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Our best understanding of how the known elementary particles and three of the forces (electromagnetic, weak and strong) are related to each other is encapsulated in the Standard Model of particle physics. However, the Standard Model is incomplete as it fails to explain a number of phenomena. The Standard Model relies on a set of elementary particles which are also known to be incomplete. This paper presents a complete set of elementary particles to serve as the basis for an expanded Standard Model. The set of elementary particles contains all known elementary particles and 6 extra elementary particles which relate only to mass and gravity. They include the graviton, a Higgs-like particle (but 6.13 times heavier than the Higgs), 2 dark matter particles and 2 dark energy particles for a total of 22 elementary particles (the W and Z bosons are seen as manifestations of a single particle).

It is widely accepted by the scientific community that everything in the universe is made from several elementary particles and is governed by four fundamental forces. Our best understanding of how the known elementary particles and three of the fundamental forces (electromagnetic, weak and strong) are related to each other is encapsulated in the Standard Model of particle physics.

As successful as the Standard Model is, we know it’s incomplete in several areas. For example: the Standard Model does not incorporate gravity; it does not deal with dark matter and energy particles; it does not explain why there are three levels of matter particles and it fails to provide a relationship between 19 parameters that must be derived experimentally, including the masses of most of the particles.

As the Large Hadron Collider (LHC) continues to produce more results we expect to see physics expand beyond the Standard Model. In fact, in late 2015 it’s possible that a new particle in the 750 GeV range was observed [

As the Standard Model sheds little light on the elementary particle masses, we have little guidance as to where to look for new particles.

This paper proposes a model for a complete set of elementary particles, including those not dealt with by the Standard Model. The Standard Model has 12 matter particles (that come in three generations of 6 quarks and 6 leptons), 4 force carrier particles (2 for the weak force) and the Higgs. The proposed set of elementary particles presented in this paper includes these particles, in addition to 6 other particles that relate only to mass and gravity. These 6 other particles include: the graviton (thought to be the force carrier for gravity), a Higgs-like particle but 6.13 times heavier than the Higgs, 2 dark matter particles and 2 dark energy particles, for a total of 22 particles (as will be shown in this proposed model the W and Z bosons governing the weak interaction are seen as manifestations of a single entity).

The complete set of 22 elementary particles is derived from a manuscript [

The author understands that it is unacceptable to use these kinds of manuscripts in order to motivate new theories. Nonetheless, the manuscript does shed much light on what is already known and does predict additional particles not found in the Standard Model. In addition, most of the extensions of the Standard Model are motivated by a belief in unification and simplicity, also without any scientific source, but in fact, in agreement with the source text of the manuscript relied upon herein.

The complete set of 22 elementary particles in the proposed model is shown in

We note the following characteristics of the 22 particle proposed model depicted in

1) There are 3 letters along horizontal lines (horizontal particles), there are 12 letters along diagonal lines (diagonal particles), and there are 7 letters along vertical lines (vertical particles).

2) Horizontal particles. The 3 horizontal particles [

3) Diagonal particles. There are 12 diagonal particles [

4) Vertical particles. There are 7 vertical particles [

Name | Alef | Bet | Gimel | Dalet | Hey | Vav | Zayin | Het |
---|---|---|---|---|---|---|---|---|

Symbol | א | ב | ג | ד | ה | ו | ז | ח |

Value | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Simple value | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Name | Tet | Yud | Kaf | Lamed | Mem | Nun | Samesh | Ayin |

Symbol | ט | י | כ | ל | מ | נ | ס | ע |

Value | 9 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |

Simple value | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

Name | Pe | Tsadi | Kuf | Resh | Shin | Tav | ||

Symbol | פ | צ | ק | ר | ש | ת | ||

Value | 80 | 90 | 100 | 200 | 300 | 400 | ||

Simple value | 17 | 18 | 19 | 20 | 21 | 22 |

particles. These vertical particles occur only at the second and third energy levels (note that the dark boxes identify energy levels for diagonal particles only) with the exception of the graviton at the first energy level (represented by the Tavת).

5) Horizontal and vertical axis are independent. Thus, vertical particles do not interact via horizontal particles, i.e., via the 3 non-gravitational forces, they only interact with the force of gravity. Diagonal particles interact with horizontal and vertical forces, i.e., all forces and also vertical mass particles in the middle pillar (Higgs and Higgs-like).

