref. [6]), corresponding to the principal quantum number n
(for the Hamiltonian "undisturbed "). These energy levels are defined by (m=electron mass):
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Fèvre, R. (2023). Composite H, W, Z Bosons: A Model Explaining the Different Experimental Values of their Masses Other Results: Pi-Meson, Nucleons,
Heavy bosons, Dark Matter Masses. European Journal of Applied Sciences, Vol - 11(6). 317-330.
URL: http://dx.doi.org/10.14738/aivp.116.16092
En = −
α
2mc
2
4n2
(12)
The Second Solution (10), the one that interests us here, is ultra-relativistic, the velocity of the
two particles is close to that of light; using the relationship:
E =
mc
2
√1−
v
2
c
2
(13)
With (8) the energy levels are obtained:
En =
2mc
2
sα
n (14)
We have to distinguish again two cases:
The Classical Trajectory Is Circular: s = 1
E1 =
2mc
2
α
; (15)
The mass-energy of the UR leptonium is in this case (the antiparticle is denoted by *):
ml,l
∗
(circular) =
2ml
α
; (16)
The classical trajectory is elliptic, with necessary a high eccentricity: s = 4
E1 =
mc
2
2α
; (17)
The mass-energy of the UR leptonium in this case is the sum of two states: the kinetic energy at
the studied vertex and the inertial mass energy at the other vertex.
ml,l
∗
(elliptic) = (
1
2α
+ 2) ml
; (18)
THE MASS OF UR TAUONIUM
We apply the results above in the case of the tau quark with an elliptic trajectory:
mτ,τ∗ = (
1
2α
+ 2) mτ
(19)
Numerically, the mass of tau being equal to 1.7768 GeV (PDT), we obtain for the UR-tauonium:
mτ,τ∗ = 125.296 GeV (20)
The most precise mass of the Higgs boson given by the CMS detector of the CERN in 2019
(combined measurements) is:
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mH(exp) = 125.38 ± 0.14 GeV (21)
It can be seen that the calculated value of ultra-relativistic tauonium corresponds closely to the
measured value of the particle observed at CERN.
A SOFT APPROACH OF QCD; THE MASS OF UR BOTTOMONIUM
This particle is a pair of b quark-antiquark; it should normally be studied within the QCD
theoretical framework. We know that in this context, numerical calculation of the mass of a
composite particle from the mass of its components is extremely difficult and out of reach of
the author of this article. We will return to the previous case of tauonium, arguing that the
intensity of the strong interaction of quarks tends toward the constant of the electrostatic
interaction α at weak length (asymptotic freedom) which is the case here. We can then venture
the hypothesis that the above model for tauonium also applies to bottomonium.
If the coupling of the strong interaction at weak length is α, and if f denotes the full elementary
strong charge, taking into account the fact we have 3 colors and 3 anti-colors, we can write:
f
2 = 6e
2 = 6αħc (22)
The strong (or color) charge and the electric charge of both tau particles must intervene in the
equations written above.
It is known that the electric charge of the bottom is e / 3, thus the corresponding electric
coupling with the anti-bottom is α / 9.
Assume that the value of the color charge is 2f / 3 for this quark, the value of color coupling b,
anti-b is 24α / 9 (cf. 22)
Adding the value of the interactions of the partial electric charge, we find the total value of the
b, b*interaction coupling
IC(b, b
∗
) =
25α
9
; (23)
Using (17) we can write the expression of the level 1 of the UR bottomonium in the elliptic case:
E1 =
mbc
2
2IC(b,b∗)
=
9mbc
2
50α
; (24)
With the same relationship as (19), we obtain for the mass of the UR bottomonium:
mb,b
∗ = (
9
50α
+ 2) mb; (25)
Here, the bottom quark mass we will take is close to half that of the upsilon boson mass because
this particle is clearly not an ultra-relativistic bottomonium;
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Fèvre, R. (2023). Composite H, W, Z Bosons: A Model Explaining the Different Experimental Values of their Masses Other Results: Pi-Meson, Nucleons,
Heavy bosons, Dark Matter Masses. European Journal of Applied Sciences, Vol - 11(6). 317-330.
URL: http://dx.doi.org/10.14738/aivp.116.16092
mU(exp. ) = 9.4602 GeV
We can calculate the bottom mass taking into account the energy level of the bottom composing
the upsilon boson in the weakly relativistic case, given by eq. (12) with IC = 25α/9:
E1 = −
1
4
(
25α
9
)
2
mbc
2 = −0.486 MeV
We obtain the bottom mass with (25):
mb =
mU
2
+ E1 = 4.7296 GeV;
And the UR bottomonium mass with eq. (25):
mb,b
∗ = 126.121 GeV; (26)
This value is very close to the experimental value measured by the ATLAS detector (Run 1) for
the 2-photons decay of H boson (126.02 GeV).
