Journal of Modern Physics, 2012, 3, 1450-1457 Published Online October 2012 (
On Neutrino Oscillations and Predicting the 125 GEV Two
Photon Emission State from p-p Collisions Based on the
5D Homogeneous Space-Time Projection Model
K. W. Wong1, G. Dreschhoff1, H. Jungner2
1Department of Physics and Astronomy, University of Kansas, Lawrence, USA
2Radiocarbon Dating Lab, University of Helsinki, Helsinki, Finland
Received August 8, 2012; revised September 11, 2012; accepted September 18, 2012
Previously the 5D homogeneous space-time metric was introduced with explicitly given projection operators in matrix
form which map the 5D space-time manifold into a Lorentzian space-time. Based on this projection model, vector field
and spinor solutions are found to be expressible in terms of SU(2)xL and SU(3)xL, where L is the 4D Lorentz
space-time group. The spinor solutions give the SU(2) leptonic states arising from space-time projection, whereas the
SU(3) representation arises from conformal projection and gives the quarks, and due to gauge requirement leads to me-
sons and baryons. This process of mapping the 5D space-time manifold into the 4D space-time is at the basis of an
analysis of the recent CERN experimental results, the presence of neutrino oscillations and the observed 125 GeV reso-
nance in the p-p collisions, respectively. In fact, it is found that the spinor solution contains an oscillating phase, and the
125 GeV resonance is shown to be predictable, thereby 1) eliminating the need to introduce a Higgs vacuum, and 2) can
be shown possibly to be an indicator for a missing heavy baryon octet.
Keywords: Neutrino Oscillation; 125 GeV p-p Bound State; Hadron Mass Levels; 5D Homogeneous Space-Time
1. Introduction
Recently there was some excitement within the physics
community related to results of two fundamental experi-
mental findings. By far the more publicized is the finding
of a 125 GeV two photon emission obtained from the p-p
collision experiment done by the CERN Large Hadron
Collider [1,2] and the Tevatron [3]. It is billed as an in-
dication of the existence of the Higgs Boson, which was
advanced some half a century ago by Higgs [4] for giv-
ing the quarks of Gell-Mann’s standard model [5] their
basic masses. It is clear that in the 4D space-time domain,
mass cannot be generated by interactions of mass-less
fields. The second experimental finding is the oscillation
of the neutrino states [6-8], making the three leptonic
neutrinos able to evolve into each other on their propaga-
tion through space-time. It is these two interesting results
that we like to discuss in this paper. Not long ago, we
proposed a 5D homogeneous space-time domain [9], and
showed that we can derive the quarks of the standard
model by imposing a projection action. In fact, this pro-
jection can be separated into a pure space to time axis
projection P0, which would necessarily produce the lep-
tons plus their corresponding neutrinos as given by the
SU(2) representation. The space-space projection P1 is a
conformal projection, and readily gives the SU(3) quarks,
with fractional charges and with corresponding intrinsic
masses. Therefore, this 5D theory requires no Higgs Bo-
sons to give quarks their masses. Hence if the observed
125 GeV two photon emission state cannot be explained
by our 5D model, then perhaps this result would be more
convincing that it is a verification of the Higgs field ex-
istence. We separate our discussions into three parts. For
the first part, we show explicitly, the neutrino oscillation
as obtained by the 5D projection theory [9]. In the second
part, we will show that according to our theory and the
SU(3) representations, there should exist a yet not dis-
covered very high energy octet representation of the ba-
ryons. It is also pointed out that due to the extremely
large masses of these eight baryons, they could be nearly
degenerate, if the mass splitting between them is negligi-
bly small. In fact then the total sum for a pair of all eight
baryon masses also amounts to the order of 120 GeV
accidentally, but might not be correlated to the p-p result.
From there in the third part, we put forward a discussion
on the 125 GeV resonance created by the p-p collision,
which is suggested to be predictable from the 5D projec-
tion model, and perhaps has no correlation to the exis-
opyright © 2012 SciRes. JMP
K. W. WONG ET AL. 1451
tence of a Higgs field.
2. The Neutrino Solution
The supposition that the universe is in the 5D homoge-
neous space-time manifold might be verifiable from
mass-less fields that are solutions of the 5D metric op-
erator via boundary conditions in the 4D coordinate vol-
ume projected into the Lorentz 4D space-time domain
that they must satisfy. Of these fields, there are the pho-
tons, e-trinos, and neutrinos. The photons satisfy the 4D
Maxwell operator, hence cannot provide boundary con-
ditions that are in 5D, while the e-trinos can only exist in
5D and not in Lorentz 4D, thus cannot be observed by us
that live in the Lorentz 4D domain. We are therefore
confined to studying the solutions of the neutrinos.
The neutrino is a solution of a projection on the
5D spinor, as given by
 
