Paper Menu >>

Journal Menu >>

Journal of Modern Physics, 2013, 4, 21-26
http://dx.doi.org/10.4236/jmp.2013.44A004 Published Online April 2013 (http://www.scirp.org/journal/jmp)
The Higgs Boson in the Periodic System of
Elementary Particles
Ding-Yu Chung1, Ray Hefferlin2
1Utica, Michigan, USA
2Department of Physics, Southern Adventist University, Collegedale, USA
Email: [email protected], [email protected]
Received February 12, 2013; revised March 15, 2013; accepted March 27, 2013
Copyright © 2013 Ding-Yu Chung, Ray Hefferlin. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
It is proposed that the observed Higgs Boson at the LHC is the Standard Model Higgs boson that adopts the existence of
the hidden lepton condensate. The hidden lepton is in the forbidden lepton family, outside of the three lepton families of the
Standard Model. Being forbidden, a single hidden lepton cannot exist alone; so it must exist in the lepton condensate as a
composite of μ’ and μ’± hidden leptons and their corresponding antileptons. The calculated average mass of the hidden lep-
ton condensate is 128.8 GeV in good agreements with the observed 125 or 126 GeV. The masses of the hidden lepton con-
densate and all elementary particles including leptons, quarks, and gauge bosons are derived from the periodic system of
elementary particles. The calculated constituent masses are in good agreement with the observed values by using only four
known constants: the number of the extra spatial dimensions in the eleven-dimensional membrane, the mass of electron, the
mass of Z boson, and the fine structure constant.
Keywords: Higgs Boson; Periodic System; Elementary Particles
1. Introduction
As described in “In Molecular Taxonomy: String, quark,
hadron, nuclear, atomic and chemical molecule periodic
or invariant systems” [1], chemists and physicists have
accumulated vast libraries of data about the properties
and atoms and molecules via the simplest to the most
complex experiments; from Bohr to Schrödinger theory;
and using back-of-the-envelope to supercomputer com-
putation. Much of it is distilled into the periodic chart of
the elements and models about the various molecular
bonds. Though starting more recently, scientists have
garnered as many or more numbers describing character-
istics of nuclei, the essence of which is seen in the chart
of the isotopes. Still more recently, the simplest funda-
mental particle properties have been epitomized in the
geometric patterns showing hadrons and their quark con-
stituents. And now even string theory has produced a
periodic system, such as the periodic system of elemen-
tary particles [2,3].
At the LHC (Large Hadron Collider), the ATLAS and
CMS experiments of CERN experiments observe a new
particle in the mass region around 125 - 126 GeV with a
high degree of certainty, and the decay modes and the
spin of the new particle point to the Standard Model
Higgs boson [4,5].
In this paper, the periodic system of elementary parti-
cles based on string theory is used to describe the newly
discovered Higgs boson at the LHC, and the calculated
mass from this periodic system of elementary particles is
in good agreement with the observed value.
2. The Periodic System of Elementary
Particles
The periodic system of elementary particles is based on
the “überparticles” of our universe. An überparticle con-
sists of two four dimensional particles each with its own
set of seven “dimensional orbitals”. The seven dimen-
sional orbitals represent originally [6] the seven extra
spatial dimensions in the eleven dimensional membrane
of string theory.
In an überparticle, one four dimensional particle has
the seven “principal dimensional orbitals”, while the
other four dimensional particle has the seven “auxiliary
dimensional orbitals” that are superimposed on the seven
principal dimensional orbitals. In an überparticle, the
auxiliary orbitals are dependent on the principal orbitals,
so only one set of dimensional orbitals appears. The
principal dimensional orbitals are mainly for leptons and
C
opyright © 2013 SciRes. JMP
D.-Y. CHUNG, R. HEFFERLIN
22
gauge bosons, and the auxiliary dimensional orbitals are
mainly for individual quarks. Because of the dependence
of the auxiliary dimensional orbitals, individual quarks
are hidden. The configuration of dimensional orbitals and
the periodic system of elementary particles are shown in
Figure 1 and Table 1.
