Identition Zones (36-102)

As we know all forces can be unified in GUT or TOE the forces could be an example of polar opposite, the strong and weak forces could be opposites electromagnetism could be its own opposite which makes sense but what about gravity?

• Well I believe dark matter/dark energy is the opposite of gravity which makes sense.
• I also believe the strong/weak force and dark matter-energy/gravity are opposites which makes sense in my opinion.

To solve quantum gravity we can treat gravity like electromagnetism and have gravity as waves which has basically already been proven because gravitational waves have been proven, light could produce the gravitron particle. All the particles and forces correspond to the 4/5 elements. (The Octonion Math)

Nothing prevents a theory from including more than 4 dimensions. In the case of string theory, consistency requires spacetime to have 10, 11 or 26 dimensions. The conflict between observation and theory is resolved by making the unobserved dimensions compactified. (Astrophysics Research)

There are several open questions that need to be addressed to convert the model studied here into a realistic theory.

• First and foremost, one must find a dynamical mechanism for driving the compactification radius φ to unity to produce a small cosmological constant. Similar issue is present in the usual Kaluza–Klein scenarios where one needs to provide a mechanism for spontaneous compactification. We note, however, that the situation in theory (4) is somewhat better than in the usual KK setup. In the latter case, apart from the case of compactification on S1, the pure gravity theory in 4 + D dimensions usually does not have solutions of the form of the product of Minkowski spacetime and (compact) internal manifolds. For this reason one usually extends the pure gravity theory in 4 + D dimensions with extra fields, e.g. by considering the Einstein–Yang–Mills system. The stress–energy tensor of these extra fields then allows for solutions of the required product form, see e.g. [20], Section 3. Probably the most famous compactification mechanism is that due to Freund and Rubin [21], where the 3-form field of the 11D supergravity is doing the job. In contrast, the theory (4) admits the solution that is the S3 fibration over S4, see [14] for an explicit description. Thus, at least there is a solution of (4) of the desired type without having to introduce extra fields. However, the cosmological constant for the S3 fibration over S4 solution is too large, see [14]. This is similar to the situation with the Freund–Rubin solution. Thus, a compactification mechanism that would result in an appropriately small cosmological constant is a very serious open issue for our setup. It is possible that the only way forward is to add other fields. We then remark that there is a very natural extension of the theory (4) that adds forms of all odd degrees. This is the theory that appeared in [12], formula (29). It would be interesting to study 4D compactifications of this more general theory. We hope to analyse this in the future.
• Another open problem of the present approach is that of coupling to matter. Again, a natural way to proceed is suggested by supergravity. One does not couple supergravity to extra fields, one simply studies what the modes already present become when viewed from the 4D perspective. In particular, when compactifying on a coset manifold all modes related to isometries of the internal space are known to be important. Indeed, recall that the gauge group that arises in the KK compactification is the group of isometries of the internal manifold, and its dimension may be larger than the dimension of the internal space itself. In this paper we have considered a compactification on a group manifold, but only retained half of the relevant isometries by considering the invariant dimensional reduction ansatz. It is clear that additional fields will arise by enlarging the ansatz by taking into account all the isometries. In this case, however, one must be careful about the issue of consistent truncation, see e.g. [22] for a clear description of all the issues arising. We leave a study of the dimensional reduction on S3 viewed as a coset S3 = SO(4)/SO(3) to future research.
• Third, there is a question of how to describe Lorentzian signature metrics using this formalism. To do this one must make the 3-form C complex-valued, and then impose some appropriate reality conditions. Similar issues exist in all Plebanski-related formulations. We postpone their resolution to future work.Finally, to avoid confusion, we would like to say that our present use of G2 structures (3-forms in 7D) is different from what one can find in the literature on Kaluza–Klein compactifications of supergravity.

In our approach a 3-form is not an object that exist in addition to the metric — it is the only object that exist. The metric, and in particular the 4D metric, is defined by the 3-forvia (2). Also, in the supergravity context a 7D manifold with a G2 structure is used for compactifying the 11D supergravity down to 4D. In contrast, we compactify from 7D to 4D. (General relativity from three-forms in seven dimensions - pdf)

To define them, or make them unambiguous, a continuum limit must carefully remove “construction scaffolding” of lattices at various scales.

• Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values. That is, the experimental value of the physical quantity yields practical applications, but due to their empirical nature the observed measurement represents areas of quantum field theory that require deeper derivation from theoretical bases.
• Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory.
• Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics.

