DRAFT 31May2013
Families of Elementary Particles in Preon Model #3
Abstract
Structures of families of elementary particles as combinations of preons are suggested in this paper to try to make Preon Model #3 more complete. Model #3 uses a modification of the Rishon preon model by elimination of the zero electric charge preon which has been replaced by two oppositely electrically charged preons. A preon has chirality, moves as speed c and is open ended in fermions and has closed ends in bosons and hence appears to be a string. It is suggested that the gluons have the same preon content as the higgs but that the preon pairing arrangement of the gluons is for a boson [i.e. (LL’) and (RR’) pairs] whereas the higgs has a (LR’) and (L’R) pairing of an electron or quark or dark matter particle. The gluon is suggested to be one particle in eight guises rather than eight different particles. A massles version of a Z particle is suggested and the massive Z is suggested to have (LR’) and (L’R) pairings of preons, making it, and the higgs, dark particles as they are neutral in charge. A dark matter particle is suggested with a mass of 65.7 GeV/c2. A table of interrelated masses of electron, quarks and dark matter particles is constructed shedding some light on the structures of these families of particles and which does not pair s with c nor b with t quarks. The baryon octet has been used to imply a structure for the strange quark’s preon contents.
Structures of families of elementary particles
Bosons
 The bosons in Model #3 have pairings of preons in the form LL’ and RR’ ( See The Structure of Elementary Particles: Preon Model #3).
Table 1 shows three potential bosons of Model #3.
Table 1 Bosons
Number of preons (half are LL’ and half are RR’) 
Particle 
24 
photon 
48 
{massless Z ?} 
96 (and 192) 
gluon 
The photon has 24 preons, with six pairs of LL’ and six of RR’. It is this preon pairing structure which gives the photon its linear speed c. Eight preons have red colour charge, eight have green and eight have blue. Overall the photon is symmetrically balanced in numbers and types of preons, and similarly with a neutral balance of electric charge and colour charge. Similarly, the Z particle has the same symmetry but with double the photon’s number of preons. The Z particle shown in Table 1 would be a boson and massless in Model #3 whereas the Standard Model Z boson has mass 91.2 GeV/c^{2}.
The gluon also has the same symmetry and overall neutrality of properties of the massless Z of Model #3. Why is the gluon in Model #3 a single particle when it is well known that the gluon is an octet described using SU(3)? In the same way that a Z particle is still a single particle despite being describable as a redup/antiredantiup quark pairing and at the same time a blueup/antiblueantiup quark pairing . It is still only one Z particle. A gluon can be a combination of those two quark pairings ie a redup/antiredantiup quark pairing plus a blueup/antiblueantiup quark pairing. But, despite all those colours and anticolours, the gluon is colour neutral in total, just as is the Z particle. But although the colour green was not mentioned in those names, that gluon is not deficient in green or antigreen. That is because in Model #3, a red quark is not wholly and exclusively red, but is does have more red preons than green or blue ones. A red up quark:
red up quark  (LR’) (L’R)(L’R) (L’R)(L’R)(L’R)(L’R)(L’R)(L’R)(L’R)(L’R) (LR’)
(g’b’) (rb) (gr) (rg) (br) (bg) (gr) (rb) (rg) (gb) (br) – (b’g’) 
has 8 red, 6 green, 6 blue, 2 antigreen and 2 antiblue preons. The antired antiup quark:
antired antiup quark  (L’R) – (LR’) (LR’)(LR’) (LR’)(LR’) (LR’) (LR’)(LR’) (LR’) (LR’) – (L’R)
(gb) – (r’b’)(g’r’)(r’g’)(b’r’)(b’g’)(g’r’)(r’b’)(r’g’)(g’b’)(b’r’) – (bg) 
has 8 antired, 6 antigreen, 6 antiblue, 2 green and 2 blue preons. In total, for the Z particle, that adds to 8 red, 8 antired, 8 green, 8 antigreen, 8 blue and 8 antiblue preons which is symmetrical and neutral in all colours.