Figure 1 shows leptons and quarks. The symbols of
the top row represent leptons and their components.
e, e,
μ, and
are on the principal dimensional orbitals, 5, 6,
7, and 8, respectively. Other leptons (
, τ, and
quarks appear on and higher than d = 9, which is outside
of the Standard Model and the seven auxiliary dimen-
sional orbitals. f9 and f10 are the principal fermions on d =
9 and 10, respectively. The gauge bosons are not shown,
and can be located on the top row at principal dimen-
sional orbitals as shown in Table 1.
) are
the composites of both the principal components (e and
)
and auxiliary components (
7,
7 and
8) as shown in
Table 2. The symbols below the numbers are the princi-
pal and auxiliary components of quarks. All quarks are
the composites of both principal components (u5, d6,
,
and
') and auxiliary components (u7, d7, s7, c7, b7, t7, b8,
and t8) as shown in Table 2. The seven auxiliary dimen-
sional orbitals can accommodate only three families of
lepton-quark as in the Standard Model. No leptons and
Figure 1. The überparticle represented by leptons and
quarks in the seven principal dimensional orbitals (solid
lines) denoted by the principal dimensional orbital number
d and the seven auxiliary dimensional orbitals (dash-dotted
lines) denoted by the auxiliary dimensional number a.
Table 1. The überparticle represented by the periodic system of elementary particles d = principal dimensional orbital num-
ber, a = auxiliary dimensional orbital number.
d a = 0 1 2 a = 0 1 2 3 4 5
Lepton Quark Boson
5 l5 =
e q5 = u5 B5 = A
6 l6 = e q6 = d6
B6 = 12
π
0
7 l7 =
7
7 q7 =
u7/d7 s7 c7 b7 t7 B7 =
L
Z
8 l8 =
8 q8 =
' (hidden) b8 (hidden) t8 B8 = XR
9 f9 B9 = XL
10 f10
B10 = 0
R
Z
11 B11
Table 2. The compositions and the constituent masses of leptons and quarks d = principal dimensional orbital number and a
= auxiliary dimensional orbital number.
da Composition Calculated Mass
Leptons dafor leptons
e 50
e ≈0
e 60 e 0.51 MeV(given)
70
≈0
80
≈0
60 + 70 + 71 e +
+
7 105.6 MeV
60 + 70 + 72 e +
+
7 1786 MeV
60 + 70 + 72 + 80 + 81 e +
+
7 +
+
8 (3/2 Z°) 136.9 GeV
1
8
8
60 + 70 + 72 + 80 + e +
+
7 +
+
(3/2 W± ) 120.7 GeV
Quarks da for quarks
u 50 + 70 + 71 q5 + q7 + u7 330.8 MeV
d 60 + 70 + 71 q6 + q7 + d7 332.3 MeV
s 60 + 70 + 72 q6 + q7 + s7 558 MeV
c 50 + 70 + 73 q5 + q7 + c7 1701 MeV
b 60 + 70 + 74 q6 + q7 + b7 5318 MeV
t 50 + 70 + 75 + 80 + 82 q5 + q7 + t7 + q8 + t8 176.5 GeV
Copyright © 2013 SciRes. JMP
D.-Y. CHUNG, R. HEFFERLIN 23
Table 1 shows leptons, quarks, and gauge bosons. For
leptons, the leptons at a = 0 are the principal leptons (
e,
e,
μ, and
). Other leptons (
, τ, and
) are the com-
posites of both the principal components (e and
at a = 0)
and auxiliary components (
7,
7 and
8 at a > 0) as
shown in Table 2. All quarks are the composites of both
principal components (u5, d6,
, and
at a = 0) and
auxiliary components (u7, d7, s7, c7, b7, t7, b8, and t8 at a >
0) as shown in Table 2. Outside of the Standard Model,
,,,
,
dB dB
MM
is hidden, and is balanced by the hidden b8. No lep-
tons and quarks appear on and higher than d = 9, which is
outside of the Standard Model and the seven auxiliary
dimensional orbitals. The bosons, B5, B6, B7, B8, B9, B10,
and B11 are shown in Table 3.
The principal dimensional orbitals are for gauge bos-
ons of the force fields, as shown in Table 1. It will be
shown shortly that Fd has lower energy than Bd. and simi-
larly the seven principal dimensional orbitals are ar-
ranged as F5 B5 F6 B6 F7 B7 F8 B8 F9 B9 F10 B10 F11 B11,
where B and F are the boson and fermion in each orbital.
In previous communications [3] we have shown that the
masses of fundamental particles are related to each other
with three simple formulae, and that the use of accepted
mass data allows calculation of masses of many other
particles. The formulae are
dF
,, ,
dF dF
MM
(1a)
1,d B
2
1, ,
dB dBd
MM
(1b)
, (1c)
where d is the dimensional orbital number from 6 to 11.
E5,B and E11,B are the energies for the 5d dimensional or-
bital and the 11d dimensional orbital, respectively. Each
dimension has its own
d, and all d
s except
7 (
w) of
the seventh dimension (weak interaction) are equal to
,
the fine structure constant of electromagnetism. The
lowest energy boson is the Coulombic field for electro-
magnetism and the second lowest boson energy is 12
(a spin 1 boson as a half of the spin 0 pion) for the strong
interaction.
π
5, 6,
M
B
Fe
MM. (2a)
2
6, 5,π2
BB e
MMM M