Despite his later skepticism, it was Paul Dirac who pioneered renormalization. (Wikipedia)

By contrast, the pariah groups stand apart, as the name suggests. Exceptional objects related to the number 8 include the following.

• The octonions are 8-dimensional. The E8 lattice can be realized as the integral octonions (up to a scale factor).
• The exceptional Lie groups can be seen as symmetries of the octonions and structures derived from the octonions;[19] further, the E8 algebra is related to the E8 lattice, as the notation implies (the lattice is generated by the root system of the algebra).
• Triality occurs for Spin(8), which also connects to 8 · 3 = 24.Likewise, exceptional objects related to the number 24 include The Leech lattice is 24-dimensional.
• Most sporadic simple groups can be related to the Leech lattice, or more broadly the Monster. The exceptional Jordan algebra has a representation in terms of 24×24 real matrices together with the Jordan product rule.
• These objects are connected to various other phenomena in math which may be considered surprising but not themselves “exceptional”. For example, in algebraic topology, 8-fold real Bott periodicity can be seen as coming from the octonions. In the theory of modular forms, the 24-dimensional nature of the Leech lattice underlies the presence of 24 in the formulas for the Dedekind eta function and the modular discriminant, which connection is deepened by Monstrous moonshine, a development that related modular functions to the Monster group.

In string theory and superstring theory we often find that particular dimensions are singled out as a result of exceptional algebraic phenomena. For example, bosonic string theory requires a spacetime of dimension 26 which is directly related to the presence of 24 in the Dedekind eta function. Similarly, the possible dimensions of supergravity are related to the dimensions of the division algebras. (Wikipedia)

It is known that the recently reported shift of **the W boson mass can be easily explained by an SU(2)L triplet Higgs boson”” with a zero hypercharge if it obtains a vacuum expectation value (VEV) of O(1) GeV.

• Surprisingly, the addition of a TeV scale complex triplet Higgs boson to the standard model (SM) leads to a precise unification of the gauge couplings at around 10¹⁴GeV.
• We consider that it is a consequence of SU(5) grand unification and show a possible potential for the Higgs fields yielding a weak scale complex SU(2) triplet scalar boson.
• Although it seems the proton decay constraint would doom such a low-scale unification, we show that the constraint can be avoided by introducing vector-like fermions which mix with the SM fermions through mass terms involving the VEV of GUT breaking Higgs field.

Importantly, the simplest viable model only requires the addition of one pair of vector-like fermions transforming 10 and 10. (W boson mass anomaly and grand unification - pdf)

Summing the principal and secondary diagonals gives us 1200 + 960 = 2160 = 360 * 6 = 432 * 5. And aligning the principal and secondary diagonals forms this string of 24 dyads summing to 90 each, again for a total of 2160 (and note that only terminating digits 1 and 9 are present and that there are also 24 diagonal dyads summing to 90 each, as somewhat crudely illustrated) (Primesdemystified)

In particle physics, a lepton is an elementary particle of half-integer spin (spin 1⁄2) that does not undergo strong interactions.[1]

• Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutral leptons (better known as neutrinos).
• Charged leptons can combine with other particles to form various composite particles such as atoms and positronium, while neutrinos rarely interact with anything, and are consequently rarely observed.
• The best known of all leptons is the electron. There are six types of leptons, known as flavours, grouped in three generations.[2]
• The first-generation leptons, also called electronic leptons, comprise the electron (e−) and the electron neutrino (νe); the second are the muonic leptons, comprising the muon (μ−) and the muon neutrino (νμ); and the third are the tauonic leptons, comprising the tau (τ−) and the tau neutrino (ντ).
• Electrons have the least mass of all the charged leptons. The heavier muons and taus will rapidly change into electrons and neutrinos through a process of particle decay: the transformation from a higher mass state to a lower mass state.
• Thus electrons are stable and the most common charged lepton in the universe, whereas muons and taus can only be produced in high energy collisions (such as those involving cosmic rays and those carried out in particle accelerators).
• Leptons have various intrinsic properties, including electric charge, spin, mass.
• Unlike quarks, however, leptons are not subject to the strong interaction, but they are subject to the other three fundamental interactions: gravitation, the weak interaction, and to electromagnetism, of which the latter is proportional to charge, and is thus zero for the electrically neutral neutrinos.