where 2πq is the quantum flux for a charge “q”.
Note “q” is not necessary “e”, it is simply a coupling
constant between the spinor and the vector potential
fields, as we have discussed in ref. [9],
is a finite con-
stant = qm , and is a vector field independent spi-
nor in 5D space-time manifold, via gauge transformation.
It should be noted that d2π
, where 
is in the 4D Maxwell space-time, must go to infinity as q
goes to zero, meaning the charge-less spinor is not cou-
pled to the vector fields in the 4D Hilbert subspace of the
(4x1)D manifold, thus the flux loop must enclose the
entire 4D Hilbert subspace of the universe.
It is then obvious that produces the SU(2) group,
with or 0. For , we have the Dirac equation
for a charged massive spinor. However if q
, we
must have , such that
0mqm can remain a constant.
In order that the phase factor in Equation (2.1) is prop-
erly defined we also must have the limit Φ 42πp
Since Φ diverges as “q” goes to zero, 4 must simulta-
neously go to zero. It is this solution that makes the neu-
trino both charge-less and mass-less. It is easy to see
without 0 action, it is a 5D plane wave, without boun-
dary [9].
The neutrino equation in Lorentz space-time is not
simply eliminating m from the Dirac equation as QED
will have. Actually, the neutrino, being charge-less, is in
the 4D Lorentz energy-momentum space without making
a 0 projection. The 4D Lorentz energy-momentum
space is different from the 4D Lorentz space-time, as
fixing the rest mass equal to zero, implies from Fourier
transformation fixing x4 equal to infinity. However the
5D homogeneous space-time metric makes all coordi-
nates finite at a fixed time t, thus this requirement cannot
be satisfied. On the other hand, the 5D homogeneous
metric operator implies all field solutions of it must be
mass-less. These contradictions must be due to not im-
posing the boundary conditions to the field solutions. Or
that these 5D fields must satisfy boundary conditions on
the boundary of the universe as defined by the time t of
its absolute age. Therefore to find it, we return to the
spinor equation given in the 5D homogeneous space-time
where we now transform the 5D spinor into the form
given by Equation (2.1).
The linear 5D operator can be explicitly expressed in
terms of two additive terms. The first term is purely that
due to the x4 component, while the second term is just the
4D Dirac operator without mass.
 
as the phase factor is subject to the first term operator. In
order to perform the differentiation, we make the Fourier
transformation to p4, we get for the first term
444 4
ei e
 
Substituting Equation (2.4) into Equation (2.3) we ob-
where 422
There are 3 independent loop planes in a volume of 4D
coordinates, as depicted by a doughnut 3D figure instead
of a 3D homogeneous sphere following Perelman’s proof
of the Poincaré conjecture. Hence the quantum flux actu-
ally is a pseudo vector in the 4D coordinate space. From
the 5D metric 4
, where is the age of the
universe. As increases to a very large value, the loop
length for the flux will also. Hence it is possible that 4
is finite. In fact for the boundary condition to be un-
changed with , 4
must be constant. To show that
fixed 4
gives the needed boundary condition on the
mass-less fields in the finite universe, let us reformulate
the 4
22 2
From the 5D metric
 