 (2b)
The bosons generated in this manner are the dimen-
sional orbital bosons or BD as shown in Table 3.
In Table 3,
=
e (the fine structure constant for elec-
tromagnetic field), cos
Z
ww
M
Mq 2
sin q
, and ww
19
1. 110G eV
19
2 10GeV
[7].
w is not same as
e because there is a mixing be-
tween B5 and B7 as the symmetry mixing between U(1)
and SU(2) in the standard theory of the electroweak in-
teraction, and sin
w is not equal to 1. The calculated
value for
w is 0.02973, and sin2
w is 0.2454 in good
agreement with 0.2312 for the observed value of sin2
w
[8]. The calculated energy for B11 is in
good agreement with the Planck mass, 1. .
The strong interaction, represented by 12 (half of a
pion), is for the interactions among quarks and for the
hiding of individual quarks in auxiliary orbitals. The
weak interaction, represented by
π
0
L
Z
, is for the interac-
tion involving changing flavors among quarks and lep-
tons. The auxiliary dimensional orbitals are derived from
principal dimensional orbitals. They are for high-mass
leptons and individual quarks.
All leptons and quarks with d’s, a’s and the calculated
masses are listed in Table 2 as discussed in Ref. [3]
Table 2 shows the compositions of leptons and quarks.
Each fermion can be defined by principal dimensional
orbital numbers (d’s) and auxiliary dimensional orbital
numbers (a’s). For examples, e is 60 that means it has d
(principal dimensional orbital number) = 6 and a (auxil-
iary dimensional orbital number) = 0, so e is a principal
dimensional fermion. All neutrinos are nearly massless
because of chiral symmetry (permanent chiral symmetry).
As shown in Table 2,
and
are the hidden (for-
bidden) leptons outside of the three lepton families in the
Standard Model. All elementary particles (gauge bosons,
leptons, and quarks) are in the periodic system of ele-
mentary particles with the calculated constituent masses
in good agreement with the observed values [9,10] by
using only four known constants: the number of the extra
Table 3. The Masses of the dimensional orbital gauge bosons:
=
e, d = dimensional orbital number.
Bd Md GeV (calculated) Gauge boson Interaction
B5 Me
6
3.7 10
A = photon Electromagnetic
B6 Me/
2
710
12
π
2
w
Strong
B7 M6/
cos
w 91.177 (given) 0
L
Z
weak (left)
B8 M7/
2 6
1. 710
10
3.210
14
6.0 100
XR CP (right) nonconservation
B9 M8/
2 XL CP (left) nonconservation
B10 M9/
2
R
Z
weak (right)
B11 M10/19
1. 110 G Gravity
2
Copyright © 2013 SciRes. JMP
D.-Y. CHUNG, R. HEFFERLIN
24
ensions in thdimensional membrane, spatial dime eleven-
8
00201
78
3
2
67788
W
e