For every lepton flavor, there is a corresponding type of antiparticle, known as an antilepton, that differs from the lepton only in that some of its properties have equal magnitude but opposite sign. According to certain theories, neutrinos may be their own antiparticle. It is not currently known whether this is the case. (Wikipedia)

This is where the idea of 12 fermion fields and 12 boson fields come from. These fields are excitations of the underlying theories (the Standard Model) that describe the known Universe in its entirety, and include:

• The six (6): up-, down-, strange-, charm-, bottom-, top-quarks, and their antiquark counterparts,
• The three (3) charged (electron, muon, tau) and three (3) neutral (electron neutrino, muon neutrino, tau neutrino) leptons, and their antimatter counterparts,
• The eight (8) gluons (because of the eight possible color combinations),
• The one (1) electromagnetic (photon) boson,
• The two (2) weak (W-and-Z) bosons,
• And the Higgs boson.

The quarks and leptons are fermions, which is why they have antimatter counterparts, and the W boson comes in two equal-and-opposite varieties (positively and negatively charged), but all told, there are 24 unique, fundamental excitations of quantum fields possible. This is where the 24 fields idea comes from. (Forbes)

String Theory which states there could be 11 dimensions (9 dimensions of space, 1 dimension of time, and 1 dimension for other universes) - the diagram below can sum it up for the 9 dimensions of space. Then the Cosmos would be the 11th dimension where (+/-) Binary Universes are born from Nothingness. Where Nothingness = 0 = (+) universe of regular matter and (-) universe of dark matter. (Quora)

Spin networks constitute a basis that minimize the degree of over-completeness of the loop basis, and for trivalent intersections eliminate it entirely.

• The edges are labelled by spins together with `intertwiners’ at the vertices which are prescription for how to sum over different ways the spins are rerouted.
• The sum over rerouting are chosen as such to make the form of the intertwiner invariant under Gauss gauge transformations.

Some of these relations are rooted in a relation to superstring theory and quantum gravity which is directly related to the quantization of general relativity. (Wikipedia)

Because particles and antiparticles have opposite conserved charges, Majorana fermions have zero charge, hence among the fundamental particles, the only fermions that could be Majorana are sterile neutrinos, if they exist.

• All the other elementary fermions of the Standard Model have gauge charges, so they cannot have fundamental Majorana masses: Even the Standard Model’s left-handed neutrinos and right-handed antineutrinos have non-zero weak isospin, a charge-like quantum number.
• However, if they exist, the so-called “sterile neutrinos” (left-handed antineutrinos and right-handed neutrinos) would be truly neutral particles (assuming no other, unknown gauge charges exist).
• Ettore Majorana hypothesised the existence of Majorana fermions in 1937. The sterile neutrinos introduced to explain neutrino oscillation and anomalously small S.M. neutrino masses could have Majorana masses.

If they do, then at low energy (after electroweak symmetry breaking), by the seesaw mechanism, the neutrino fields would naturally behave as six Majorana fields, with three of them expected to have very high masses (comparable to the GUT scale) and the other three expected to have very low masses (below 1 eV). (Wikipedia)

The work performed in this thesis will focus on two different models, that both can be used in the creation of a GUT. Both models are based on having SO(10) as the unification gauge group.

• Such models are more complex than the original suggestions, but can also accommodate more physics. In these two models, it is not possible to achieve unification among the gauge couplings with tree-level matching conditions.
• However, so-called threshold effects appear when matching the couplings at a higher order in perturbation theory, which are a result of particles with masses around the symmetry breaking scales.

Specifically, it will be investigated if threshold effects can save these two models, and thereby allowing unification. (Threshold Effects in SO(10) Grand Unified Theories - pdf)

It has been long known that the SO(10) model is free from all perturbative local anomalies, computable by Feynman diagrams. However, it only became clear in 2018 that the SO(10) model is also free from all nonperturbative global anomalies on non-spin manifolds — an important rule for confirming the consistency of SO(10) grand unified theory, with a Spin(10) gauge group and chiral fermions in the 16-dimensional spinor representations, defined on non-spin manifolds. (Wikipedia)

As in E8 with 16 of the 2^8 = 256 binary representations excluded from the group, there are 32 excluded octonions from the 2^9 = 512. As in E8, excluded particles are associated with the color=0, generation=0 (bosons) which are the positive (and negative) generators commonly associated with the 8-orthoplex with 16permutations of {±1, 0, 0, 0, 0, 0, 0, 0}.

The Mathematical Elementary Cell 30 (MEC30) standard unites the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement. (Google Patent DE102011101032A9)

Finally NG′ is the number of parameters of the group G′, the subgroup of G still unbroken by the flavour matrices.

