Abstract

There are currently eight connected major unanswered questions in physics and astrophysics. The most important of these are:

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• Where do the extremely high-energy cosmic rays that occur in the energy range beyond the GZK cutoff come from?
• How can the theories of symmetry and the Higgs field be used to calculate the masses of the fundamental particles

 A self-consistent theory called Model W1 (or just Model 1) has been developed that answers these questions quantitatively. The unique features of this model are:

• There are two spaces in the universe, particle space and quantum vacuum space. A potential barrier separates them. One space contains visible matter, and the other space contains dark matter.

• There is a cycling of mass-energy between these spaces through the black holes that connect them. Particles pass from our space through black holes where they are converted into super particles (energy ~10¹⁷GeV) that operate with unified force. They then pass into the high-energy vacuum space where they become dark matter (super particles) operating behind the potential barrier (potential energy ~10¹⁹GeV).

• Dark matter particles interact with each other and form a slowly building and moving bubble centered on a galaxy. Corridors of dark matter form a cosmic web between the galaxies, which guide the development of new galaxies and connect the bubbles of dark matter to each other.

• The dark matter particles in vacuum space gain energy and eventually exceed the ability of the barrier to contain them. They then explode back into particle space as a big bang (Type 1). This process repeats to make a series of new universes, each with higher entropy.  Eventually, the entropy is high enough that a Type 1 big bang cannot occur, and the balance of pressure and density in particle space shifts, causing a complete collapse and a different type of big bang (Type 2). This Type 2 big bang restarts the Type 1 cycles. 

• After the big bang exhausts itself, super particles continue to tunnel through the barrier into particle space. The super particles are unstable and break down into particles (protons) with extreme kinetic energy. In doing so, they give up potential energy into particle space. The potential energy gradually builds up to become the dark energy that we observe as the cause of our accelerating, expanding universe. The extreme energy protons are observed as cosmic rays with energy between the energy of force unification and the Planck energy, which is beyond the GZK cutoff. 

 Considerable work has been done to show how Model 1 answers the important questions named and is an accurate description of nature (ref 3, AP4.7). In working out mass rotation for Model 1, some questions over the origin of the enormous mass (~10¹⁷GeV) of the shielded super particles surfaced. In order to answer these questions, it became necessary to work out a model that allows us to calculate the mass of the proton and the fundamental particles that make it up. This model (part of Model 1) then allowed us to work out a theory of the mass of the super particle, and its shield that is made up of a Higgs field. As an unexpected side result of this theory, some surprises surfaced. In this paper we will describe this theory and the surprises.

 

The Problem

Higgs found out that elementary particle mass is connected to a field that permeates space (Kane, 97). Schumm points out that mass appears to be the charge for the gravitational field (Schumm, 10). Shumm also notes that mass can be modeled by a screening effect with the Higgs field (see Shumm, 293-299). Most important, Einstein described a background independent way to connect mass to the curvature of space in the field equation (Misner, 431 and 41). In all of this, it seems that there is not an intrinsic mass in the fundamental particles of the nucleus. The mass appears to come from the interaction of the Higgs field and the mass charge of the particle.

In this paper, we will connect the Higgs field to mass. Also, we will construct a logical assembly of the standard model components, including the Higgs, into the masses we observe for the particles. Thus the mass can be calculated by adding a Higgs states to the Standard Model particle states. Further, we will extend the theory that allows us to determine the standard model particle masses to deduce the existence of the shielded super particle of Model 1. It is interesting to note that some surprises surfaced in exploring the results of this theory. These surprises will be duly noted.

 

The Solution

We propose that mass (as charge) generates the Higgs field, and distorts space as shown by Einstein in the field equations (Misner, 431), through the Higgs field. The Einstein equations account for inertia and gravitation as shown by Misner (Misner, 47). Further, the mass of particles is due to the interaction of the Higgs field with the particles as described by the Standard Model of particle physics, and is calculable.

Here we will first account for the inertial effects of mass through the Higgs field. Then we will calculate the mass of the basic particles. Then we will calculate the mass  of a proton, which is about 1 GeV. Further, we will extend these calculations to calculate the mass of the super particle of Model 1. We will finally calculate the mass of the barrier shell of Model 1.