the mass of electron, the mass of Z boson, and the fine
structure constant. For an example, the calculated mass
of top quark is 176.5 GeV in good agreement with the
observed 173.5 GeV [11].
3. The Observed Higgs Boson
We propose that the observed Higgs boson is the Stan-
dard Model Higgs boson that adopts the existence of the
hidden lepton condensate. We describes the hidden lep-
ton condensate first, and the adoption of the hidden lep-
ton condensate later. The hidden lepton condensate is
similar to the top quark condensate. The top quark con-
densate is a composite field composed of the top quark
and its antiquark. The top quark condenses with its meas-
ured mass (173 GeV) comparable to the mass of the W
and Z Bosons, so Vladimir Miransky, Masaharu Tana-
bashi, and Koichi Yamawaki [12] proposed that the top
quark condensate is responsible for the mass of the W
and Z bosons. The top quark condensate is analogous to
Cooper pairs in a BCS superconductor and nucleons in
the Nambu-Jona-Lasinio model [13]. Anna Hasenfratz
and Peter Hasenfratz et al. [14] claimed that the top
quark condensate is approximately equivalent to a Higgs
scalar field. S. F. King proposed a tau lepton condensate
to feed the tau mass to the muon and the electron [15,16].
By analogy to the top quark condensate, the hidden
lepton condensate is a field composed of the hidden lep-
tons and antileptons ,,


, and
as shown in
Table 2. Just as the observed top quark is a bare quark
with the observed mass of about 173 GeV instead of
about 346 GeV for top quark-antitop quark, the observed
hidden lepton is a bare average hidden lepton instead of
,

and,


.However, unlike the top quark con-
densate, the hidden lepton condensate is outside of the
standard three lepton-quark families in the Standard
Model. Being forbidden, a single hidden lepton cannot
exist alone, so the hidden leptons must exist in the lepton
condensate as the composite of the leptons-antileptons
,,


, and
.
To match l8 (
) at d = 8, quarks include qat d = 8 as a
8
part of the t quark. In the same way that q7 = 3 , q8 in-
volves
.
is the sum of e,
, and
8 (auxiliary di-
mensional leptons). Using Equation (14) of Ref. [3], the
mass of
8 equals to 3/2 of the mass of B7, which is Z0,
and the mass of 8
equals to 3/2 of the mass of 7
B
,
which is W±. From these we can calculate the masses of
and
.
0
8
00
3
2
67
Z
e
201
78
788

 

 


 