• In this case, G′ corresponds to two U(1) symmetries, baryon number conservation and lepton number conservation and therefore NG′ = 2.
• Furthermore Eq. (79) can be applied separately to phases and moduli. In this way, and taking into account that a U(N) matrix contains n(n − 1)/2 moduli and n(n + 1)/2 phases.
• It is straightforward to obtain that we have, and Nmod = 84 − 5 × 3 = 69 moduli in the flavour sector and Nph = 69 − 5 × 6 + 2 = 41 phases.
• This amounts to a total of 123 parameters in the model4, out of which 44 are CP violating phases!!

As we know, in the SM, there is only one observable CP violating phase, the CKM phase, and therefore we have here 43 new phases, 40 in the flavour sector and three in the flavour independent sector. (Flavour Physics and Grand Unification - pdf)

Notice that the divisions in the original square have been done according to some Fibonacci numbers: 5, 8 and 13=5+8; therefore the sides of the transformed rectangle are also Fibonacci numbers because it has been constructed additively. Now, do you guess how could we correct the dimensions of the initial square so that the above transformation into a rectangle was area-preserving? Yes, as it could not be another way round, we need to introduce the Golden Ratio! If the pieces of the square are constructed according to Golden proportions, then the area of the resulting rectangle will coincide with the area of the square. (Phi particle physics)

This pattern of eigenvalues and eigenvectors strongly suggests that E8 (and H4) passes through a“geometric identity” as it folds (or unfolds), respectively. This makes establishing a unit determinantof these matrices interesting (E8 to H4 folding matrix - pdf)

One of the most promising attempts to go beyond the standard model of particle physics is superstring theory. As it is well known, special relativity fused time and space together, then came general relativity and introduced a curvature to space-time. Kaluza and later on Klein added one more dimension to the classical four in order to unify general relativity and electromagnetism. The dimensionality of space-time plays a paramount role in the theoretical physics of unification and has led to the introduction of the 26 dimensions of string theory, the 10 dimensions of superstring theory, and finally the heterotic string theory with the dimensional hierarchy 4, 6, 10, 16 and 26

In this article I am going to introduce the main results of a new theory of elemetary particle physics developed by the engineer M.S. El Nachie.

• This theory provides a fractal model of quantum space-time, the so-called E-infinity space, that allows the precise determination of the mass-energy of most elementary particles -and much more- in close agreement with their experimental values.
• The Golden Ratio emerges naturally in this theory, and turns out to be the central piece that connects the fractal dimension of quantum space-time with the mass-energy of every fundamental particle, and also with several fundamental physical quantities such as the Fine Structure constant.
• El Nachie has been severely criticised by his non-orthodoxal publication methods -he uses to publish his papers in a Journal where he is the editor in chief. Despite this fact, I think that his theory deserves consideration so I will try to summarize it in the lines that follow.
• The intervention of the Golden Ratio can be seen as a way to enter the quantum world, the world of subtle vibrations, in which we observe increasing energy levels as we move to smaller and smaller scales.
• El Nachie has proposed a way of calculating the fractal dimension of quantum space-time. The resulting value (Figure 7) suggests that the quantum world is composed of an infinite number or scaled copies of our ordinary 4-dimensional space-time.
• Setting k=0 one obtains the classical dimensions of heterotic superstring theory, namely 26, 16, 10, 6 and 4, as well as the constant of super-symmetric (αgs=26) and non super-symmetric (αg=42) unification of all fundamental forces.

As we have seen in section 2, the above is a Fibonacci-like sequence with a very concise geometrical interpetation related to numbers 5, 11 and φ. (Phi in Particle Physics)

The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively.[ (Wikipedia)

The 13 circles of the Metatron’s cube can be seen as a diagonal axis projection of a 3-dimensional cube, as 8 corner spheres and 6 face-centered spheres. Two spheres are projected into the center from a 3-fold symmetry axis. The face-centered points represent an octahedron. Combined these 14 points represent the face-centered cubic lattice cell. (Wikipedia)

Georgi and Glashow have chosen the SU(5) where a single gauge coupling constant is manifestly incorporated.

