The Higgs Boson in the Periodic System of Elementary Particles

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Ray Hefferlin

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This Article is brought to you for free and open access by the Physics and Engineering Department at KnowledgeExchange@Southern. It has been accepted for inclusion in Faculty Works by an authorized administrator of KnowledgeExchange@Southern. For more information, please contact [email protected]. Journal of Modern Physics, 2013, 4, 21-26 doi: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 lepton condensate is 128.8 GeV in good agreements with the observed 125 or 126 GeV. The masses of the hidden lepton condensate 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 Higgs boson [4,5]. In this paper, the periodic system of elementary parti- As described in “In Molecular Taxonomy: String, quark, cles based on string theory is used to describe the newly hadron, nuclear, atomic and chemical molecule periodic discovered Higgs boson at the LHC, and the calculated or invariant systems” [1], chemists and physicists have mass from this periodic system of elementary particles is accumulated vast libraries of data about the properties in good agreement with the observed value. and atoms and molecules via the simplest to the most complex experiments; from Bohr to Schrödinger theory; 2. The Periodic System of Elementary and using back-of-the-envelope to supercomputer com- Particles putation. Much of it is distilled into the periodic chart of the elements and models about the various molecular The periodic system of elementary particles is based on bonds. Though starting more recently, scientists have the “überparticles” of our universe. An überparticle con- garnered as many or more numbers describing character- sists of two four dimensional particles each with its own istics of nuclei, the essence of which is seen in the chart set of seven “dimensional orbitals”. The seven dimen- of the isotopes. Still more recently, the simplest funda- sional orbitals represent originally [6] the seven extra mental particle properties have been epitomized in the spatial dimensions in the eleven dimensional membrane geometric patterns showing hadrons and their quark con- of string theory. stituents. And now even string theory has produced a In an überparticle, one four dimensional particle has periodic system, such as the periodic system of elemen- the seven “principal dimensional orbitals”, while the tary particles [2,3]. other four dimensional particle has the seven “auxiliary At the LHC (Large Hadron Collider), the ATLAS and dimensional orbitals” that are superimposed on the seven CMS experiments of CERN experiments observe a new principal dimensional orbitals. In an überparticle, the particle in the mass region around 125 - 126 GeV with a auxiliary orbitals are dependent on the principal orbitals, high degree of certainty, and the decay modes and the so only one set of dimensional orbitals appears. The spin of the new particle point to the Standard Model principal dimensional orbitals are mainly for leptons and

Copyright © 2013 SciRes. JMP 22 D.-Y. CHUNG, R. HEFFERLIN gauge bosons, and the auxiliary dimensional orbitals are quarks appear on and higher than d = 9, which is outside mainly for individual quarks. Because of the dependence of the Standard Model and the seven auxiliary dimen- of the auxiliary dimensional orbitals, individual quarks sional orbitals. f9 and f10 are the principal fermions on d = are hidden. The configuration of dimensional orbitals and 9 and 10, respectively. The gauge bosons are not shown, the periodic system of elementary particles are shown in and can be located on the top row at principal dimen- Figure 1 and Table 1. sional orbitals as shown in 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  ) 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 principal and auxiliary components of quarks. All quarks are the composites of both principal components (u , d , , 5 6 Figure 1. The überparticle represented by leptons and and ') and auxiliary components (u , d , s , c , b , t , b , 7 7 7 7 7 7 8 quarks in the seven principal dimensional orbitals (solid and t8) as shown in Table 2. The seven auxiliary dimen- lines) denoted by the principal dimensional orbital number sional orbitals can accommodate only three families of d and the seven auxiliary dimensional orbitals (dash-dotted lepton-quark as in the Standard Model. No leptons and lines) denoted by the auxiliary dimensional number a.

Table 1. The überparticle represented by the periodic system of elementary particles d = principal dimensional orbital number, 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 = π12

0 7 l7 =  7 7 q7 =  u7/d7 s7 c7 b7 t7 B7 = Z L

8 l8 =  8 q8 = ' (hidden) b8 (hidden) t8 B8 = XR

9 f9 B9 = XL 0 10 f10 B10 = Z R

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

   ±  60 + 70 + 72 + 80 + 81 e +  + 7 +  + 8 (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 5 + 7 + 7 + 8 + 8 q + q + t + q + t 176.5 GeV 0 0 5 0 2 5 7 7 8 8