The Inertial Effects of Mass 

Mass inertial effects can be modeled by a screening effect with the Higgs field (see Shumm, 293-299) that explains mass formation. To explain this effect, we compare it with the screening effect of electrons on photons. If a photon passes through a medium filled with free electrons, its oscillating electric field oscillates the electron charges, and they generate opposing photons that tend to interfere with the oscillation of the original photon field. Thus the electric field in the medium will oppose the constant oscillation of the original photon field, and reduce it. This tendency is called screening, and it gives a finite range to a photon in conducting media. We can model this effect by saying that the screening electric field generates an “effective mass” for the photon even though the photon has zero mass and infinite range. This screening range is similar to the range of a field with massive exchange particles, shown in the equation (see Kane, 29).

            φ =  φ_o /4πr exp(-mr) (natural units)

Note that the field is significant in size only out to a range of r ~ 1/m (natural units), where m is the “effective mass”.

In a similar manner, we can model the mass of a quark with a Higgs field that “drags” on the quark as it accelerates. If an accelerating quark passes through a medium (vacuum) filled with particles that create a uniform Higgs field, the accelerating quark generates an accelerating Higgs field that interferes with the Higgs field in the vacuum, and causes it to push back to reduce the relative motion toward zero relative acceleration. Thus the Higgs field in the vacuum will oppose the acceleration, and slow it down toward a constant velocity. We can model this effect by saying that the screening Higgs field generates an “effective mass” for the accelerating quark as shown above. There does not appear to be any free mass to a quark other than the Higgs “effective” mass.

This explanation does not yet show the details of the connection between the Higgs field and the field in the field equation of General Relativity. We must show mathematically how mass and the Higgs field determine the curvature of space. This question is beyond the scope of this paper, however.

Nevertheless we can see how the Higgs field makes free particles act like they have inertia and resist acceleration, but it does not yet explain how to calculate the mass. To do this, we must investigate the matrix nature of the Higgs field, as we will below.

The Origin of Mass Through the Higgs Field

Kane (Kane, 261) describes mass as due to three sources:

• Higgs free mass of the particles
• Confinement mass-i.e. the mass-energy that holds the particles together.
• Interaction mass.

Free mass is given to quarks and leptons through interaction with the Higgs field. As will be shown below, confined mass is given to confined particles by interaction of quarks confined into protons with the Higgs field. The interaction mass is small and calculable and will not be pursued further here because it is treated elsewhere (Kane, 262).

Here we will work out the theory for, and the values of, each component.

Higgs Free Mass of the Particles

Origin of the Higgs Field

We start with an example. Consider a universe without force as shown in Appendix 1. In this universe, space is linear. By experiment, we find that the laws governing motion of particles are invariant under translation. By Noether’s theorem, there must be a conserved quantity attached to this invariance of law. This conserved quantity is momentum. Similar arguments yield the conserved quantities angular momentum and energy.

Now consider a universe with the gravitational force. We start with an example. Gravitational force requires description in curved space. By experiment, we find that the laws governing the motion of particles are invariant after translation in curved space. By Noether’s theorem, there must be a conserved quantity attached to this invariance of law. This conserved quantity is the mass-energy of the particle (Schumm, 10), the gravitational charge.

We conclude that the Higgs field has as its source, the mass charge just as the electric field has as its source, the electric charge. As with the electric charge and the electric field, the Higgs field would be expected to diverge from its proton and neutron mass source and have the for 

             φ_h =  φ_ho m /r²               

We expect the Higgs field to be uniform, but the above equation indicates that the Higgs field might be lumpy, i.e. concentrated around mass particles.. To explain why this conflict does not exist, we must look at three cases.