• As has been discussed in the introduction, the SM gauge group has a rank four and the simple groups which contain complex representations of rank four are just SU(3) × SU(3) and SU(5).
• Further, the fermions of the Standard Model can be arranged in terms of the fundamental ¯5 and the anti-symmetric 10 representation of the SU(5) [30].
• To begin with, let us study the fermion masses in the prototype SU(5).Given that fermions are in 5 and 10 representations
• We conclude that the scalars that form Yukawa couplings are:
• It is easy to check that this combination of the representations is anomaly free. The gauge theory of SU(5) contains 24 gauge bosons.
• They are decomposed in terms of the standard model gauge group SU(3) × SU(2) × U(1) as: 24 = (8, 1) + (1, 3) + (1, 1) + (3, 2) + (¯3, 2) (10)
• The first component represents the gluon fields (G) mediating the colour, the second one corresponds to the Standard Model SU(2) mediators (W) and the third component corresponds to the U(1) mediator (B).
• The fourth and fifth components carry both colour as well as the SU(2) indices and are called the X and gauge bosons. Schematically, the gauge bosons can be represented in terms of the 5 × 5 matrix:

Notice that in this case the couplings of the triplets to the fermions is not related to the fermion massesas the Higgs triplets are now a mixing between the triplets in the 5H and the triplets in the 50. Thereforewe have some unknown Yukawa coupling Y50. (Flavour Physics and Grand Unification - pdf)

We analyze a simple extension of the Standard Model (SM) with a dark sector composed of a scalar and a fermion, both singlets under the SM gauge group but charged under a dark sector symmetry group.

• Sterile neutrinos, which are singlets under both groups, mediate the interactions between the dark sectorand the SM particles, and generate masses for the active neutrinos via the seesawmechanism.
• We explore the parameter space region where the observed Dark Matter relic abundance is determined by the annihilation into sterile neutrinos, both for fermion and scalar Dark Matter particles. The scalar Dark Matter case provides an interesting alternative to the usual Higgs portal scenario.

We also study the constraints from direct Dark Matter searches and the prospects for indirect detectionvia sterile neutrino decays to leptons, which may be able to rule out Dark Matter masses below and around 100 GeV. (Sterile Neutrino portal to Dark Matter II - pdf)

If the angle was 0, the U(1) group would remain unbroken and there would be no mixing with the SU(2) group. This would lead to a single massless boson and 3 remaining massless bosons: Ws and photon. On the other hand, if the angle was 90, the SU(2) group would remain unbroken and there would be no mixing with the U(1) group. This would lead to a single massive boson and 3 remaining massless bosons: Ws and photon. (PhysicsForums)

The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play an important role. The cosmological reflection of particle symmetry and the mechanisms of its breaking are the subject of the present review. (MDPI)

When the standard three-neutrino theory is considered, the matrix is 3×3. If only two neutrinos are considered, a 2×2 matrix is used. If one or more sterile neutrinos are added, it is 4×4 or larger. (Wikipedia)

There are four (4) main features of QCD confinement, which appear to parallel the development of the previous section.

• These parallels are best specified with reference to baryons, as follows: Establish any closed surface over a baryon source density P. Then:
• While gluons may flow within the closed surface across various open surfaces, there can be no net flux of gluons in to or out of any closed surface.
• This may possibly be represented by = 0 dG , and the invariance of F → F’ = F under the transformation F → F’= F − dG .
• While quarks may flow within the closed surface across various open surfaces, there can be no net flux of individual quarks in to or out of any closed surface.
• This may possibly be represented by the invariance of P → P’= P under the transformation F → F’= F − dG .
• While there can be no net flux of individual quarks in to or out of any closed surface, there can indeed be a net flux of quark-antiquark pairs in to or out of any closed surface.
• The antiquark cancels the quark, thereby averting a net flux, and in this way, quarks do flow in to or out of the closed surface, but only paired with antiquarks, as mesons.
• This may possibly be represented as 02 ≠ i gG .
• It does not matter how hard or in what manner one “smashes” a baryon, one can still never extract a net flux of quarks or a net flux of gluons, but only a large number of meson jets.
• This may be possibly represented by the fact that in all of the foregoing, the volume and surfaceintegrals apply to any and all closed surfaces.
• One can choose a small closed surface, a large closed surface, a spherical closed surface, an oblong closed surface, and indeed, a closed surface of any shape and size. The choice of closed surface does not matter.
• These mathematical rules for what does and does not flow across any closed surface, in fact, thereby impose very stringent dynamical constraints on the behaviors of these non-Abelian magnetic sources: No matter what flows across various open surfaces, they may never be a net flux of anything across any closedsurface. The only exceptions, which may flow across a closed surface, are physical entities represented by.

Where is the author going with this?