So a gluon could be [rr’bb’] where r’ indicates an antired quark. The rr’ part would be colour neutral as would be the bb’ part. So the gluon is colour neutral. In Model #3, the gluon must be colour neutral in order to be a boson. If the gluon retained its fourquark components within it then it could remain an octet, but that would make it a composite particle, not elementary and that would surely destroy its speed c. The gluon needs to be an elementary particle to attain speed c and masslessness and to allow the preon pairings to be released at a point in its interactions. This does lead to a question as to how the gluon knows which quarks to form at an interaction. At each quarkquark interaction mediated by a gluon, there is an input of a two quarks and an output of two quarks, so the gluon is not acting on its own and the inputted quarks lead to the determination of the outputted quarks after the interaction.
There is a second form of gluon with 192 preons which is the original gluon with two virtual pairs of samecolour quarkantiquark pairs inserted into the particle. For example, the gluon [rr’gg’{bb’}{bb’}] is the single gluon (described, say, using its guise [rr’gg’]) but with the inclusion of two virtual {bb’} pairs of quarks. The gluon is therefore not an octet, despite having an octet of names or guises.
Dark matter particles?
2. The higgs has 96 preons as does the massless gluon and, in model #3, the preons of the higgs are paired in the same manner as are quarks, i.e. in (LR’) and (L’R) pairings. Note that the higgs mass given in Table 2 is the heavier version, i.e. 126.6 (Contradictory Higgs boson measurements emerge at the LHC) rather than 125.3 as that enables the masses of a family of nhiggs particles to be modelled according to a simple formula. The Z^{0} is a boson with mass 91.2 GeV/c2 in the Standard Model, but there is a place for a massless boson in Model #3 (see Table 1). In this model, the higgs and massive Z^{0} are not bosons but are dark matter particles which are not completely uninteractive and so are perhaps are only semidark particles. These particles are neutral in electrical charge and in colour charge. The smallest particle with 24 preons is the candidate for the darkest dark matter particle as it is presumed to be easier to make that particle in an interaction that to recombine two of them into larger particle(s). A simple formula (= 91.2/1.388) has been used to calculate that the hypothetical dark matter particle with 24 preons has mass 65.7 GeV/c^{2}.
Table 2 Dark matter particles/ vacuum fields
Number of preons (half are LR’ and half are L’R) 
Particle 
Mass (GeV/c^{2}) 
24 
dark matter ? 
65.7 ? 
48 
Z^{0} 
91.2 
96 
higgs 
126.6 
2 times 96 
2higgs 
176 * 
4 times 96 
4higgs 
244 * 
8 times 96 
8higgs 
338 * 
16 times 96 
16higgs 
470 
32 times 96 
32higgs 
652 
64 times 96 
64higgs 
905 
128 times 96 
128higgs 
1256 
256 times 96 
256higgs 
1744 * 
512 times 96 
512higgs 
2420 * 
1024 times 96 
1024higgs 
3360 * 
* There is a tentative match of these calculated masses with empirical data here.
Neutrinos
3. The electron neutrino has 24 preons paired as (LR) and (L’R’). This pairing structure provides the neutrino with speed c and zero mass in Model #3. The pairing pattern is the only difference in structure between three particles: the photon, the neutrino and the hypothetical dark matter particle. It is speculated that the muon neutrino has 48 preons and the tauon neutrino has 96 preons. (Table 3.)
Table 3 Neutrinos
Number of preons (half are LR and half are L’R’) 
particle 
24 
neutrino 
48 
muon neutrino 
96 
tauon neutrino 
Electrons and quarks
4. Table 4 shows a straightforward suggestion for a structure of families of electrons and quarks. The main question is why there should be 48 and 96 preons, respectively, for the heavier siblings.
Table 4 Electrons and quarks