THE MASS OF UR TAUBOTTOMONIUM
Leptoquarks are particles imagined in some theories beyond the standard model. We assume a
taubottom particle (mixed particle consisting of a tau and a bottom) with a mass equal to the
half sum of tau and bottom masses, and who’s the coupling with its anti-particle is the half sum
of the tau and b couplings (quantum superposition).
mτb =
mτ+mb
2
; IC(τb, τ
∗b
∗
) =
1
2
(
25α
9
+ α) =
34α
2×9
; (27)
Using the same calculation as above, we obtain for the mass energy of this hypothetic
taubottomonium with an elliptic trajectory:
mτb,τ
∗b
∗ =
mτ+mb
2
(
9
34α
+ 2) = 124.514 GeV; (28)
This value is very close to the measure of the H boson mass by ATLAS (Run 1) in the case of 4-
leptons decay (124.51 GeV).
COMMENTARIES ON THE EXPERIMENTAL VALUES OF HIGGS BOSON MASS
The latest experimental values given by the ATLAS detector with Run 1 (7 TeV) + Run 2 (13
TeV) are:
H → γγ; mH = 125.22 ± 0.14 GeV
H → 4l; mH = 124.94 ± 0.18 GeV
These values differ from each other and also differ from the values obtained with Run 1 alone.
Thus, we see that the experimental Higgs boson mass depends on the decay mode, but also on
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the energy of the incident protons. This does not conform to the standard model which predicts
an elementary and unique Higgs boson. The composite model, on the contrary, can explain
these differences by different proportions of the three composite particles described above,
depending on the decay mode and the energy of production.
We can make similar remarks about the combined measurements of detectors ATLAS and CMS,
which are questionable in their principle.
CMS: mH = 125.38 ± 0.14 GeV
ATLAS: mH = 125.11 ± 0.11 GeV
These two values differ with disjoint errors bars; it is not possible that these two values
correspond to one unique particle.
QUARK INTERACTIONS
Using the calculation above, we can give the coupling of UR interaction pairs of quarks as below,
adding for each pair the color (always attractive) and the electric (attractive or repulsive)
interactions. Note that we can replace in these relationships ‘up’ by ‘charm’ or ‘top’ and ‘down’
by ‘strange’ or ‘bottom’, and each particle by its antiparticle.
IC(u, u
∗
) =
6α
9
+
4α
9
=
10α
9
IC(u, u) =
6α
9
−
4α
9
=
2α
9
IC(d, d
∗
) =
24α
9
+
α
9
=
25α
9
IC(d, d) =
24α
9
−
α
9
=
23α
9
IC(u, d) =
12α
9
+
2α
9
=
14α
9
IC(u, d
∗
) =
12α
9
−
2α
9
=
10α
9
THE MASS OF Z BOSON
We assume that the Z boson is also a taubottomonium, which is the half sum of two ultra- relativistic interactions of the below pairs of leptoquarks (quantum superposition):
a)
b + τ
2
;
b
∗ + τ
∗
2
; b)
b + τ
∗
2
;
b
∗ + τ
2
:
The case b) introduces an interaction type (u, u*)
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Fèvre, R. (2023). Composite H, W, Z Bosons: A Model Explaining the Different Experimental Values of their Masses Other Results: Pi-Meson, Nucleons,
Heavy bosons, Dark Matter Masses. European Journal of Applied Sciences, Vol - 11(6). 317-330.
URL: http://dx.doi.org/10.14738/aivp.116.16092
IC(Z) = IC(bb
∗ + uu
∗ + ττ
∗
) =
(25 + 10 + 9)α
9
=
44α
9
In the case of a circular trajectory, we obtain for the half sum of the mass energy:
mZ =
9
44α
.
mb+mτ
2
= 91.187 5 GeV; ( exp: 91.187 6 (21) GeV) (29)
THE MASS OF W BOSON
We assume an elliptic interaction for W- between 2 leptoquarks with a mass equal to the
average constituent masses, taking into account IC(2b,2b) = IC (u, u):
3b + τ
4
and
3b + τ
∗
4
; with IC(W−) = IC(bb + uu + ττ
∗
) =
(23 + 2 + 9)α
9
=
34α
9
b → b
∗ => W− → W+;IC(W−) = IC(W+)
We find:
mW = (
9
2×34α
+ 2) .