• The magnetic three-form P, and its associated third-rank antisymmetric tensorσµν P , has allthe characteristics of a baryon current density.
• These σµν P , among their other properties, are naturally occurring sources containing exactlythree fermions. These constituent fermions are most-sensibly interpreted as quarks.
• The surface symmetri F → F’ = F under the transformation F → F’= F − dG , tells us that there is no net flow of gluons across any closed surface over the baryon density.
• The volume symmetry
  P → P’= P under F → F’= F − dG , tells us that there is no net flow of quarks across any closed surface over the baryon density.
• The physical entities represented by 2 igG , when examined in further detail, have thecharacteristics of mesons.

It tells us that mesons are the only entities which may flow across any closedsurface of the baryon density. (Lab Notes)

Only more accurate analysis on the involved spectra and on the relative brightness of the two rings, and mainly the discovery of other double rings systems, could be used to finally choose which among these two interpretations is more likely to hold. As to using Klein bottle holes to check the physical existence of other universes, it appears just a matter of time to find a double truncated spiral blurred enough to clearly show a connection with other universes. (Observing another Universe - pdf)

The GUT group E6 contains SO(10), but models based upon it are significantly more complicated. The primary reason for studying E6 models comes from E8 × E8 heterotic string theory. (Wikipedia)

While gravitons are presumed to be massless, they would still carry energy, as does any other quantum particle. Photon energy and gluon energy are also carried by massless particles.

• It is unclear which variables might determine graviton energy, the amount of energy carried by a single graviton.
• Alternatively, if gravitons are massive at all, the analysis of gravitational waves yielded a new upper bound on the mass of gravitons.
• The graviton’s Compton wavelength is at least 1.6×10^16 m, or about 1.6 light-years, corresponding to a graviton mass of no more than 7.7×10−23 eV/c2.[22]
• This relation between wavelength and mass-energy is calculated with the Planck–Einstein relation, the same formula that relates electromagnetic wavelength to photon energy.
• However, if gravitons are the quanta of gravitational waves, then the relation between wavelength and corresponding particle energy is fundamentally different for gravitons than for photons, since the Compton wavelength of the graviton is not equal to the gravitational-wave wavelength.
• Instead, the lower-bound graviton Compton wavelength is about 9×109 times greater than the gravitational wavelength for the GW170104 event, which was ~ 1,700 km. The report[22] did not elaborate on the source of this ratio.

It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way. (Wikipedia)

As Penrose points out, proton decay is a possibility contemplated in various speculative extensions of the Standard Model, but it has never been observed. Moreover, all electrons must also decay, or lose their charge and/or mass, and no conventional speculations allow for this.

In his Nobel Prize Lecture video, Roger Penrose moderated his previous requirement for no mass, beginning at 26:30 in the video, allowing some mass particles to be present as long as the amounts are insignificant with nearly all of their energy being kinetic, and in a conformal geometry dominated by photons. (Wikipedia)

The Prime Spiral Sieve possesses remarkable structural and numeric symmetries.

• For starters, the intervals between the prime roots (and every subsequent row or rotation of the sieve) are perfectly balanced, with a period 8 difference sequence of: {6, 4, 2, 4, 2, 4, 6, 2}. The entire domain can thus be defined as 1 {+6 +4 +2 +4 +2 +4 +6 +2} {repeat … ∞}.
• As we’ve already suggested, the number 30 figures large in our modulo 30 domain. The Prime Spiral Sieve is Archimedean in that the separation distance between turns equals 30, ad infinitum. The first two rotations increment as follows:
• Interestingly, the sum of the 2nd rotation = 360, the product of the first three primorials, 2 x 6 x 30 = 360, and when you multiply the first five Fibonacci numbers in sequence, you produce 1, 2, 6 and 30? And, speaking of the Fibonacci number sequence, there is symmetry mirroring the above in the relationship between the terminating digits of Fibonacci numbers and their index numbers equating to members of the array populating the Prime Spiral Sieve:
• Remarkably, the sequence of Fibonacci terminating digits indexed to our domain (natural numbers not divisible by 2, 3 or 5), 13,937,179 (see graphic, above), is a prime number and a member of a twin prime pair (with 13,937,177). In case you’re wondering, 13,937,179 is not a reversible prime (as the reversal is a semi-prime: 9,461 x 10,271 = 97,173,931). However, given all the repunits that follow, we take note that both of the reversal’s factors are congruent to 11 (mod 30 & 90). [Note: Repunits are abbreviated Rn, where n designates the number of unit 1’s. Thus 1 is R1 and 11 is R2.]
• Perhaps most remarkable of all, 13,937,179 when added to its reversal 97,173,931 = 111,111,110 (in strict digital root terms, the sum is 11,111,111, or R8) and the entire repeating (and palindromic) Fibo sequence end-to-end (equivalent to two rotations around the sieve) gives you this palindromic equivalency: 1,393,717,997,173,931 ≌ 11,111,111 (mod 111,111,110)… (and interestingly, 11,111,111 * 111,111,110 = 123456776543210).
• Another point of interest: the terminating digits of the first 8 Fibonacci numbers indexed to our domain (13937179) contain two each 1’s, 3’s, 7’s, and 9’s. This is also true of the terminating digits of the first eight members of our domain (17137939).
• Echoing the Fibonacci patterns just described, the terminating digits of the prime roots (17,137,939), when added to their reversal (93,973,171) = 111,111,110. [And note that 111,111,111 * 111,111,110 = 12345678876543210.].
• Yet another related dimension of symmetry: The terminating digits of the prime root angles (24,264,868; see illustration of Prime Spiral Sieve) when added to their reversal (86,846,242) = 111,111,110, not to mention this sequence possesses symmetries that dovetail perfectly with the prime root and Fibo sequences.