By differentiating Equation (2.6) with
, Equation
Copyright © 2012 SciRes. JMP
(2.6) becomes
This simple solution of
implies several philoso-
phical implications:
I. The vector potential
increases linearly with the
expansion of the Lorentzian manifold as given by
irrespective of any projection of the 4
II. Such an increase in
as the 5D homogeneous
space-time expands means the mass-less vector and spi-
nor field energies also increase in proportion.
III. At the Lorentzian space-time boundary the vector
is given by
As there cannot be
outside the 5D manifold or
must be zero on the surface enclosing the 5D
domain as given by the 4D Maxwellian space-time. Cor-
ollary, it means
, which is at the boundary of
the 5D universe as depicted by
, and there can be no
vector potential field , or no sources for the vector poten-
tials as given by charged spinors, and no light reflection.
In other words, the boundary of the universe is not ob-
servable. Since no fields can exist beyond the 5D mani-
fold Equation (2.8) represents the fixed boundary condi-
tion for
as well as that for the neutrino, which is not
coupled to
within R
. As maps the
boundary, it is obvious that if t is unidirectional, then the
coordinate boundary is given by a spherical surface with
radius ct.
IV. If the Lorentzian universe, which is created by the
projection of the 5D homogeneous space-time manifold
has a 3D space volume in the form of a doughnut as de-
rived by Perelman, then such a 3D volume has 3 inde-
pendent normals, namely 1) a normal to the surface of
the doughnut, 2) a normal to the cross-section of the
doughnut tube, 3) a normal to the doughnut ring cross-
section. When R is transformed into a sphere, the sphere
has more than just a single normal as depicted by the
radius vector, but also an up and down orientation and
Equation (2.8) is split into 3 coordinate vector equations
with their respective different 4
values. Hence it is
very important to keep q finite first and solve the equa-
tion before taking the limit q going to zero! By keeping α
finite, the solution to Equation (2.5) is a spin-space os-
cillator which satisfies the space-time metric, that is valid
at any T, in the finite 4D space. This is the origin of this
proper limiting procedure that will give us the 3 sets of
charged massive leptons with their associated neutrinos
due to the 3 remaining momentum space degrees of
freedom. We can now rewrite the neutrino equation un-
der 0
P projectionet with p4 = 0
 
, we g
where 044
is the PC violating neutrino oscillation
x (2.10)
The 5D gamma matrices can be eas
energy. Tlimiting procedure of making neutrinos
mass-less brings its solution back to a simple plane wave.
Each neutrino is associated with a massive lepton. In the
matter universe, the leptons can exist up to the boundary
of the finite 4D Lorentz space-time domain, thus the
neutrino solution need to be put into the exponentially
oscillating form which must satisfy the boundary before
taking the limit.
ily constructed
om the Dirac 4D gamma matrices, which can be con-
structed in terms of spin matrices [9], and will not be
presented here.
It should be noted that the neutrino exist in the 5D
homogeneous space-time manifold, and only when gauge
transformation is enacted the spin-space oscillation is
created, and thus split into 3 neutrinos coupled to the 3
massive leptons.
As a specific lepton and its corresponding neutrino is
created within a 3D spherical volume at time t, through
Perelman’s reverse mapping this neutrino state in ques-
tion would evolve into the superposition of the 3 distinct
cross-section loops due to the doughnut structure of the
universe at its boundary as given by the age of the uni-
verse as depicted by the 5D metric [9]. It is this continu-
ous growing of the 5D universe that introduces the oscil-
lating factor into the evolving neutrino state with time
from one into another among the three states as given by
SU(2) representation.
An anti-lepton within the matter universe could not
survive through all space before being annihilated. Hence,
the anti-neutrino associated with this anti-lepton must
also be confined to a very limited space domain that con-
fines the anti-lepton. In another word the anti-neutrino
associated with the anti-lepton, its coordinate oscillating
frequency 4
will become zero as the flux
must be
finite due to a finite loop, like in a lab eironment,
while 2
x approaches infinity with 2
x being fi-
nitely cfin and as T increases to exmely large
values. It is this physical picture that produces an
a-symmetry between the neutrino and the anti-neutrino.
Or conversely, it is the short ranged feature of the an-
ti-neutrinos, caused by the annihilation of the anti-lepton
that indicates we have a matter universe.
Since the neutrinos must have zero mass, by choosing
on edtre
e a-symmetry neutrino representation, they actually can
cross over from one to the other as the anti-lepton anni-
hilates. Choosing the limiting process that can only occur
in the anti-particle domain will still maintain SU(2). As
Copyright © 2012 SciRes. JMP
K. W. WONG ET AL. 1453
pointed out in recent experiments, the a-symmetry be-
tween leptons and anti-leptons was observed and it was
suggested that such a-symmetry could be the reason we
have a predominantly matter universe [6,7], therefore
such finding is consistent with our 5D homogeneous
space-time projection model.
3. Fine Structure Mass Splitting in SU(3)
Representations of Hadrons a nd I ts E ff ec t
gluved through their strength factors
on Fixing the Gluon Potential Generate
Mass Levels
our recent papers [9] and [10], we illustrated how th
on potentials are deri
from the Lorentz sum rules coupled with gauge invari-
ance constraint and the restriction, that the quark con-
stituents in the hadron must be Bohr-Sommerfeld quan-
tized on the flux loop provided by the gauge constraint.
However, as shown in these two papers, the numerical
estimated values did not follow and obey these require-
ments exactly. As an illustration, we used a static model
for the pion mass splitting in ref. [9], and deduced that
the unit rest mass for the quark is 52.5 MeV, and hence
obtained the pion gluon generated mass level as 129
MeV. These values have to be somewhat inaccurate, as
we can see that, based on the scaling of the gluon poten-
tial, the K mesons in the octet would need to have a mass
greater than 516 MeV. The K meson masses are only
around 494 MeV. Thus it is obvious that the unit strength
scale of 129 MeV is too large. Secondly, the Bohr-
Sommerfeld quantization requirement on the quark con-
stituents in the pions implies that a static model is invalid.
We will now show how these problems are removed.
According to the explicit meson-gluon potential form
Equation (4.3) in ref. [9], the gluon generated mass le
inversely proportional to the loop radius r2. In paper
[10], we showed via Bohr-Sommerfeld quantization that
, and
is the unit quark rest mass.
he constituent relativistically indep
generated mass level p
the corrected mass level becomes
where m
Let tendent gluon
er unit m factor be proportional to
M0, then
22 2
The bare quark relativistic mass m' is given by
Hence the meson mass M is given by
 (3.4)
Let us now consider the ma
e neutral pion s
< 1. If we denote the relativistic f
smC C
Since the left hand side is positive, hence if 0
ss splitting between the
arged pion and the neutral pion.
For the charged pion s = 1, while for th
actor for the charged
ons as C, and that of the neutral pions as C', it is obvi-
ous from Lenz’s Law that we must have C' > C > 1.
With these formulas, we obtain the mass difference
2424 24
dπcharge neutralMM M
 