3mb+mτ
4
= 80.375 GeV; (30)
The most precise experimental results are:
mW = 80.370 (19) GeV (ATLAS 2017); mW = 80.360 (16) GeV (ATLAS 2023);
We assume the same elliptic interaction with the belonging leptoquarks:
3(b + u + u
∗
) + τ
4
and
3(b + u + u
∗
) + τ
∗
4
We find:
mW = (
9
2×34α
+ 2) .
3(mb+2mu)+mτ
4
= 80.435 7 GeV; (31)
The last experimental value given by Fermilab for the W boson mass:
mW(exp. ) = 80.433 5 (9.4) GeV; (32)
These results seem to show that there are two composite W bosons of slightly different masses
due to a difference of composition of the constituent leptoquarks. The mode of production of
the W boson may explain this difference (p-p* interaction in LHC, p-p in Fermilab).
THE MASSES OF PROTON AND NEUTRON
We apply the model to calculate the proton and neutron masses.
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Proton
Empirically we find for the proton mass the below relationship given by a circular movement
of the mixed particles {u, d*} and {u*, d} with IC (e, e*) = α, and a rest mass of u, u*, d, d*, quark
combination:
mp =
2
α
.
mu + md
2
+
2mu + md
2
+ mu
With the main values given by C. Davies [8] for the mass of u and d quarks:
mu = 2.01 ± 0.14 MeV; md = 4.79 ± 0.16 MeV
mp = 938.245 MeV
For the below values contained in the error bars from C. Davies calculation:
mu = 2.009 MeV; md = 4.7912;
We obtain exactly the experimental value for the proton mass:
mp = 938.272 MeV; (33)
Neutron
The relationship for the neutron is:
mn =
2
α
.
mu + md
2
+
2md + mu
4
+ md
With the values of C. Davies for the u and d masses we find:
mn = 939.532 MeV
With the values of u and d masses given above for the proton we find above a value very close
to the experimental mass of the neutron(−5 × 10−6
):
mn = 939.560 MeV; (34)
THE MASS OF PI-MESONS
We assume that pi-mesons are UR leptoquarkonia whose constituents are leptoquarks particles
(d, e)
Neutral pi-meson (π o)
We obtain for a circular leptoquark interaction of the mixed particles below:
2d + d
∗ + e
8
;
2d
∗ + d + e
∗
8
;
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Fèvre, R. (2023). Composite H, W, Z Bosons: A Model Explaining the Different Experimental Values of their Masses Other Results: Pi-Meson, Nucleons,
Heavy bosons, Dark Matter Masses. European Journal of Applied Sciences, Vol - 11(6). 317-330.
URL: http://dx.doi.org/10.14738/aivp.116.16092
IC = IC(dd
∗ + ee
∗
) = (
25
9
+ 1) α =
34
9
α
m(π
0
) =
2×9
34α
.
3md+me
8
= 134.9764 MeV; (35)
m(π
0
)exp. = 134.9766 (6)MeV; with md = 4.791 MeV;
Charged pi-meson (π ±)
With an elliptic interaction of the below leptoquarks:
3d + e
8
;
3d + e
∗
8
; IC (2d, 2d) = IC(u, u)
IC =
IC
3
(uu + dd + ee
∗ + 3ud) =
2 + 23 + 9 + 42
3 × 9
α =
76α
3 × 9
We obtain, taking into account the kinetic energy three times corresponding to the three colors:
m(π ±) = (
3×3×9
2×76α
+ 2) .
3md+me
8
= 139.5854 GeV: (36)
m(π ±)exp. = 139.57018 (35) MeV
HEAVY COMPOSITE BOSONS WITH A TOP QUARK CONSTITUENT:
Top-onium
IC(t,t
∗
) = IC(u, u
∗
) =
10α
9
mtt
∗ = (
9
2×10α
+ 2) mt = 11 141.6 GeV; (37)
Top-tau-onium
IC =
1
2
.[IC(t,t
∗
) + IC(τ, τ
∗
)] =
10 + 9
2 × 9
α =
19α
2 × 9
mtτ,t
∗τ
∗ =
(
9
19α
+2)(mt+mτ
)
2
= 5858.7 GeV; (38)
Top-b-onium
The mass of this composite particle is the half sum of the masses of two pairs of particles
corresponding to two UR interactions:
t + b
2
t
∗ + b
∗
2
;
t + b
∗
2
t
∗ + b
2
For the first interaction, the coupling is the half sum of the couplings of all the concerned
quarks;
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t t* b b* t b* b t* IC =
55α
2×9
For the second interaction, the coupling is that of the lepton: α/2; the half sum of the couplings
is: 32α
2×9
; then:
mtb,t
∗b
∗ = (
9
32α
+ 2) .
mt+mb
2
= 3609.6 GeV ; (39)
This value corresponds to a bump observed at high energy by the ATLAS detector in ref. [9]
DARK MATTER
In ref [4], [7], we give the below relationship on elementary particle masses:
m = mp exp (−
na
2θ
) ; (40)
The parameter θ and the quantum number n characterize the elementary particle.