And when you combine the terminating digit symmetries described above, capturing three (3) rotations around the sieve in their actual sequences, you produce the ultimate combinatorial symmetry. (PrimesDemystified)

Here is an elegant model to define the elementary particles of the Standard Model in Physics.

• The black spheres are the bosons, the green ones leptons and the rest of the colored ones Murray Gell-Mann’s quarks (red for Generation I, blue for II and orange for III).
• Higgs Boson (aka the God particle) that does not have charge is the vertex between the matter and anti-matter particles.
• The z-boson and its counterpart would lie in the centroids of the tetrahedrons created by folding the triangles to meet up at the Higgs particle.

The next step is to re-gigg the model to account for the collisions and annihilations. Gluons and Photons that don’t have mass are not in the model, but will be the consequences of the interactions. (Hypercomplex-Math)

In physical cosmology, the baryon asymmetry problem, also known as the matter asymmetry problem or the matter–antimatter asymmetry problem,[1][2] is the observed imbalance in baryonic matter (the type of matter experienced in everyday life) and antibaryonic matter in the observable universe.

• Neither the standard model of particle physics nor the theory of general relativity provides a known explanation for why this should be so, and it is a natural assumption that the universe is neutral with all conserved charges.[3]
• The Big Bang should have produced equal amounts of matter and antimatter. Since this does not seem to have been the case, it is likely some physical laws must have acted differently or did not exist for matter and/or antimatter.

Several competing hypotheses exist to explain the imbalance of matter and antimatter that resulted in baryogenesis. However, there is as of yet no consensus theory to explain the phenomenon, which has been described as “one of the great mysteries in physics“. (Wikipedia)

Consider a (purple) world-line String of one World of the MacroSpace of Many-Worlds and its interactions with another (gold) world-line World String, from the point of view of one point of the (purple) World String, seen so close-up that you don’t see in the diagram that the (purple) and (gold) World Strings are both really closed strings when seen at very large scale:

• massless spin-2 Gravitons travel along the (red) MacroSpace light-cones to interact with the intersection points of those (red) light-cones with the (gold) World String;
• scalar Dilatons, with effectively real mass, travel within the (yellow) MacroSpace light-cone time-like interior to interact with the intersection region of the (yellow) light-cone time-like interior region with the (gold) World String; and
• Tachyons, with imaginary mass, travel within the (cyan) MacroSpace light-cone space-like exterior to interact with the intersection points of the (cyan) light-cone space-like exterior region with the (gold) World String.
• Metod Saniga, inphysics/0012033 D4-D5-E6-E7-E8 VoDou Physics Model: It is a well-known fact that on a generic cubic surface, K3, the lines are seen to form three (3) separate groups.
• The first two groups, each comprising six (6)lines, are known as Schlafli’s double-six. The third group consists of fifteen lines. The basics of the algebra can simply be expressed as 27 = 12 + 15.

Note that Gravity may not propagate in the 26 dimensions of the MacroSpace of the Many-Worlds in exactly the same way as it propagates in our 4-dimensional physical SpaceTime. (Tony Smith’s)

Supersymmetry predicts that each of the particles in the Standard Model has a partner with a spin that differs by half of a unit.