01 1
0 term as long as C2 > C'2s2, and the coefficient for the M
is very small, then there exist a consistent solution.
It is this requirement that guarantees the simultaneous
gang uge and Bohr-Sommerfeld constraint thus givi
2222 2
1 1sCCC C
 (3.6)
Under this equality the pion mass difference given by
Equation (3.5), reduces to
222 2
22 2
The unit gluon potential induced mass is, therefore
dK 1MmC
f 120 MeV instead of the 129
MeV as given by the static model whic
Bohr-Sommerfeld quantization, as well
For tuhe K mesons, its gluon indced mass level is 4
d the mass splitting is
Hence, from the pions, combined with the K masses
we obtain the mass level o
h does not obey
as mC and d, d'.
ote m is not fixed by the quantization, as long as it is a
constant, in agreement with the 5D homogeneous space-
time P1 projection mathematical requirement [9].
It should be pointed out that this lower gluon mass
level unit of 120 MeV will eliminate the K meson mass
problem we pointed out for the static model above. The
pion mass difference is then purely dictated by d and
making the Gell-Mann-Okubo mass formula valid, ex-
actly in the same manner as that between the neutron and
proton masses as we have discussed in paper [10]. With
the new scale factor for the mass levels, we now adjust
the meson SU(3) mass levels diagrams as shown in Fig-
ures 1(a) and (b).
It should be noted that there are no more inconsisten-
cies with all the remaining mesons within the two known
Copyright © 2012 SciRes. JMP
(a) (b)
Figure 1. Consistent meson SU(3) mass level diagrams.
octets. As for the very heavy mesons, such as the J/Ψ and
the Ys, whic [10], their re-
sp -
vel is 2880 MeV instead of the mass of J/Ψ,
ref. [9] and ref. [10]
h we have discussed in paper
ective gluon generated mass levels must also be ad
The J/Ψ gluon potential strength factor is obtained
from the residual terms in the jet sum rule terms. We
showed in paper [9], that it is 2(2/9)2 + (4/9)2. Hence its
mass le
hich is 3096 MeV. Therefore, it means the constituent
quark contribution to the mass is 216 MeV, a clear indi-
cation that the relativistic factor C is very large. The two
Y mesons of 9460 MeV and 4140 MeV were assumed to
be generated by the (qqqq) intermediate quark currents.
In fact, other earlier discovered heavy mesons, such as
the D, and B particles have been speculated as given by
SU(6) representations [5]. In our model, we believe that
the (qqqq) currents can be approximated as the direct
product between two (qq) currents. Since Y(4140) was
observed to decay into J/Ψ(3096) and φ(1056), we can
formulate the gluon potential strength factor as {2(2/9)2 +
(4/9)2} × (9/9)2 + {3(2/9)2} × (9/9)2 such that the decay
would conserve mass. Under this representation, we ob-
tain the unit strength from the 4140 MeV upper bound of
1.419 MeV. Hence in order to be able to include the bare
quark constituents’ contribution to the Y mass, we reduce
the unit strength mass correspondence to 1.41 MeV and
obtain the quark mass term as 38 MeV. This modest con-
tribution from the quark constituents makes this meson
reasonably stable. The very heavy Y(9460) can only be
generated by all the (qqqq) current terms, or (9/9)2(9/9)2.
Hence its gluon mass level is 9251 MeV and the quark
constituents are at 109 MeV. A detailed analysis of the D
and B masses could further improve the estimation on the
per unit strength mass correspondence. But it is clear that
these quark potentials do not imply that the heavy mes-
ons satisfy a SU(6) representation.
Following the simultaneous gauge and Bohr-Som-
merfeld constraint analysis, by changing the r depend-
ence of the gluon potential, the baryon-gluon potentials
unit strength scale that was given in
ve to be reduced, as the baryon-gluon potential falls
off as r3. Therefore the proton, neutron mass level is
given by
1.5 1.5
323 2
 