 
The calculated masses of the hidden lepton are 120.7
GeV (for the mass of
) and 136.9 GeV (for the mass
of
) with the average as 128.8 GeV for the hidden
lepton condensate, in good agreements with the results
from LHC (125 GeV or 126 GeV).
It is proposed that the Higgs scalar boson itself is a vir-
tual zero-energy scalar boson without permanent energy
to
ct
on
the electroweak in-
te
s, and gauge bosons, in the elec-
tro
in the form of another life.
Th
avoid the cosmological constant problem from the
huge gravitational effeby the non-zero-energy Higgs
bos [17]. Without permanent energy, the Higgs boson
emerges and disappears by borrowing energy from and
returning energy to the particles in
raction, respectively. The returning of energy from the
Higgs scalar boson to the particles is through the absorp-
tion of the Higgs scalar boson by the particles. When a
massless particle in the electroweak interaction absorbs
the Higgs scalar boson, the Higgs scalar boson becomes
the longitudinal component of the massless particle, re-
sulting in the massive particle and the disappearance of
the Higgs scalar boson.
The observed Higgs boson at the LHC is a remnant of
the Higgs boson. At the beginning of the universe, all
particles in the electroweak interaction were massless.
The Higgs boson appeared by borrowing energy sym-
metrically from all particles in the electroweak interac-
tion. The Higgs boson coupled with all massless particles,
including leptons, quark
weak interaction. All massless particles except photon
as the gauge boson for electromagnetism absorbed the
Higgs boson as their longitudinal components to become
massive particles. The asymmetrical returning of energy
from the Higgs boson by the absorption of the Higgs
boson is called the symmetrical breaking of the elec-
troweak interaction in the Standard Model. In the cases
of such massive particles, including leptons, quarks, and
weak gauge bosons, the Higgs boson disappeared. In the
case of massless photon as the gauge boson of electro-
magnetism, the un-absorbed Higgs boson became the
remnant of the Higgs boson.
Being specific to the electroweak interaction, the rem-
nant of the Higgs boson could not return the borrowed
energy to any other massless particles, so it adopted the
existence of another scalar boson, and returned the pure
borrowed energy without the longitudinal component to
photon. Essentially, the remnant of the Higgs boson be-
came an avatar as a life born
e remnant of the Higgs boson could not adopt the ex-
istence of any scalar boson that already represented an
independent elementary particle. The only available sca-
Copyright © 2013 SciRes. JMP
D.-Y. CHUNG, R. HEFFERLIN 25
lar boson came from the scalar hidden lepton conden-
sate. Consequently, the remnant of the Higgs boson as
the Standard Model Higgs boson adopted the existence
of the hidden lepton condensate, and became the Avatar
Higgs boson.
The two possibilities for the Standard Model Higgs
boson that adopts the hidden lepton condensate are the
pure Standard Model Higgs boson and the dual particle
consisting of the Standard Model Higgs boson and the
non-Standard Model hidden lepton condensate. The de-
cay of the pure Standard Model Higgs boson follows the
decay modes of the Standard Model.
vidence for th
ce
Being outside of the Standard Model of the elec-
troweak interaction, the hidden lepton condensate cannot
decay into the particles in the electroweak interaction,
and decay into diphoton via the internal annihilation of-
particle-antiparticle. As a result, the decay of the dual
particle generates excess diphoton deviated from the
Standard Model. The experimental ee ex-
ss diphoton is inconclusive [18-20].
4. Summary
It is proposed that all elementary particles including lep-
tons, quarks, and gauge bosons can be placed in the pe-
riodic system of elementary particles. The periodicity is
derived from the two sets of seven mass orbitals where
seven comes from the seven extra dimensions in the
al membrane in the string theory. The
uent masses are in good agreement with
gi
of
ensate as a composite of
eleven-dimension
calculated constit
the observed values by using only four known constants:
the number of the extra spatial dimensions in the
eleven-dimensional membrane, the mass of electron, the
mass of Z boson, and the fine structure constant.
It is proposed that the Higgs boson itself is a virtual
zero-energy gauge boson by borrowing energy from and
returning energy to the particles in the electroweak in-
teraction. When a massless particle in the electroweak
interaction absorbs the Higgs boson, the Higgs boson
becomes the longitudinal component of the massless par-