Particle


Number of preons

12 (LR’) pairs and 0 (L’R) pairs, and any remaining preons equally of these two types of pairs 
2 (LR’) pairs and 10 (L’R) pairs, and any remaining preons equally of these two types of pairs 
8 (LR’) pairs and 4 (L’R) pairs, and any remaining preons equally of these two types of pairs 
24 
electron 
up quark 
down quark 
48 
muon 
charm quark 
strange quark 
96 
tauon 
top quark 
bottom quark 
The muon was speculated to contain 48 preons because of the baryon octet structure. The baryon octet is: n, p, Λ^{0}, Σ, Σ+, Σ^{0}, Ξ and Ξ^{0} and unlike the gluons, the eight baryons are all different particles.
In terms of quarks the octet is: udd, uud, uds, dds, uus, uds, dss and uss. Note that Λ^{0} and Σ^{0} have identical quark structures. From an octet diagram, it is easy to see that n is diagonally opposite to Ξ^{0}. These two particles form an exact split of a larger entity, which is n + Ξ^{0} = udd + uss = 2(uds). This immediately gives Σ^{ 0} (and therefore also Λ0 which has the same structure) as a symmetric half of the whole entity which is why these two particles are at the centre of the octet diagram. Assuming that the octet is derived from different ways of halving the 2higgs, then a 2higgs is double the average element of this set. Ie 2u+2d+2s = 2higgs in terms of preon content. A 2Higgs has 192 preons while d and u each have 24 preons. So 2s must have 192 – 2*24 – 2*24 = 96 preons and therefore s has 48 preons. Also, s = d + Z/2. That makes the muon, in terms of preon content, an electron plus a half Z^{0} (massive) particle.
There appears to be an anomaly with particle masses in this structure. In swimming manuals (Counsilman, 1977), advice for the crawl stroke is to push one’s hand against as much different water as possible. I.e. to push against still water and not to push against the same water which you have already set moving away. The same may apply to the quarks. It is the electron which seems to have the structure which spins most consistently one way. The antiup quark is most like the electron and should spin less vigorously but maybe its structure is biting on more of the static higgs field, and hence the up may be heavier than the electron. The down quark is the least consistent in spin direction and maybe therefore be the heaviest of the three particles. The hypothetical dark particle with 24 preons may be even heavier as it is half rotating clockwise and half rotating anticlockwise. That arrangement might tend to give the most ‘still water to bite on’ as the ‘water’ is swished back and forth.
5. That analogy fails in the ordering of the masses of the s, c, b and t quarks in Table 4. An alternative structure, therefore, is tentatively suggested in Table 5.
Table 5 Electrons and quarks: tentative model structure
(with the dark matter particles for comparison; masses in MeV/c^{2})


Particle



Number of preons

12 (LR’) pairs and 0 (L’R) pairs, and any remaining preons equally of these two types of pairs 
2 (LR’) pairs and 10 (L’R) pairs, and any remaining preons equally of these two types of pairs 
8 (LR’) pairs and 4 (L’R) pairs, and any remaining preons equally of these two types of pairs 
Dark matter.
Preons equally of two types of pairs: (LR’) and (L’R) 
24 
electron (0.5) 
up quark (2.4) 
down quark (4.8) 
dark matter? (65700) 
48 
strange quark (104) 
Z^{0} (91200) 

96 
muon (106) 
charm quark (1270) 
bottom quark (4200) 
Higgs (126600) 
192 
2Higgs (176000) 