 
where s(p) = 5/3, s(n) = 4/3 and C, C' are the proton
quarks and neutron quarks relativistic factors, respec
tively. 0
is the C, s independent factor of the glu
generated mass. It should be noted that the b
n requirement.
mbda particle at the center, as
masses do not fix the bare quark unit mass m, similar to
the mesons. Hence as long as m is a constant the theory is
consistent. This conclusion has physical implication in
that m is like e and h, a universal constant of the 5D ho-
mogeneous space-time projection theory.
It was found experimentally that the quark constituent
in the proton contributed 11 MeV to its mass [11,12],
instead of the static model’s 4 MeV, which is a direct
proof to the Bohr-Sommerfeld quantizatio
ased on this, we already know that the gluon potential
induced mass has to be less than 934 MeV provided by
the static model. In order to get the 11 MeV contribution
from the quark mass, we find that the gluon induced
mass level is 927.26 MeV. With this value we then de-
duced that the unit scale (1/27) for the gluon strength is
equivalent close to the value of 44.19 MeV replacing the
value of 44.5 MeV obtained from the static model for the
eigenvalue of the gluon repulsive potential [9]. This
change might seem small, but is sufficient to eliminate
some mass inconsistencies of certain baryons. The ad-
justed mass levels shown in Figure 2 of ref. [10] are
re-illustrated in Figure 2.
It is interesting to observe that the mass level for the
Σ(Sigmas) in the octet representation is reduced from
1115 MeV to 1105 MeV. This is clearly important for the
mass consistency of the La
actual mass is only 1115.6 MeV and therefore can not
be consistent with a mass level of 1115 MeV, because
the quark constituents contribution will always be greater
than 0.6 MeV. A similar inconsistency mass problem
arises for the Σ(Sigmas) in the decuplet, without the re-
duction of the unit gluon mass scale.
The possible degenerate missing octet of heavy bary-
ons can be analyzed as follows:
In order that this missing octet is nearly degenerate,
(a) (b)
Figure 2. Self consistent baryon mass levels in the octet (a)
and the decuplet (b).
Copyright © 2012 SciRes. JMP
K. W. WONG ET AL. 1455
the three mass levels must be the same. From the sum
rule, we obtained the remaining strength factors:
This factor must be split into 3 identical levels plus 1
singlet value, and maintaining the sum rule:
Hence, we can rewrite these levels as
Singlet. 23BD
such that
827 2127C
4227 127Dabc
where a, b, c are integers, such that 2B > 3D.
e seen that there is a wide range of choices.
For minimum, it w mean D = 0.
For this case the total mass strength of the missing oc-
tet is
It could b
oul d
producing a mass equivalent of
44.19 MeV, a pair of all the octet baryons will have a
mass energy [A jet that balances momentumbut in-
der to get from E = 94.74 to
ute a facto 42 to 43. To get
that, we can have a = 2, b = 2, c = 2, or c = 3. Which
stituents contribu-
tion, it can only account for a small correction, no more
than the (1/27)2 factor would. Hence we will choose
In terms of (1/27)2
cludes all the octet particles in pairs]:
27 , 244.198EABCD  
244.19278EABC  or 2 × 44.19 ×
8 × 134 = 94.74 GeV In or
125 GeV, D has to contribr of
eans D has a strength factor equivalent of 2(16 + 4 + 1),
or 2(16 + 4) + 3 × 1. This estimation did not account for
the inter-level mass splittings. However, due to the
smaller values from the bare quark con
427227 127abc
. This jet produc-
tion, although having an energy similar in value as the 2
photons emission detected in the CERN experiment, is
not the same process. In fact, the choice of a = b = c = 2
produces 2B < 3D, which violates the rule that no baryon
can have negative mass! To Adjust that, we can choose
a = 2, b = 1, c = 0 for example. It is instructive to rewrite
the singlet and octet masses, due to this choice of the
gluon strength factors. We get for the singlet:
 