6) The right-side, left-side and middle pillars are associated with the pillar’s numbers of 248, 365 and 613, respectively^{1}.

7) Each energy level has a particular scale factor which, when multiplied by the Hebrew letter value, determines the particle’s mass, as will be shown in Section 4, entitled Particle Masses-some predictions. a) To determine the scale factor of a higher energy level one multiplies the scale factor of the lower energy level by the associated pillar number then divides by 2, e.g., by 365/2 for the left-side pillar. b) To correlate scale factors at the lowest level on the right-side with the left-side pillars one simply multiplies the scale factor by the ratio of the pillar numbers; thus to go from scale factor on the right-side pillar to the scale factor on the left-side pillar one multiplies by 365/248. c) To correlate the scale factors at the lowest level on the middle pillar with the right-side pillar one multiplies the right-side pillar lowest level scale factor by 40; the value of the letter Memמ connecting the lowest levels.

8) Each Hebrew letter shape reveals an underlying reality and will be illustrated in Section 3, entitled Letter Shapes and Particles.

The Hebrew alphabet consists of 22 letters. Each Hebrew letter has 3 modalities; a pictogram, a letter and a number. Each of these modalities provides underlying information about it as a building block of nature. We examine the three horizontal force particles and their associated letter shapes, for illustration purposes.

1) Electromagnetic force: The Shinש has 3 heads and is actually pronounced differently when a dot is placed over the rightmost or leftmost head. These two ways to pronounce the letter Shinש correlate to polarizations of the photon.

2) The Strong force: the Memמ actually comes in 2 shapes―the 1^{st} shape (shown in ^{nd} Mem shapeם, (which is a simple square) is used when the letter Mem appears at the end of a word. Thus, one Memם consists of four lines (sides of a square) and the other Memמ consists of 2 lines at the right and bottom and 2 modified lines at the top and left. In total the Mem consists of 8 components (6 identical and 2 slightly different). These 8 components correspond to the 8 gluons (6 of which have mathematically symmetrical characterizations).

3) The Weak force: the Alephאis actually a composite of 3 letters; on the top right and bottom left are 2 identical Yudsי, and separating them is 1 diagonal Vavו. The 2 Yuds clearly represent the ±W boson, and the Vav represents the Z boson.

Measured Particle masses versus predicted particle masses are illustrated in

Column 1 of

1) Matter particles: The electron, with its well defined mass, is used as the control factor to compute the matter particle masses. The electron corresponds to the letter Yudי, whose value is 10.The scale factor for level 1 (lowest energy) on the right-side pillar is the electron mass divided by 10 or 0.0511. To obtain the scale factor for level 1 on the left-side pillar we multiply by the pillar ratio 365/248 and obtain 0.0752. Then to obtain level 2 scale factor on the left-side pillar we multiply level 1 scale factor by 365/2 and again to obtain the level 3 scale factor we multiply the level 2 scale factor by 365/2. To obtain the predicted mass for any given particle we multiply the particle value by the scale factor by (Column 5 times Column 6). All results for quarks (rows above the electron on

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|

Particle | Measured mass | Error/range | Letter | Letter value | Scale factor | Predicted mass | Predicted/actual | Comment |

(Mev/c2) | (Mev/c2) | |||||||

Up quark | 2.3 | +0.7, −0.5 | lamed | 30 | 0.0752 | 2.26 | 0.981 | <1 sigma |

Down quark | 4.8 | +0.5, −0.3 | samesh | 60 | 0.0752 | 4.51 | 0.940 | <1 sigma |

Charm quark | 1275.0 | ±25 | tzadi | 90 | 13.7254 | 1235.28 | 0.969 | <2 sigma |

Strange quark | 95.0 | ±5 | zayin | 7 | 13.7254 | 96.08 | 1.011 | <1 sigma |

Top quark | 173,200.0 | 176,500 | ayin | 70 | 2504.8799 | 175,341.59 | 1.012 | In range |

Bottom quark | 4180.0 | 4660 | vav | 6 | 2504.8799 | 15,029.28 | 3.596 | Out of range |