ticle, resulting in the massive particle. At the benning
the universe, all particles in the electroweak interac-
tion were massless. The symmetrical borrowing of en-
ergy from the particles and the asymmetrical returning of
energy by the absorption of the Higgs boson resulted in
the asymmetrical breaking of electroweak interaction and
the remnant of the Higgs boson from the absence of the
absorption of the Higgs boson by photon. The remnant of
the Higgs boson adopted the existence of the scalar hid-
den lepton condensate and returned the borrowed energy
to photon.
The observed Higgs Boson at the LHC is the Standard
Model Higgs boson that adopts the existence of the hid-
den lepton condensate. The hidden lepton is in the for-
bidden lepton family, outside of the three lepton fami-
lies of the Standard Model. Being forbidden, a single
hidden lepton cannot exist alone; so it must exist in the
lepton cond
and
hid-
de
lar Taxonomy: String, Quark, Had-
ron, Nuclear, Atomic and Chemical Molecule Periodic or
Invariant Systemic Publish-
ing, Section 7, 2
/papers/0111/0111147.pdf
ger, et al., (Particle Data Group), “Electroweak
-rev-top-quark.pd
, No. 11, 1989, pp. 1043-
n leptons and their corresponding antileptons. The
calculated average mass of the hidden lepton condensate
is 128.8 GeV in good agreements with the observed 125
or 126 GeV.
REFERENCES
[1] R. Hefferlin, “Molecular Taxonomy: String, Quark, Had-
ron, Nuclear, Atomic and Chemical Molecule Periodic or
Invariant Systems,” LAP LAMBERT Academic Publish-
ing, Saarbrücken, 2011.
[2] R. Hefferlin, “Molecu
ems,” LAP LAMBERT Acad
011. pp. 35-38
[3] D. Chung, “The Periodic System of Elementary Particles
and the Composition of Hadrons,” Speculations in Sci-
ence and Technology, Vol. 20, 1997, pp. 259-268
http://arxiv.org/ftp/hep-th
[4] The ATLAS Collaboration, “Observation of a New Parti-
cle in the Search for the Standard Model Higgs Boson
with the ATLAS Detector at the LHC,” 2012.
arXiv:1207.7235v1[hep-ex]
[5] The CMS Collaboration, “Observation of a New Boson at
a Mass of 125 GeV with the CMS Experiment at the
LHC,” 2012. arXiv:1207.7235v1[hep-ex]
[6] D. Chung and V. Krasnoholovets, “The Cosmic Organ-
ism Theory,” Scientific Inquiry, Vol. 8, 2007, pp. 165-182.
http://www.iigss.net/Scientific-Inquiry/Dec07/3-krasnoho
lovets.pdf
[7] A. Salam, “Weak and Electromagnetic Interactions,” In:
W. Svartholm, Ed., Elementary Particle Theory, Alm-
quist and Wiksell, Stockholm, 1968, pp. 367-387.
[8] J. Beringe, et al., (Particle Data Group), “Electroweak
Model and Constraints on New Physics,” Physical Re-
view D, Vol. 86, 2012, Article ID: 010001.
http://pdg.lbl.gov/2012/reviews/rpp2012-rev-standard-mo
del.pdf
[9] D. Griffiths, “Introduction to Elementary Particles,”
WILEY-VCH, Hoboken, 2008, p. 135
[10] M. H. MacGregor, “Electron Generation of Leptons and
Hadrons with Conjugate α-Quantized Lifetimes and
Masses,” International Journal of Modern Physics A, Vol.
20, No. 4, 2005, pp. 719-798.
[11] J. Berin
Model and Constraints on New Physics,” Physical Re-
view D, Vol. 86, 2012, Article ID: 010001.
http://pdg.lbl.gov/2012/reviews/rpp2012
f
[12] V. A. Miransky, M. Tanabashi and K. Yamawaki, “Is the
t Quark Responsible for the Mass of W and Z Bosons,”
Modern Physics Letter A, Vol. 4
1063. doi:10.1142/S0217732389001210
Copyright © 2013 SciRes. JMP
D.-Y. CHUNG, R. HEFFERLIN
Copyright © 2013 SciRes. JMP
26
with Supe
. 246-254. doi:10.1103/PhysRev.124.246
[13] Y. Nambu and G. Jona-Lasinio, “Dynamical Model of
Elementary Particles Based on an Analogy
conductivity, II,” Physical Review, Vol. 124, No. 1, 1961,
pp
r-
[14] A. Hasenfratz, P. Hasenfratz, K. Jansen, J. Kuti and Y.
Shen, “The Equivalence of the Top Quark Condensate
and the Elementary Higgs Field,” Nuclear Physics B, Vol.
365, No. 1, 1991, pp. 79-97.
doi:10.1016/0550-3213(91)90607-Y
[15] S. F. King, “Four-Family Lepton Mixing,” Physical Re-
view D, Vol. 46, 1992, pp. 4804-4807.
[16] S. F. King, “Low Scale Technicolour at LEP,” Physics
Letter B, Vol. 314, No. 3-4, 1993, pp. 364-370.
doi:10.1016/0370-2693(93)91250-Q
[17] S. Weinberg, “The Cosmological Constant Problem,”
Review Modern Physics, Vol. 61, No. 1, 1989, pp. 1-23.
doi:10.1103/RevModPhys.61.1
[18] P. P. Giardino, K. Kannike, M. Raidal and A. Strumia, “Is
ations), “Search
xcess in Higgs Decays to
the Resonance at 125 GeV the Higgs Boson?” 2012.
arXiv:1207.1347v1 [hep-ph]
[19] K. R. Bland, (for the CDF, D0 Collabor
for the Higgs boson in H- > γγ Decays in $p\bar{p}$ Col-
lisions at 1.96 TeV,” 2012. arXiv:1110.1747v1[hep-ex]
[20] M. Strassler, “CMS Sees No E
Photons,” 2013.
http://profmattstrassler.com/2013/03/14/cms-sees-no-exce
ss-in-higgs-decays-to-photons/#more-5655