222 2
32 427227127
32 276 127
282734 2752 2732 27.
  
This factor contains all the 4 distinct strength factors,
while the degenerate octet levels are given by:
23282722 27BD 
 
 
 
82721272 4272227
4 278 2722ABCD
 
 
 
 
 
which involves all 4 strength factor terms, (8/27)2,
(4/27)2, (2/27)2 and (1/27)2.
It is easy to estimate the singlet mass. We have
44.19 6426161041244.194
 or 176.8
MeV. While the octet levels will give a total 2 octet ba-
ryon mass of 44.19 × 2 × 8 × 170 MeV or 118 GeV. It
should be pointed out, that by changing D slightly, we
can get to 2B being nearly equal to 3D, and such a singlet
could be mistaken as a heavy lepton? While the dege
ate octet jet will have a resonance at 120 GeV, but can
never reach the 125 GeV value.
modynamics that is valid for mesons, and per
The fact that the well known octet and decuplet only
contain the three strength factors (4/27)2, (2/27)2 an
(1/ 2
27) , allows one to develop a theory based on chro-
haps might
be the reason why we had difficulty identifying this de-
generate remaining octet and the singlet experimentally,
as the factor (8/27)2 is unique to these baryon states only.
Of course, it is totally possible that this missing octet is
not degenerate, then the experimental resonance around
120 GeV has no relationship to the missing octet.
In conclusion, we have shown that the relativistic mass
corrections to the quark constituents due to the require-
ment of the simultaneous gauge and Bohr-Sommerfeld
quantization are of vital importance to the proper deter-
mination of the gluon potentials generated mass levels in
the SU(3) representations of hadrons, and it is not just for
the lesser mass splitting between particles within the
same mass level.
4. Comments on the Observed 125 GeV Two
Photon Emission State from the p-p
Scattering Experiment
Recently physicists celebrated the finding of a 2 photons
emission state at 125 GeV obtained from the direct p-p
scattering in the CERN Large Hadron Collider, as a pos-
sible verification of the existence of a Higgs Boson [1,2].
In this note, we would like to point out that there are al-
Copyright © 2012 SciRes. JMP
ternative possibilities to explain this result without in-
voking the presence of a Higgs field.
It is well recognized that the proton, a composite of 2u
ba the
ga composite mass is fur-
ass as discussed previously. It was found that
the SU(3) representations for the mesons and baryons
ass levels within each representations
e gluon fields strength factors which
rgy region,
stant, like
and 1d quarks, derives its mass from two factors: 1) The
re masses of the 2u and 1d quarks, held together by
uge confinement. 2) This final
ther significantly modified by the gluon fields acting
between the quarks. The gluon fields are obviously of
short range and might or might not be repulsive. Should
they be repulsive, then they contribute to increasing the
proton mass above the sum of the bare quark masses. In
the p-p collision experiment, if an intermediate hadron
state is formed, then it must consist of 4u and 2d quarks.
This composite carries a net charge of 2e. Hence the
gauge transformation will give a quantum flux of h/2e,
instead of h/e. This state actually could be viewed as a
complex Cooper pair state. Because of the reduction of
the quantum flux by 1/2, it is possible that it also reduces
the 2p-hadron size r by 1/2. Hence if the gluon fields are
repulsive, and vary as (1/r)n, then it would follow that the
resultant mass contribution from them would increase by
the order 2 × (2)n. For n = 6, we would expect this state
to have a mass 128 times that of the proton. Of course
that would give the observed 125 GeV resonance. This
argument is only a possibility, but is there a theory to
prove that n = 6 is in fact the size dependence of the
gluon field for the 2p state? In the next paragraph, we
shall use the 5D projection model theory [9,10] to show
that this is exactly the case, and hence the 125 GeV 2
photons emission is totally predictable.
According to the 5D projection theory, the gluon field
is the result from the vector potentials generated by the
intermediate quark currents. Thus for the proton, it comes