Electron | 0.5 | yud | 10 | 0.0511 | 0.51 | 1.000 | Control | |

Muon | 105.7 | ±0.0000035 | kuf | 100 | 1.0561 | 105.61 | 1.000 | Out of range |

Tau | 1776.9 | ±0.12 | hey | 5 | 355.4411 | 1777.21 | 1.000 | <3 sigma |

Dark 1 | pe | 80 | 13.7254 | 1098.03 | ||||

Dark 2 | gimel | 3 | 2504.8799 | 7514.64 | ||||

Dark 3 | kaf | 20 | 1.0561 | 21.12 | ||||

Dark 4 | bet | 2 | 355.4411 | 710.88 | ||||

Higgs boson | 125,090 | ±240 | resh | 200 | 626.4847 | 125,296.94 | 1.002 | <1 sigma |

Higgs-like | dalet | 4 | 192,017.556 | 768,070.22 | ||||

Z boson | 91,187.6 | ±2.1 | alef-yud | 91,187.60 | 1.000 | Control | ||

W boson | 80,385 | ±15 | alef-vav | 0.8831 | 80,524.53 | 1.002 | Out of range |

computed in a similar way. However, an extra scale factor relating to cross letter ratios must be applied to obtain a fit to the data. At level 2 the scale factor is modified by dividing it by 6, the ratio of the letters Sameshס to Yudי, and at the level 3 it is further modified by dividing by 7/19, the ratio of the letters Zayinז over Kufכ (using their simple values as shown in

2) Dark particles: These same scale factors derived above are used in the same manner to predict dark particle masses. One obtains a dark matter particle around 1.1 GeV and a dark energy partners at about 21 MeV (of the order a tau neutrino mass?) with corresponding higher energy pairs at 7.5 GeV and 711 MeV. As expected, from the vertical particles discussion in Section 2, the left-side dark particles are heavy (GeV’s) or the dark matter particles, and the right-side dark particles are the lighter (MeV’s) or dark energy particles.

3) Higgs-like particle: The scale factor for level 1 (lowest energy) on the right-side pillar is 0.0511. To obtain the scale factor for level 1 on the middle pillar we multiply by 40 and obtain 2.044. Then to obtain level 2 scale factor on the middle pillar we multiply level 1 scale factor by 613/2 and again to obtain the level 3 scale factor we multiply the level 2 scale factor by 613/2. To obtain the predicted mass for any given particle we multiply the particle value by the scale factor by (Column 5 times Column 6). The Higgs (a level 2 particle) predicted mass is within measurement error its higher mass cousin at exactly 6.13 times the Higgs mass or 768 GeV. This compares with preliminary observations of a potential particle at around 750 GeV (750 and 760 respectively for ATLAS and CMS) [

4) Weak force particles: Intuitively the horizontal particles would be expected to have zero mass. We know, however, that the weak force particles have mass due to symmetry breaking. The ratio of the components of the letter Alephא: Vavו (6) over Yudי (10); times the ratio of the pillars they connect (365/248) yields 0.883 for the ratio of the mass of W boson over the Z boson force particles. This ratio is used to predict the W boson mass from the Z boson mass. The predicted W boson mass is approximately correct but outside of measurement error.

The Standard Model is a triumph of physics. However, it is incomplete in several areas. In particular, it does not incorporate gravity; it does not deal with dark matter and energy particles; it does not explain why there are three levels of matter particles, and it fails to provide a relationship between the masses of most of the particles. An ancient manuscript contains a model for all building blocks of the physical world that is more complete. This model consists of 22 particles at 3 energy levels. It includes both matter particles, force particles and several gravity/mass particles which do not interact with the known forces other than with gravity. It also provides a means to calculate particle masses. Such a model sheds some light on where we might look to find more particles. Among the model’s predictions are 1) a heavier Higgs-like particle at 6.13 times the Higgs mass, 2) dark matter particles at about 1.1 and 7.5 GeV, and 3) dark energy particles at around 21 and 711 MeV.

Further ongoing research is required to refine the predictions of this proposed model. However, with results coming out of the LHC it is felt that the preliminary analysis presented herein should be shared while further refinements of the proposed model continue to be developed.

Daniel E. Friedmann, (2016) A Complete Set of 22 Elementary Particles for an Expanded Standard Model. Open Access Library Journal,03,1-6. doi: 10.4236/oalib.1102641