• The Higgs field averaged over the bubble universe. Here, the Higgs field comes mostly from the total distribution of mass in the universe. That distribution is smooth on a large scale. Thus the Higgs field is smooth until the test particle passing through the field passes close to another particle. In this case, the time of passage of the test particle through the zone of high field is less than the Heisenberg uncertainty time, so the particle cannot sense and respond to the high field in that zone. In addition, most of the Higgs field comes from the confinement mass and kinetic energy of particles which is more diffuse. 
• The Higgs field averaged over the bubble shell of the super particle. Here, the Higgs field comes partly from the mass of the bubble shell, which provides a smooth field. Some also comes from the kinetic energy of the super particle moving within the bubble shell, which also gives a smooth field. Finally, only a small part comes from the localized quark masses in the super particle. Also these masses move rapidly in the bubble inside its barrier shell. Thus they are smoothed out down to within a Heisenberg uncertainty time.
• The Higgs field averaged over the particles in a black hole. Here, the Higgs field is dominated by the average kinetic energy of the many particles in the black hole. Also, the quark particles are moving fast enough, so that their particle mass is smoothed out to within a Heisenberg uncertainty time 

We note, however, that the Higgs field is not a simple scalar. It is Lie group as we shall see.

Interaction of a Particle Field with a Uniform Higgs Field

Here, we describe the formation of the free mass of particles (quarks) by the Higgs field for one simple case-reflective symmetry. We start with the Lagrangian (see Kane, 122) of a Higgs field of a particle passing through a uniform vacuum Higgs field caused by many particles in a vacuum.

            ½∂_μφ ∂ ^μφ- (½μ²φ ²+ ¼ λφ⁴)

Note that the potential energy V is related to the Higgs field as follows

            V = ½μ²φ ²+ ¼ λφ ⁴

            Where:

            λ = self interaction coefficient

            φ  = Higgs field 

The first term is the interaction of the particle Higgs field with the many particle vacuum Higgs field. The second term is the interaction of the particle field with itself. Note the reflection symmetry; V(f) =V( –f). To find the excitation energies, and thus the masses, we must find the minimum of the potential and expand around the minimum to get excitations, which are the particles. In field theory, it is conventional to call the minimum the ground or vacuum state, and the perturbation terms are excitations. The form of the Lagrangian determines the mass of the particles.

To get the minimum of the potential, we take the derivative, set it equal to zero, and get 

            φ ² = – μ²/ λ = ν²

The value ν is the vacuum expectation value, and φ  is called the Higgs field. We do not limit φ ² to positive values, and so get a Mexican Hat shaped potential. We have to work with one value, so we choose the positive root. To expand the function, we set:

            φ(x) = ν + η(x)

We then get for the Lagrangian:

            ½∂_μ η ∂ ^μ η – (λ ν² η ²+ λ ν η ³ + ¼ λ η ⁴) + constant          

This Lagrangian represents the description of a particle with rest mass

            m _η² = 2 λ ν² = -2 μ²  = mass 

The reflection symmetry is gone here. The symmetry was broken when a specific vacuum state was chosen, so the vacuum does not have the symmetry of the original Lagrangian, and therefore the solutions do not. When this occurs, it is called “spontaneous symmetry breaking”. Note that the mass found is a screening by product of the Higgs field as described above 

Kane goes on to describe the Higgs mechanism for other symmetries (Global, Albelian and Standard Model), which are more complex, but the basic mechanism and the equations are similar. The above equations are enough for the purposes of this paper, however.

Recall that

            V = ½μ²φ²+ ¼ λφ⁴ 

            Where:

            m _η² = 2 λ ν² = -2 μ² = mass             

            λ = self interaction coefficient

             φ = Higgs field 

We see that this can be written:

            V = – m _η²φ ²+ ¼ λ φ⁴= -(m _η²– ¼ λφ ²)φ ²

                = particle mass energy

We will take the mass of the particle m_p to be:

            m_p = (m_η²– ¼ λ(s)φ^2p) = Higgs charge corrected for self interaction.

                   = m_η²f ^2p (1- (¼λ/m _η²)

                   =Km_η²(1- λ_t(n,s,m)φ^2p), K determines units of energy

Now in order to get the particle masses, we must establish the particle mass wave functions. To do this, we start with the particle wave function (Kane, 90), and multiply by the Higgs factor as follows.