from the product of three vector potentials (see Equa-
tiona (4.25) and (4.26) of ref. [9]). Therefore the gluon
field r dependence in the proton is (1/r)3. Because the p-p
Cooper pair Boson state contains 6 quarks instead of 3,
the gluon field then generated by its intermediate quark
state currents must also vary as (1/r)6. Thus if the argu-
ment holds that r is reduced by 1/2 as compared to the
proton size, than it is clear that a resonance of the order
of 125 GeV, that would decay into 2 photons, is expected,
since the rest mass of the proton is close to 1 GeV. We
mentioned earlier that gauge confinement of the quarks
suggests that the value of r in the 2p Cooper state can be
1/2 that of the proton. However, gauge transformation is
dependent on the imposed vector potential to define the
loop integral, yet we have no idea what proper vector
potential is involved within these hadrons in question,
except we do know that it must be generated by the u and
d quarks motion within these hadrons. Therefore, instead
of looking at the charge currents, we look at the angular
momenta from the bare masses of the u and d quark con-
stituents. As was shown in [9], these angular momenta
must also obey Bohr-Sommerfeld quantization. Hence,
by simply comparing the ground state, the fact that the 2p
state contains quarks that is twice as massive as those in
the p state, it is clear that r of the 2p state is 1/2 of that of
the proton. Of course other modifications also play a
minor corrective role. For example, the velocity of the
quarks within these two hadronic states might be slightly
different, etc. None-the-less, it is clear that the 5D pro-
jection theory would have predicted such a 125 GeV 2
photon emission, hence its interpretation as an indication
of the existence of a Higgs field is suggested to be pre-
5. Conclusions
Although we have only presented the basic points through
the projection operations on the 5D homogeneous space-
time manifold we have shown that we not only can get the
standard model, where quarks have mass, but the explicit
formulation of the gluon fields and through them the ac-
tual values for the meson and baryon masses.
In fact, the gluon fields together with quantum gauge
constraint are responsible for the major portion of the
hadron m
together with the m
are generated by th
form their respective Lorentz jet sum rules. Furthermore,
we deduce from the meson jet sum rule the remaining
mesons, the J/Ψ particle with the exact mass of 3096
MeV, and the Y particles with mass 9460 MeV and 4140
MeV. For the baryons, there might be the not yet found
octet with mass levels in the 5 to 8 GeV ene
ith mass levels may be also in the GeV range, far high-
er than those in the known octet and decuplet.
In conclusion, it was found that the simultaneous
gauge and Bohr-Sommerfeld quantization on the quark
constituents in hadrons is shown explicitly affecting the
gluon potential induced mass levels in the SU(3) repre-
sentations, as well as the fine mass structure splittings
within each mass level, based on the 5D homogeneous
space-time projection theory [9]. It was also shown that
violating this constraint could lead to inconsistencies
with the actual masses of the hadrons. Furthermore, the
analysis of the hadron masses leads to the suggestion that
the unit quark mass “m” from the 5D homogeneous
space-time projection theory is a universal con
and h.
We like to emphasize that not only the representations
and individual masses of the known hadrons can be nu-
merically deduced from the 5D homogeneous space-time
projection model for the establishment of the standard
model, but it actually predicts the oscillation of the neu-
trino, and the finding of a 125 GeV 2 photon emission
Copyright © 2012 SciRes. JMP
Copyright © 2012 SciRes. JMP
state created by the p-p collision CERN experiment,
without any necessity of introducing a condensed Higgs
Boson vacuum state for the universe. In fact for the 5D
theory, matter will never totally revert to pure mass-less
energy fields, as there is no vacuum phase transition ever
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