Table 1 shows leptons, quarks, and gauge bosons. For M 5,B  M6,F Me. (2a) leptons, the leptons at a = 0 are the principal leptons (e, 2 e, μ, and ). Other leptons (, τ, and  ) are the com- MM6,BB 5,  M e Mπ 2 (2b) posites of both the principal components (e and  at a = 0) The bosons generated in this manner are the dimen- and auxiliary components ( ,  and  at a > 0) as 7 7 8 sional orbital bosons or B as shown in Table 3. shown in Table 2. All quarks are the composites of both D In Table 3,  = e (the fine structure constant for elec- principal components (u , d , , and  at a = 0) and 2 5 6 tromagnetic field), M  Mcos q, and    sin q auxiliary components (u , d , s , c , b , t , b , and t at a > Z ww ww 7 7 7 7 7 7 8 8 [7].  is not same as  because there is a mixing be- 0) as shown in Table 2. Outside of the Standard Model, w e tween B and B as the symmetry mixing between U(1)  is hidden, and is balanced by the hidden b . No lep- 5 7 8 and SU(2) in the standard theory of the electroweak in- tons and quarks appear on and higher than d = 9, which is teraction, and sinw is not equal to 1. The calculated outside of the Standard Model and the seven auxiliary 2 value for w is 0.02973, and sin w is 0.2454 in good dimensional orbitals. The bosons, B5, B6, B7, B8, B9, B10, 2 agreement with 0.2312 for the observed value of sin w and B11 are shown in Table 3. 19 [8]. The calculated energy for B11 is 1.1 10 GeV in The principal dimensional orbitals are for gauge bos- 19 good agreement with the Planck mass, 1.2 10 GeV . ons of the force fields, as shown in Table 1. It will be The strong interaction, represented by π (half of a shown shortly that F has lower energy than B . and simi- 12 d d pion), is for the interactions among quarks and for the larly the seven principal dimensional orbitals are ar- hiding of individual quarks in auxiliary orbitals. The ranged as F B F B F B F B F B F B F B , 0 5 5 6 6 7 7 8 8 9 9 10 10 11 11 weak interaction, represented by Z , is for the interac- where B and F are the boson and fermion in each orbital. L tion involving changing flavors among quarks and lep- In previous communications [3] we have shown that the tons. The auxiliary dimensional orbitals are derived from masses of fundamental particles are related to each other principal dimensional orbitals. They are for high-mass with three simple formulae, and that the use of accepted leptons and individual quarks. mass data allows calculation of masses of many other All leptons and quarks with d’s, a’s and the calculated particles. The formulae are masses are listed in Table 2 as discussed in Ref. [3]

MMdF,, dB dB,, (1a) Table 2 shows the compositions of leptons and quarks. Each fermion can be defined by principal dimensional MM  , (1b) d1, B dF , dF , orbital numbers (d’s) and auxiliary dimensional orbital MM  2 , (1c) numbers (a’s). For examples, e is 60 that means it has d dB1, dBd , (principal dimensional orbital number) = 6 and a (auxil- where d is the dimensional orbital number from 6 to 11. iary dimensional orbital number) = 0, so e is a principal E5,B and E11,B are the energies for the 5d dimensional or- dimensional fermion. All neutrinos are nearly massless bital and the 11d dimensional orbital, respectively. Each because of chiral symmetry (permanent chiral symmetry).  dimension has its own d, and all d s except 7 (w) of As shown in Table 2,  and  are the hidden (for- the seventh dimension (weak interaction) are equal to , bidden) leptons outside of the three lepton families in the the fine structure constant of electromagnetism. The Standard Model. All elementary particles (gauge bosons, lowest energy boson is the Coulombic field for electro- leptons, and quarks) are in the periodic system of ele- magnetism and the second lowest boson energy is π12 mentary particles with the calculated constituent masses (a spin 1 boson as a half of the spin 0 pion) for the strong in good agreement with the observed values [9,10] by interaction. 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

6 B5 Me 3.7 10 A = photon Electromagnetic

2 B6 Me/ 710 π12 Strong

2 0 B7 M6/  w cosw 91.177 (given) Z L weak (left)

2 6 B8 M7/ 1. 7 10 XR CP (right) nonconservation

2 10 B9 M8/ 3.2 10 XL CP (left) nonconservation

2 14 0 B10 M9/ 6.0 10 Z R weak (right)