The Fermion mass state is:

            Let m_e be a particular electromagnetic mass state, then:

            m_e = (space factor)x(spin factor)x(U(1) factor)x(SU*(4) factor)

            Then the particular Isospin mass state is:

            m_i = (space factor)x(spin factor)x(U(1) factor)x(SU(2) factor)x (SU*(4) Higgs factor)

            Then the particular Quark mass state is:

            m_q= (space factor)x(spin factor)x(U(1) factor)x(SU(2)factor)x(SU(3) factor)x(SU*(4) Higgs               factor)

The Boson mass state is:

           The particle Isospin boson mass state is:

            m_ib = (space factor)x(spin factor)x(U(1) factor)x(SU(2)factor)x(SU*(4) factor)

            Then the particle Higgs boson mass state is:

            m_ih = (space factor)x(spin factor)x(U(1) factor)x(SU(4)factor)x(SU*(4) factor)

The particle factors for a particle with particle number n and Higgs number m are as follows:

Space Factor

            (space factor) = n = particle number

Symmetry Factor

The symmetry factor for all four forces is:

            (U(1) factor)x(SU(2) factor)x(SU(3) factor)x(SU(4) factor)

            = 1x2x3x4 = 4!

So for each particle number n, the symmetry factor is n! = (n)(n-1)(n-2)…(1)

            Where:

            n = 1, electromagnetic particle

            n = 2, isospin particle

            n = 3, quark particle

            n = 4, Higgs particle

Spin Factor

Note that the up and down quarks are correlated with the Higgs number m.       

            Up                      Down

            m                       (m+(m-1))

 

(SU*(4) or Higgs factor

            (Higgs factor) = (exterior Higgs factor)(self-interaction factor)

The exterior Higgs factor acts on the exterior states of the particle and determines how many times (m) the space factor is used in interacting with the Higgs field, so the space factor n becomes

             n^2m’f ²

            Where:

            m’ = m or (m+(m-1))

 The Self-interaction factor is:

            (1- λ_tf ²/m _η²)

            Where:

            λ_tf ²/m _η² = internal states factor

                                 = (single self-interaction factor) /(exterior factor)(total self-interaction factor)

                                 = H / (exterior Higgs factor)

                                 = H/4 for a Higgs state for one boson

                                 = H/4×1/3 or 1/4×2/3 for a Higgs state for three bosons (SU(2)case)

            And:

                             H = single self interaction ratio = 1,2,3,4.                    

Thus the total mass-energy function is:

            m_p c² = K n! n^2m’f ² (1- λ_tf ²/m _η²),

                          = K n! n^2m’f ² (1- H/4),

Calculation of the particle masses

            Fermions                                                         Bosons

K = Constant that determines the units of the energy. Note that equations were developed in natural units (see Kane, 11), so the units are as follows.

            If  K = 1, units are MeV                                 If K = 1, units are GeV

m _η² = mass interaction coefficient

            m!n^2m    or m!n^2(m+(m-1))                        m!n^2m or m!n^2(m+(m-1))

H/4  = internal states facto            

            Down                               Up                                                    Down                             Up

     (n,m),    H/4                    (n,m+(m-1)),  H/4                    (n,m),     H/4            (n,m+(m-1)),H/4

     (1,0)      1 (neutrino)    (1,(1+0))           2/4                    (4,1)        4/4             (2,(2+1)) = 1/4                        

     (2,0)      1 (neutrino)    (2,(2+1))           2/4×1/3          (4,2)       3/4             (3,(3+2)) = 2/4

     (3,0)      1 (neutrino)    (2,(3+2))           2/4×1/3          (4,3)       2/4

     (3,1)       3/4                     (3,(1+0))           2/4                    (4,4)       1/4

     (3,2)       2/4×2/3           (3,(2+1))           2/4×1/3          (4,6)       0

     (3,3)       0 or 1/4            (3,(3+2))           2/4                    (4,10)    0

                                                                                                             (3,2)       2/4

                                                                                   

Notes

1). Note that we have ended with a doublet (Up, Down) set of particles as required by the Higgs mechanism (Kane, 105). The notation is simpler than it should be, but it is useful for the mass calculations of interest here.

2). The Higgs SU(4) factors come in descending increments of 1/4. They operate both with Fermions and Bosons.