For the 3 elementary charged particles of the first family, we empirically determined the below
values of θ and n, with the electron experimental mass as a reference (other masses are
calculated).
Electron:
θ = 3√2; n = 3; me = 0.511 MeV (exp. )
Up quark:
θ = 2√2 + 3; n = 4; mu = 2.13 MeV;
Down quark:
θ = √2 + 6; n = 5; md = 4.80 MeV;
We have the empirical relationships below for the parameters:
θ(k, l) = √2k + 3l; n = k + 2l; k, l = [0,1,2,3] k + l = 3;
These numerical relationships that appear between parameters of the electric charge and the
color charge of these 3 particles allow us to suppose the existence of a dark quark (without
electric charge) with parameters and mass below:
k = 0; l = 3; => θ = 3 × 3 = 9; n = 6; mdq = 8.163 MeV; (41)
We can assume now a neutral color dark baryon composed of 3 dark quarks of 3 different colors
(each with a strong charge = f/3). As there are 3 pairs of dark quarks, then 3 possible
movements, we can calculate the dark boson mass as 3 times the mass of an elliptic UR dark
quarkonium. Using the above calculation of the model mass:
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Fèvre, R. (2023). Composite H, W, Z Bosons: A Model Explaining the Different Experimental Values of their Masses Other Results: Pi-Meson, Nucleons,
Heavy bosons, Dark Matter Masses. European Journal of Applied Sciences, Vol - 11(6). 317-330.
URL: http://dx.doi.org/10.14738/aivp.116.16092
IC(dq, dq) =
6α
9
; mdb = 3 (
9
12α
+ 2) mdq = 2566 MeV; (42)
Calculate now the ratio:
2mdb
mp+me
= 5.467; (43)
We can see that this ratio is very close to the ratio: dark matter / ordinary matter:
% dark matter
% ordinary matter
=
26.8
4.9
= 5.469; (44)
Then, the existence in the Universe of two dark baryons for one proton and one electron can
explain the ratio “dark matter/ ordinary matter”. This can be justified as below when
elementary particles appeared at the end of the quadratic period of the expansion (see ref 3).
The table below presents all possible color (noted a, b, c) combinations allowing to form dark
quarks with a constraint: only one active color per dark quark (example: a, a* is not active). We
then obtain 9 dark quarks giving 3 color neutral dark baryons. We assume that combinations
type a, a*, a; are unstable, decay and give u or d quarks. Then the corresponding dark baryon
decay to one proton and one electron or one neutron.
Dark Baryons Table
2 dark quarks +1 quark d; 2 dark quarks +1 quark u or d; 2 dark quarks +1 quark u
Dark baryon 1 a, a*, c b, b*, a c, c*, b
Dark baryon 2 a, a*, b b, b*, c c, c*, a
Dark baryon decays a*, a, a b, b*, b c, c*, c =>
Proton + Electron -|e|/3, a, a (d-quark) 2|e|/3, b (u-quark) 2|e|/3, c (u-quark)
or Neutron -|e|/3, a, a (d-quark) -|e|/3, b, b (d-quark) 2|e|/3, c (u-quark)
This approach gives 2 dark baryons per 1 proton and 1 electron (or 1 neutron).
It is possible that exits a neutral dark quark wearing 3 colors a, b, c; its mass would also be:
8.163 MeV.
CONCLUSION
This article shows that three hypothetic composite particles have a mass close to 125 GeV
which explain the different experimental masses of the Higgs boson observed in the CERN
detectors. Perhaps a new analysis of the signal at this energy will allow us to know if the Higgs
boson is, or not, an elementary particle.
Historically, the BEH hypothesis was formulated to explain why the W and Z bosons, considered
as elementary particles and weak interaction vectors, have a mass (electroweak theory). For
our model, this hypothesis is not necessary since the Z and W bosons are composite particles.
The model gives for the Z boson mass a value very close to the experimental measurements.
For the W boson mass, the model provides two values, in particular the one recently measured
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by Fermilab, which surprised the specialists (m (W) = 80.433 MeV). The other value is
according to the different other measurements.
This model makes it possible to calculate the hadrons masses according to the masses of the
constituent quarks. We give the result for the proton, the neutron, the pi-mesons and composite
bosons with a top quark constituent.
Finally, the model provides an approach to the mystery of dark matter.
References
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