384 
tauon (1777) 
top quark (171200) 
4Higgs (244000) 
Table 5 satisfies a rule that the mass of a particle in a cell must be greater than the mass of any particle in a cell to the left and also be greater than the mass of any particle in a cell above. Table 5 could be used to imply that the muon neutrino might have 96 peons rather than 48, and the tauon neutrino might have 192 preons rathet than the 96 suggested in Table 3.
6. It is difficult to comprehend the huge masses of the dark matter particles in association with the small masses of the fermions to their left in the table. For that reason a tentative Model #3b structure has been suggested in Table 6 in which the dark matter masses have been reassigned to much larger assemblages of preons. The higgs particle in Table 6 is comprised of 24 * 2^{30} preons. Although there is a range of masses in the first row of Table 6 (row index zero) it is assumed that the masses in a row further down the table would be similar to the dark matter mass for that row, as the dark matter bulk would dominate the mass. The electron and up and down quarks are in row index zero in Table 6; the muon is in row 9 and the tauon in row 17. The strange is in row 9; the charm in row 16; the bottom is in row 20; while the top is in row 31, along with the 2Higgs dark matter particle. The Z is a dark matter particle in row 29 and the W is in the electron column also in row 30.
Table 6 Electrons, quarks and dark matter: tentative Model #3b
^{ }


Particles and masses in MeV/c^{2}




Number of preons (and row index) 
12 (LR’) pairs and 0 (L’R) pairs, and any remaining preons equally of these two types of pairs 
2 (LR’) pairs and 10 (L’R) pairs, and any remaining preons equally of these two types of pairs 
8 (LR’) pairs and 4 (L’R) pairs, and any remaining preons equally of these two types of pairs 
Dark matter
Preons equally of two types of pairs: (LR’) and (L’R) 

24 * 2^{0} 
electron (0.5) 
up quark (2.4) 
down quark (4.8) 
6.8^{a} 

24 * 2^{1} 
9.4 

24 * 2^{2} 
13.0 

24 * 2^{3} 
18.1 

24 * 2^{4} 
25.1 

24 * 2^{5} 
34.8 

24 * 2^{6} 
48 

24 * 2^{7} 
67 

24 * 2^{8} 
93 

24 * 2^{9} 
muon (106) 
strange quark (104) 
129 

24 * 2^{10} 
180 

24 * 2^{11} 
249 

24 * 2^{12} 
346 

24 * 2^{13} 
481 

24 * 2^{14} 
667 

24 * 2^{15} 
926 

24 * 2^{16} 
charm quark (1270) 
1285 

24 * 2^{17} 
tauon (1777) 
1783 

24 * 2^{18} 
2476 

24 * 2^{19} 
3436 

24 * 2^{20} 
bottom quark (4200) 
4770 

24 * 2^{21} 
6620 

24 * 2^{22} 
9200 

24 * 2^{23} 
12700 

24 * 2^{24} 
17700 

24 * 2^{25} 
24600 

24 * 2^{26} 
34100 

24 * 2^{27} 
47300 

24 * 2^{28} 
65700 

24 * 2^{29} 
W (80400) 
Z^{0} (91200) 

24 * 2^{30} 
Higgs (126600) 

24 * 2^{31} 
top quark (171200) 
2Higgs (176000) 

24 * 2^{32} 
4Higgs (244000) 

24 * 2^{33} 
8Higgs (338000) 

24 * 2^{34} 
470000 

24 * 2^{35} 
652000 

24 * 2^{36} 
905000 

24 * 2^{37} 
1256000 

24 * 2^{38} 
1744000 

24 * 2^{39} 
2420000 

24 * 2^{40} 
3360000  
(i.e. 24 * 2^{row index}) 