3). The factors of 1/3 and 2/3 come from the Isospin and appears with the weak force SU(2) varients.

4). The (3,2) factor occurs with two values; 2/4×2/3 for a weak force Fermion, and 2/4 for a weak force Boson, as would be expected.

5). The (3,3) case appears to connect with the (4,6) Higgs, by giving a value of 0, rather than the (4,4) Higgs value of 1/4 as expected. More will be said about this later.

 

1&2).We see that the Higgs group SU*(4) forms one family of particle masses when combined with SU(1) and two families of particles with SU(2). 

(n,m) values

 (1,0)                      (1,(1+0))                (2,0)                          (2,(2+1))              (3,0)                      (2,(3+2))                                                                                                                     

Experimental lepton mass (Kane,8)

ν_e(<2.2eV)          e(0.511MeV)        ν_μ(<0.17MeV)     μ(105.7MeV)    ν_τ(<15.5MeV)   τ(1,777MeV)

 

Lepton masses from Higgs charges and fields

(1-1)                        (1-1/2)                     (1-1)                         (1-1/2×1/3)         (1-1)                      (1-1/2×1/3)

                                 x(1×1)                                                          x(1×2)                                                   x(1×2)

                                 x1^2×1                                                           x2 ²⁽²⁺¹⁾                                             x2 ²⁽³⁺²⁾

(0eV)                    (0.50MeV)               (0eV)                      (106.2MeV)          (0eV)                  (1,700MeV)

Notes 

a). We see that the Higgs field forms one family with SU(1), and produces an electron with mass close to the observed mass. The neutrino does not interact with the Higgs field, so the primary mass energy is zero.

b). The Higgs field forms two families with SU(2), and gives two new particles, μ and τ with mass close to the observed mass. Again, the corresponding neutrinos do not interact with the Higgs field, so the primary mass energy is zero. Mass from a secondary interaction could perhaps be estimated by use of an exponential map as shown below.

 

3). We see that the Higgs SU*(4) forms three families of particles when combined with SU(3) 

(n,m) values

 (3,1)                       (3,(1+0))                (3,2)                     (3,(2+1))                    (3,3)                     (3,(3+2))                                                                                                                     

Experimental quark mass

d(2.3MeV)            u(4.8MeV)            s(95MeV)           c(1.275GeV)            b(4.18GeV)        t(173.2GeV)

 

Quark masses from Higgs charges and fields

(1-3/4)                   (1-2/4)                    (1-2/4×2/3)       (1-2/4×1/3)          (1-0)                    (1-2/4)

x(1×1)                    x(1×1)                      x(1×2)                   x(1×2)                     x(1x2x3)           x(1x2x3)

x3²                         x3^2×1                       x3^2×2                    x3^2x(2+1)              x3^2×3                 x3^2x(3+2)           

d(2.25MeV)        u(4.5MeV)             s(106.9MeV)      c(1.210GeV)         b(4.37GeV)      t(177GeV)          

Notes

a). Only the mass from case (3,2) appears outside the error bars of the experimental mass.

b). For the (3,3) case, the (1-1/4) value was expected, which would give a mass value of 3.28GeV, a poor fit to data. However, the (1-0) value gave the best fit to the data. The (3,(3+2)) case would give the same value for either case. The (1-0) value goes with the (4,6) Higgs, which is the Grand Unification value, and it gives the best fit to data. Note that the (3,2) value is too high as well, and it is a down quark as well. These two cases act as if the (4,6) Grand Unification case exists, and its existence drags the values of a lower case toward its value. It is possible that we have accidentally stumbled on the components of the super proton of Model 1 in cases (3,3) and (3,(3+2)).

 

4). We see that the Higgs SU*(4) forms the W and Z bosons when combined with the SU(2) and SU(3).

(n,m) values

 (-)                      (-)                    (3,2)                  (2,(2+1))              (4,3)                 (3,(3+2))         

                                                                                                           

Experimental boson mass

                                                     W(80.4)            Z(91.1GeV)        W’(?)                  Z’(?)

