Topic024: The Triad Structure of Quarks, Bill Tifft, 7/31/16
Leptons behave as essentially point particles, but hadrons (baryons, mesons and bosons) are constructed from quarks. Free quarks are not seen but hadron masses may be described as rest masses of quarks with relativistic corrections for quark motions and other factors in binding energies. Precise Lehto-Tifft energies can be predicted for redshifts, which involve massless photons, but such corrections prevent precise predictions for mass based structures. Initially quark masses were not studied since corrections for low mass quarks are very large. However, an adjunct faculty member, Jerry Long, at Pima Community College became aware of my work and suggested that there could be some relationships resembling Lehto-Tifft patterns. I included them and quickly found a dual doubling 3-d pattern involving alternate quarks. The top, charmed and down quarks are related by factors of 128 (2 to the seventh power) in the 1/3 Gamma mass energy levels, while the bottom, strange and up quarks are related by factors of 32 (2 to the fifth power) within the 2/3 Pi mass energy levels. When I fully recognized the role of triads, as will be discussed, the entire quark series is linked through triad compatible levels descending from level 56, centered around level 64, and terminated at the electron lepton.
The energy level pattern is indicated in book section 4.7 Table 6 of my book reproduced below. (For book information or acquisition see Post001 and Post002.) Quarks, as fermions, should and do fit within the Lehto-Tifft energy level doubling pattern. This is shown in the table and book figure 4.8 used as a terminal figure for this topic to show level and transition patterns. The table lists particles involved, levels and transitions, and energies involved. A (non-existent) Z anti-Z is included to illustrate level 56. The neutral Zo (which appears only as a transition) is also shown in the terminal figure and described in the Topic023 lead figure. The terminal figure identifies doubling levels vertically and Gamma and Pi cube root levels horizontally. Transitions are indicated between asterisks. Actual quark levels are in the last two columns with vertical doubling powers of two intervals indicated for the two differential doubling pattern spacings. Electron data appears in the Gamma N.67 column, the common value tied to all quarks. It was incorrectly in the Pi N.67 column in my book.
Level assignments are described in book section 4.7. The heavy quarks have relatively small corrections and easily fit. The bottom and charmed quarks can be assessed using their excitation spectra (a charmonium spectrum is shown in my book below figure 4.8). Published estimates were initially utilized for rest mass energies of the three lowest mass quarks. This was done before the mass scaling relationships were seen. The fact that this pattern appeared and is now known to fit triad pattern requirements tends to confirm fits. There is some deviation at the d quark value, although a stepwise doubling pattern must be maintained between levels. Further evidence that the d level quark is nearly correct is provided in a subsequent independent cosmological test.
Turning to the issue of structural properties of quarks, the following table is reproduced from the second and third portions of book section 4.8 table 7 dealing with particle structure. The first part relates to Higgs, the main part to quarks and their termination at the electron lepton. Various forms or descriptions of possible substructure are shown and noted in headings, with step by step changes in the lead column and in red below the 3-d forms. Both the Higgs and quarks begin at the 4-d 56 level where the total doubling number, at 224, plays a fundamental role in QTPP particle analysis. As noted in Topic021 the 4-d doubling arrangement can be used as a metric description of three energy dimensions and a spatial-temporal link term. The fourth term effectively vanishes once pure 3-d dynamical patterns are possible and all three terms are used as a 3-d spatial energy division. However, temporal commonality is retained at the evolutionary temporal level of the complete galaxian particle nuclear quantum dipole state. The evolving temporal link is replaced by aging evolution as the entire galaxian spatial particle flows through time.
The 4-d 56 224 state never appears as a particle or does the equivalent 3-d 224 state which corresponds to the electron anti-electron pair at the base of the quark data. The existence of matter as particles is accounted for completely in the 3-d existence zone between these two limits where the Higgs and electron form. Work searching for small `dark’ particles appears to find nothing nor has recent high energy work at CERN, and QTC needs nothing. The Higgs and the electron follow similar patterns. 4-d level 224 corresponds to precisely 32 x 7 = the combination of 32 triads. The 3-d 224 state is the matter anti-matter decay state at level 74.67 which generates the electron. Adding three doubling to the 4-d 224 pattern would yields 227 in 4-d level 56.75. Adding 4 more doubling at this level yields Higgs at total doubling level 231 = 33 x 7 + 0 a pure triad state. The Higgs and electron formation tracks are similar, one 4-d step out of sync. 227 = 32 x 7 + 3 at the 4-d level matches the electron anti-electron state in 3-d . Alternatively, direct addition of one triad to the 4-d 56 = 32 x 7 + 0 state will directly produce the Higgs, which could be sort of a heavy neutral equivalent of the electron. There are two aspects of decay processes, both doubling and triad matching is involved. As also seen in the light mesons direct transitions between Gamma and Pi vector states in simple doubling steps is avoided or forbidden. Doubling levels are involved but vector rearrangement is not. Triad related steps control transitions. For some further Higgs related comments, the 227 4-d pattern could be an s state of the Higgs which with the following four doubling places the Higgs in a Gamma p state, eight doubling above the Kaon at Gamma 65.75. Further, as noted at the end of Topic023, a misstep as the sensitive Gamma 56.00 4-d level is approached the 55.75 and 56.75 levels (which bridge the 56.00 instability) could trigger the simultaneous two photon decay at 757.7 Gev (their energy sum) possibly seen at CERN. The 227 = 33 x 7 + 3 state would seem to be a valid triad state and some passage through or over level 56 is required to generate Higgs. Although I can comment on Kaon decay in the next topic, the need to follow triad decay patterns at 4-d means Higgs decay can differ from the Kaon. I am not familiar with the Higgs decay pattern, but Higgs has no apparent role in QTC.