The Z seems a long way from the electron in Table 6, but it could decay to an electronpositron pair by releasing preons within the Z back to the vacuum as smaller particles of dark matter. Similarly, the muon can produce an electron by releasing its preons in smaller particles of dark matter at a particle interaction.
There are many dark matter particles listed in Table 6, but there is not one very close to 8600 MeV/c^{2} (Report of SuperCDMS Collaboration). The nearest is 9200 MeV/c^{2}. for a particle with 24 * 2^{22} preons. There are 40 rows shown in Table 6 but that is because the number of preons is double for each successive row. There is no reason why there could not be 24*2^{40}/24 = 2^{40} rows within Table 6. And there is no reason to stop at index 40. Two of the particle masses suggested experimentally by Dorigo (2013) appear, by my simple formulae, to correspond to the 3higgs and 6higgs which are between rows 31 and 33 in table 6.
Supersymmetry
Preon Model 3b, and Table 6, allow a better view of supersymmetry for heavy particles than in my previous models. All particles in any row of Table 6 are potential superpartners. Any dark matter particle in a row of Table 6 can have a boson and neutrino with identical preon content, but their properties will be different because of their different ways of pairing preons.
Heavy dark particles, ie particles at the bottom of Table 6 in the dark column such as the Z and Higgs, will behave as static particles (without linear speed c) as they have equal amounts of type (LR’) as of (L’R) pairings which give an equal amount of lefthanded and righthanded preons. With the higgs, for exaample, there will be 24*2^{29} lefthanded preons and 24*2^{29} righthanded preons. Their field effects cancel, on average, leaving a static field. That makes the higgs a dark matter particle. and the same for the Z particle. But the higgs and the Z could have partner particles with identical preon content in a boson column (not shown in Table 6), and also in a neutrino column (also not shown). A photon and neutrino near the top of such columns are massless with speed c, but if interference (between preons field effects) caused particles low down in the boson and neutrino columns to lose speed c and gain mass, then the Z and Higgs partners could exist with mass as bosons, rather than as dark matter particles. This effect could give the particles in the lower neutrino column to have mass. This could give rise to some massless neutrinos and some massive neutrinos, depending on position in the column. The muon neutrino might, for example, be speculated to be in row index 9 next to the muon while the tauon neutrino might be in row index 17 next to the tauon.
The W boson could be a mixture of an electron and a bosonic form of Z, rather than a mixture of an electron and a dark matter particle shown in table 6.
Although there is no news of statistically significant detection of supersymmetry from CERN, there appears to me to be a simple single formula which can be used to calculate masses of dark matter particles in CERN data. (ben6993, 2013.) These may simply be dark matter particles or bosonic particles rather than supersymmetric particles. In Preon Model #3, supersymmetry is already evident as the photon and neutrino have the same preon content but have different structures and different properties because of the different ways that their preons are arranged.
Summary
7. Structures of families of elementary particles as combinations of preons are suggested in this paper. Model #3 uses a modification of the Rishon preon model by elimination of the zero electric charge preon which has been replaced by two oppositely electrically charged preons. It is suggested that the gluons have the same preon content as the higgs, that is 96 preons, but that the preon pairing arrangement of the gluons is for a boson [i.e. (LL’) and (RR’) pairs] whereas the higgs has an (LR’) and (L’R) pairing of an electron or quark or dark matter particle. The gluon is suggested to be one particle in eight guises rather than eight different particles. A massles version of a Z particle (with 48 preons) is suggested and the massive Z is suggested to have (LR’) and (L’R) pairings of preons, making it, and the higgs, a dark particle as it is neutral in charge. A dark matter particle is suggested with a mass of 65.7 GeV/c2. A table of interrelated masses of electron, quarks and dark matter particles is constructed shedding some light on the structures of these families of particles and which does not pair s with c nor b with t quarks. The baryon octet has been used to imply a structure for the strange quark’s preon contents.
Experimental evidence for the mass of a dark particle in Table 2 would be desirable. Also, the experimental hints of masses of the nhiggs particles in Table 2 need confirmation. A mathematical treatment of the speculations in this paper might possibly be developed using string theory as a first approach as the preons appear to be strings.
An extension of the model, to Model #3b, sets the massive Z and Higgs particles as much more massive aggregations of preons than in Model #3. This allows a new range of lighter particles of dark matter. One such particle has mass 9200 Mev/c^{2} and is the closest, in Table 6, to the recently suggested dark matter particle with mass 8600 Mev/c^{2}. It also puts a very big distance between the Z and the electron/up/down particles in terms of preon numbers. In interactions involving large aggregations of preons, many preons are returnable covertly to the vacuum as dark matter particles plus lighter fermions.
Manchester
England
AJF/27May2013/v1
(revised/v3/31May2013)
References
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