 

Boson masses from Higgs charges and fields 1c = 0.5. A = 0.001, f = 31.5

                                                     (1-2/4)              (1-1/4)                 (1-2/4)             (1-2/4)

                                                     x(1×2)                x(1×2)                 x(1x2x3)          x(1x2x3)        

                                                     x3^2×2                 x2²⁽²⁺¹⁾            x4^2×3                x3²⁽³⁺²⁾                                                                                          (81GeV)             (96GeV)             (1.2×10⁴G )      (1.77×10⁵G)             

Notes

a). The interaction is mixed. The first results are from SU(2), yet for W, the number of dimensions is 3. and the Higgs field is 2. Still for Z, the number of dimensions is 2 and the number of the Higgs field is 2. The same crossing is assumed for W’ and Z’. Both use the f^2p factor because they are Bose particles. This mixing appears to be due to the peculiarities of the weak force. 

b). The W’ and Z’ particles have not been found because the energy is too high for current machines, but they are expected to exist. These cases involve an SU(4) particle which is a Higgs particle, so they will probably have some unusual properties. 

c). The next pair of particles may not exist, because the SU(5) group might be forbidden(see 5) below).

 

5). We see that the Higgs SU*(4) forms the Higgs bosons when combined with the with SU(4). We have added two additional bosons to see if the Grand Unification SU(6) and the Complete Unification SU(10) are possible.

 

(n,m) values

(4,1)                   (4,2)                    (4,3)                     (4,4)                     (4,6)                  (4,10)                                                                                                      

Experimental and other possible Higgs masses

                            H^o(125GeV)                                                                                                (~10¹⁹G

 

Masses from Higgs charges and fields

(1-4/4)              (1-3/4)                (1-2/4)                (1-1/4)               (1-0)                 (1-0)

x(1)                    x(1×2)                  x(1x2x3)            x(1x2x3x4)     x(1×2…x6)     x(1×2…x10)

x4^2×1                x4^2×2                   x4^2×3                  x4^2×4                x4^2×6               x4^2×10

(0GeV)             (128G)                  (12,300G)           (1.18×10⁶G)   (1.2×10¹⁰G)  (4.00×10¹⁸G) 

Notes

a). The second Higgs family generates a Higgs particle with the proper mass-energy-128G versus measured 125G. Also, there is a known interaction between the SU*(4) Higgs field and SU(2) particles in the weak force.

b). One other possible Higgs particle shows on the table-(4,1), but it has a 0GeV energy, so it clearly does not exist. No lower energy Higgs particle has been found, but a systematic search has not been made.

c). The Higgs field (4,2) appears to be the one that reacts with (3,1) to make a quark.

d). The heavier Higgs field (4,3) appears to be the one that interacts with (3,2) to make a heavier quark..

e). The (4,4) Higgs field may not interact with (3,3) at all as it appears to be supplanted by the (4,6) Higgs field, as noted above to make a component of the super proton.

f). The (4,6) Higgs field appears to interact with the (3,3) field to make the components of the super proton. Kane notes that a Grand Unified Force is expected at ~10¹⁷GeV (Kane, ?).  The confinement mass energy is expected to make up the difference between ~177GeV of the super quarks and ~10¹⁷GeV of the super proton. We have here a clear indication of the existence of a super particle for Model 1.  

g). The (4,10) Higgs field appears to interact with itself to generate a Complete Unification Force (including gravity) Higgs barrier shield (potential energy 4.00×10¹⁸GeV) to surround the super particle as indicated in the Model 1 description. Note that the Higgs barrier acts on mass, so electromagnetic force and photons penetrate the barrier, but massive particles are slowed or reflected.

h). The (4,5) case does not appear to exist because it does not correspond to any combination of the four forces. For example:

• U(1)xSU(2)xSU(3) = SU(6) = Grand Unification. EM, weak and strong forces are all present.
• U(1)x SU(2)xSU(3)xSU(4) = SU(10) = Complete Unification. All forces are present.
• SU(5) = SU(2)xSU(3) = unification of only weak and strong forces. Similar problems occur for SU(7), SU(8) and SU(9). It appears that all forces are required to make a unification.
• No particles or forces are expected beyond SU(10) because the energy requires is more than the Plank energy.