Returning to the quark issue, it is possible at the 4-d 56 state to transition to 3-d. 224 = 32 x 7 and 32 is 4 x 8 the product of a square and cube of 2, which opens the door to 3-d dynamical stability in spatial Keplerian patterns. If the 4th level is abandoned and the triple doubling is applied to the 3-d 56 56 56 = 7 x 24 + 0 form (which is still a triad form), including what would have been the 4th 4-d level increase (a total of 4), it generates a Gamma 57.33 level particle which is the top quark! The shift from 4-d is shown by an arrow to the left. If the full four had been added to the 4-d 56 level it would generate 4-d 228 Gamma 57.00 which can immediately decay to Pi 57.00 which is the Zo transition. There is a clear choice at this point to continue with 4-d to produce the Higgs or shift to 3-d quarks and the Zo path toward constructing hadrons. Note that although the top quark fits a doubling level fine, it cannot be represented as a three figure set of doublings shown in the right column of the structure table. There is an added + 4. This is also true of the triad form for the top quark, 24 x 7 + 4, and an addition of 4, plus or minus 1, appears to be required for 3-d triad level fits. I will comment on this below and in the following topic where certain quad or quint forms of `triads’ may be possible. Quarks are built upon triad controlled patterns, not on classical dynamics as is well known, but they are fermions out of which classical dynamical structures can be built and exist in 3-d doubling levels.
Beginning at the top quark we can now show that the lower quarks form a remarkable triad related pattern. As noted in the opening paragraph, the t – c – d quarks are spaced by 21 doubling (7 per axis), but the b – s – u set are spaced by 15 (5 per axis). The three 3-d levels differ by only 1 from 3-d symmetry (they must fit the 1/3 and 2/3 states) and the +4 will differ only by 1. This remarkable pattern is in fact possible for only six connected levels, which will explain why there can be only be six quarks in three levels of quark pairings before the terminal electron appears! To accomplish this pattern add the (4 5 4 = 13) doubling pattern (marked in red) to the top quark followed by (3 2 3 = 8) to the bottom quark to reach the charmed quark. This generates the bottom quark at level 61.67 = 26 x 7 + 3 and the charmed quark 64.33 = 27 x 7 + 4. At the same time it adds exactly 7 doubling (one triad) to each 3-d axis and borrows 1 from the +4 for the bottom quark. Now add a (2 3 2 = 7) doubling pattern (note the reversed order) to the charmed quark to get the strange quark at 66.67 = 28 x 7 + 4. The strange quark is now 5 doubling below the bottom as required and + 4 is recovered. Continue the pattern by adding a (5 4 5 = 14) pattern to the strange quark (again note the altered sequence so vertical pairs always add to 7 or 5) to reach the down quark at 71.33 = 30 x 7 + 4 now 7 doubling below the charmed quark as required and still +4. Consecutive additions add to 5 or 7, to maintain gains on each 3-d axis, but in alternate vector columns interchange the 5 and 7 differentials. To finish at the up quark add (0 1 0 = 1), retain b – s – u doubling spacing at 5, and increase the added term by 1 at level 71.33 = 30 x 7 + 5. There is now no way to extend the quark pattern and simply adding three doubling to each axis will reach the electron pair and terminate the quark sequence. Note that 9 is 1 triad + 2 to raise the + 5 to 7 and reach the unstable level of 224 = 32 x 7 where we began. Triad built quarks are where matter as we know it appears to begin. At 4-d 224 we stepped back to 3-d 168 and returned to 224 constructing the tools needed to build 3-d particles and generate space embeds within 3-d time where we can currently exist.
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