2 19 B11 M10/ 1. 1 10 G Gravity

3 spatial dimensions in the eleven- dimensional membrane,   W the mass of electron, the mass of Z boson, and the fine 8 2 structure constant. For an example, the calculated mass     6778800201 of top quark is 176.5 GeV in good agreement with the e      observed 173.5 GeV [11]. 78 The calculated masses of the hidden lepton are 120.7 3. The Observed Higgs Boson GeV (for the mass of  ) and 136.9 GeV (for the mass of  ) with the average as 128.8 GeV for the hidden We propose that the observed Higgs boson is the Stan- lepton condensate, in goo d agreements with the results dard Model Higgs boson that adopts the existence of the from LHC (125 GeV or 126 GeV). hidden lepton condensate. We describes the hidden lep- It is proposed that the Higgs scalar boson itself is a vir- ton condensate first, and the adoption of the hidden lep- tual zero-energy scalar boson without permanent energy ton condensate later. The hidden lepton condensate is to avoid the cosmological constant problem from the similar to the top quark condensate. The top quark con- huge gravitational effect by the non-zero-energy Higgs densate is a composite field composed of the top quark boson [17]. Without permanent energy, the Higgs boson and its antiquark. The top quark condenses with its meas- emerges and disappears by borrowing energy from and ured mass (173 GeV) comparable to the mass of the W returning energy to the particles in the electroweak in- and Z Bosons, so Vladimir Miransky, Masaharu Tana- teraction, respectively. The returning of energy from the bashi, and Koichi Yamawaki [12] proposed that the top Higgs scalar boson to the particles is through the absorp- quark condensate is responsible for the mass of the W tion of the Higgs scalar boson by the particles. When a and Z bosons. The top quark condensate is analogous to massless particle in the electroweak interaction absorbs Cooper pairs in a BCS superconductor and nucleons in the Higgs scalar boson, the Higgs scalar boson becomes the Nambu-Jona-Lasinio model [13]. Anna Hasenfratz the longitudinal component of the massless particle, re- and Peter Hasenfratz et al. [14] claimed that the top sulting in the massive particle and the disappearance of quark condensate is approximately equivalent to a Higgs the Higgs scalar boson. scalar field. S. F. King proposed a tau lepton condensate The observed Higgs boson at the LHC is a remnant of to feed the tau mass to the muon and the electron [15,16]. the Higgs boson. At the beginning of the universe, all By analogy to the top quark condensate, the hidden particles in the electroweak interaction were massless. lepton condensate is a field composed of the hidden lep-   The Higgs boson appeared by borrowing energy sym- tons and antileptons ,, , and  as shown in metrically from all particles in the electroweak interac- Table 2. Just as the observed top quark is a bare quark tion. The Higgs boson coupled with all massless particles, with the observed mass of about 173 GeV instead of including leptons, quarks, and gauge bosons, in the elec- about 346 GeV for top quark-antitop quark, the observed troweak interaction. All massless particles except photon hidden lepton is a bare average hidden lepton instead of  as the gauge boson for electromagnetism absorbed the ,  and ,  .However, unlike the top quark con- Higgs boson as their longitudinal components to become densate, the hidden lepton condensate is outside of the massive particles. The asymmetrical returning of energy standard three lepton-quark families in the Standard from the Higgs boson by the absorption of the Higgs Model. Being forbidden, a single hidden lepton cannot boson is called the symmetrical breaking of the elec- exist alone, so the hidden leptons must exist in the lepton troweak interaction in the Standard Model. In the cases condensate as the composite of the leptons-antileptons of such massive particles, including leptons, quarks, and   ,, , and  . weak gauge bosons, the Higgs boson disappeared. In the To match l8 () at d = 8, quarks include q8 at d = 8 as a case of massless photon as the gauge boson of electro- part of the t quark. In the same way that q7 = 3 , q8 in- magnetism, the un-absorbed Higgs boson became the volves  .  is the sum of e, , and 8 (auxiliary di- remnant of the Higgs boson. mensional leptons). Using Equation (14) of Ref. [3], the Being specific to the electroweak interaction, the rem- 0 mass of 8 equals to 3/2 of the mass of B7, which is Z , nant of the Higgs boson could not return the borrowed   and the mass of 8 equals to 3/2 of the mass of B7 , energy to any other massless particles, so it adopted the ± which is W . From these we can calculate the masses of existence of another scalar boson, and returned the pure   and  . borrowed energy without the longitudinal component to photon. Essentially, the remnant of the Higgs boson be- 3 0 8  Z came an avatar as a life born in the form of another life. 2 The remnant of the Higgs boson could not adopt the ex-  67788 00201 istence of any scalar boson that already represented an e   78    independent elementary particle. The only available sca-

D.-Y. CHUNG, R. HEFFERLIN 25 lar boson came from the scalar hidden lepton conden- bidden lepton family, outside of the three lepton fami- sate. Consequently, the remnant of the Higgs boson as lies of the Standard Model. Being forbidden, a single the Standard Model Higgs boson adopted the existence hidden lepton cannot exist alone; so it must exist in the of the hidden lepton condensate, and became the Avatar lepton condensate as a composite of  and  hid- Higgs boson. den leptons and their corresponding antileptons. The The two possibilities for the Standard Model Higgs calculated average mass of the hidden lepton condensate boson that adopts the hidden lepton condensate are the is 128.8 GeV in good agreements with the observed 125 pure Standard Model Higgs boson and the dual particle or 126 GeV. consisting of the Standard Model Higgs boson and the non-Standard Model hidden lepton condensate. 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