 

Higgs Confinement Mass of the Particles

The final mass component for the proton can be described as the energy component due to the exchange of the gluons between the quarks to maintain the confinement of the quarks. The quark combinations to make nuclei are as follows:

• u, u, d. This is the common proton in particle space
• c, c, s. This is probably a proton in particle space, but it is low probability event.
• t, t, b. This may be a super proton in vacuum space

The combination of the last family of strong force quarks and the Higgs is a good candidate for the super particle with a mass  ~10¹⁷GeV which is needed for Model 1, and so deserves to be investigated. Let us determine the mass of the proton using the same techniques for determining mass we used above for particles.

            m_pr = (space factor)x(spin factor)x(U(1) factor)x(SU*(4) factor)

We combine three quarks into a proton, and recall that the ttb case is SU(6), then:

            m_pr = (q 1 factor)x(q 1 factor)x(q 2 factor)K n! n^2mf ^2p (1- λ_t(n,s,m)f^2p)

Thus we get:

(n,m) values

                        (3,(1+0))                                  (3,(2+1))                                  (3,(6+5))                                                                                                                     

Experimental proton mass

                                    uud(938MeV)                                    ccs(?GeV)                                           ttb(~10¹⁷GeV)

 

Proton masses from Higgs charges and fields

d(2.25MeV)            (1-5/8)             c(1.21GeV)            (1-5/8)                   t(177GeV)         (1-5/8)

u(4.5MeV)              x(1x2x3)          s(107MeV)            x(1x2x3)              b(4.37GeV)       x(1x2x3x6)

uud=45.6M            x3^2x(1+0)        ccs=157G              x3^2x(2+1)            ttb=1.37 10⁵    3^2x(6+5)           

                                    uud(923MeV)                                    ccs(257GeV)                                    ttb(5.8 10¹⁶G) 

Notes

a). The mass energy for a proton matches the experimental data, and so there is reason to believe the formula is correct.

b). The mass energy for ttb matches the value for Grand Unified Force (Kane, 281) obtained by other means. This is strong evidence for the existence of a super proton.

c). There is evidence that the ccs proton exists, but there is no place to fit it into the theory.

d). The self-interaction factor for the proton (uud) is (1-5/8), and fits the data well. Note that this factor results from the fact that the self-interaction term comes from interaction with two Higgs bosons rather than one as for a particle, and so is:

            (1-λ_tf ^2p/m _η²)= (1-2/4(2/4+3/4)) = (1-2/4(5/4)) = (1–5/8)

Surprises

1). For the (3,3) case, the (1-1/4) value for internal states was expected, which would give a mass value of 3.28GeV, a poor fit to data. However, the (1-0) value gave the best fit to data. The (3,(3+2)) case would give the same value for either case. The (1-0) value goes with the (4,6) Higgs, which is the Grand Unification value, and it gives the best fit to data. Note that the (3,2) value is too high as well, and it is a down quark. These two cases act as if the (4,6) Grand Unification case exists, and its existence drags the values of a lower case toward its value. It is possible that we have accidentally stumbled on the components of the super proton of Model 1 or Grand Unification value in cases (3,3) and (3,(3+2)).

2). The (4,6) field appears to interact with the (3,3) field to make the components of the super proton. Kane notes that a Grand Unified Force is expected at ~10¹⁷GeV (Kane, 281).  Another estimate of the unification energy is given on the Internet as ~10¹⁶GeV. The confinement mass energy is expected to make up the difference between the particle ~10¹⁰GeV and ~10¹⁷GeV. We have here a clear indication of the existence of a super particle for Model 1.  

3). The (4,10) Higgs field appears to interact with itself to generate a Complete Unification Force (including gravity) Higgs barrier shield (potential energy 4.00×10¹⁸GeV) to surround the super particle as indicated in the Model 1 description. Note that the Higgs barrier acts on mass, so electromagnetic force and photons penetrate the barrier. Massive particles are slowed or reflected

4). The μ and the τ leptons are connected to the weak force (SU(2)) rather than the electromagnetic force (U(1)), and thus completes the unification of the weak and the electromagnetic forces into the electroweak force.

5). An SU(5) Grand Unification (Kane, 286) is not possible, because it does not include the EM force as shown above. An SU(6) unification appears possible, however (see above). As a result, the proton decay lifetime experiment is expected to fail, as it appears to be doing.(Kane, 289)

6). It is well known that U(1) of the electromagnetic force has one generator-the photon. Also SU(2) of the weak force has three generators-the W^+- and Z^o bosons. Further, SU(3) of the strong force has 8 generators-the gluons. All this fits with the n²-1 pattern for SU symmetry. Carrying on with this pattern, we see that (SU(4) has 15 generators-the Higgs bosons that tie the tie the particles together and give them mass. Also SU(6) has 35 Higgs boson generators of the unified force that tie the super particle elements of Model 1 together and give the super particle mass. Finally, SU(10) has 99 Higgs boson generators of the barrier shell that tie the barrier together and give it mass.

 

Unanswered Questions

1). We note that the neutrino mass has not yet been accounted for. It appears possible that it may be accounted for by use of an exponential map M(m) on the above mass matrices defined by:

            M(m) = Exp(A) = 1 + A+ A²/2! + A³/3! + … for matrix A

Here, the first term describes the primary mass of the particles seen above, and the neutrino mass may reside in the second, third or fourth terms.

2). Most important, the connection between the Higgs field and the field in the field equation of General Relativity must be fleshed out. We must show mathematically how mass and the Higgs field determine the curvature of space. This question is beyond the scope of this paper, and will be attacked later.

3). It was noted above that the (3,3) quark we are familiar with at energy 4.18 GeV may be a Grand Unification particle rather than the expected (3,3) particle at 3.28 GeV. This may be a total Grand Unification replacement or there may be 3.28 GeV particle as well. In either case, it would be helpful to know which is correct. Be forewarned that the 3.28 GeV particle is expected to produce a much fainter signal and so might be masked by the stronger 4.18 GeV signal, so it would hard to find. 

4). Unfortunately, almost all of the new particles discovered here have energies beyond the capability of existing accelerators, but they can be searched for by use of different methods (see ref 5 AP4.7D, ref 6 AP4.7I and ref 7 AP4.7L ).

 

Conclusions

In this paper, we have developed a model (part of Model 1) that allows us to understand the origin and effect of mass in the universe. Further, Model 1 allows us to calculate the masses of all of the fundamental particles. We found further that:

• There are surprises that result from investigating this theory.
• The theory proposed leaves some unanswered questions that deserve investigation.

We also found that it is possible to extend this model to calculate the mass of a possible shielded super particle, which is the principal particle of a Grand Unified Theory unifying the electroweak and the strong forces. We found that the mass-energy of this shielded super particle is ~10¹⁷GeV as predicted (Kane, 281), and consists of more massive versions of the electron, W and Z bosons and u and d quarks (i.e.-the t and b quarks) we are familiar with in the common electron and proton. Further, this super particle satisfies the SU(6) symmetry, and appears to connect to the Grand Unified force. Many of these massive particles have already been discovered. We found finally, that the barrier shell of Model 1 consists of a Higgs field that satisfies the SU(10) symmetry, and appears to connect to the Total Unified force which includes gravitation.

 

References 

1. B. A. Schumm, Deep Down Things, Baltimore, Johns Hopkins University Press, 2004.
2. G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing, 1993Kane
3. L. H. Wald, “AP4.7 DARK MATTER AND ENERGY-FUNDAMENTAL PROBLEMS IN ASTROPHYSICS” www.Aquater2050.com/2016/10/
4. Misner, Thorne and Wheeler, Gravitation, New York, Freeman and Co., 1973.
5. L. H. Wald, “AP4.7D HOW TO PROVE A THEORY’S CORRECTNESS” www.Aquater2050.com/2015/12/
6. L. H. Wald, “AP4.7I THE SUPER PARTICLE AS A COSMIC RAY” www.Aquater2050.com/2015/11/
7. L. H. Wald, “AP4.7L EXTRACTING SUPER PARTICLES FROM THE BARRIER SHELL” www.Aquater2050.com/2016/05/