• So bosons are accompanied by fermions and vice versa.
• Linked to their differences in spin are differences in their collective properties.
• Fermions are very standoffish; every one must be in a different state.
• On the other hand, bosons are very clannish; they prefer to be in the same state.

Fermions and bosons seem as different as could be, yet supersymmetry brings the two types together.

Each of the 3 Octonionic dimenisons of J3(O)o having the following physical interpretation:

• 4-dimensional physical spacetime plus 4-dimensional internal symmetry space;
• 8 first-generation fermion particles; 8 first-generation fermion anti-particles.

Thus the 26 dimensions stand as the degrees of freedom of the Worlds of the Many-Worlds. (Tony’s Web Book - pdf (800MB Size)).

In the Standard Model, elementary particles are manifestations of three “symmetry groups” — essentially, ways of interchanging subsets of the particles that leave the equations unchanged.

• These three (3) symmetry groups, SU(3), SU(2) and U(1), correspond to the strong, weak and electromagnetic forces, respectively, and they “act” on six types of quarks, two types of leptons, plus their anti-particles, with each type of particle coming in three copies, or “generations,” that are identical except for their masses.
• The fourth fundamental force, gravity, is described separately, and incompatibly, by Einstein’s general theory of relativity, which casts it as curves in the geometry of space-time.

Note that both quarks and leptons exist in three distinct sets. Each set of quark and lepton charge types is called a generation of matter (charges +2/3, -1/3, 0, and -1 as you go down each generation). The generations are organized by increasing mass.

Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space. The brighter areas represent a higher probability of finding the electron (Wikipedia).

1729th decimal digit holds significance in the decimal representation of the transcendental number e. From 1729th digit you can get the first occurrence of all ten digits consecutively and they are 0719425863. (Ramanujan taxicab 1729 - pdf)

Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed (Wikipedia)

Wave–particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances.[1]: 59  It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects.

During the 19th and early 20th centuries, light was found to behave as a wave, and then later discovered to have a particulate character, whereas electrons were found to act as particles, and then later discovered to have wavelike aspects. The concept of duality arose to name these contradictions. (Wikipedia)

Dark energy is one of the greatest mysteries in science today.

• We know very little about it, other than it is invisible, it fills the whole universe, and it pushes galaxies away from each other. This is making our cosmos expand at an accelerated rate. But what is it?
• One of the simplest explanations is that it is a cosmological constant – a result of the energy of empty space itself – an idea introduced by Albert Einstein.

Many physicists aren’t satisfied with this explanation, though. They want a more fundamental description of its nature. Is it some new type of energy field or exotic fluid? (The Conversation).

Discussing both open and closed bosonic strings, Soo-Jong Rey, in his paper Heterotic M(atrix) Strings and Their Interactions - pdf, says: We would like to conclude with a highly speculative remark on a possible:

• It is well-known that The regularizedone-loop effective action of d-dimensional Yang-Mills theory. For d=26, the gauge kinetic term does not receive radiative correction at all.
• We expect that this non-renormalization remains the same even after dimensional reductions. One may wonder if it is possible to construct for bosonic string as well despite the absence of supersymmetry and BPS states.
• M(atrix) theory description of bosonic strings bosonic Yang-Mills theory in twenty-six dimensions is rather special M(atrix)string theory. The bosonic strings also have D-brane extended solitons, whose tension scales as 1/gB for weak string coupling gB « 1.
• Given the observation that the leading order string effective action of and antisymmetric tensor field may be derived from Einstein’s Gravity in d = 27, let us make an assumption that the 27-th quantum dimension decompactifies as the string coupling gB becomes large. For D0-brane, the dilaton exchange force may be interpreted as the 27-th diagonal component of d = 27 metric.
• Gravi-photon is suppressed by compactifying 27-th direction on an rather than on a circle. Likewise, its mass may be interpreted as 27-th Kaluza-Klein momentum of a massless excitation in d = 27.

In the infinite boost limit, the light-front view of a bosonic string is that infinitely many D0-branes are threaded densely on the bosonic string. (26 Dimensions of Bosonic String Theory - pdf)

Einstein in 1916 proposed the existence of gravitational waves as an outgrowth of his ground-breaking general theory of relativity, which depicted gravity as the distortion of space and time by matter. Until their detection in 2016, scientists had found only indirect evidence of their existence, beginning in the 1970s. The gravitational wave signal was observed in 15 years’ worth of data obtained by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) Physics Frontiers Center (PFC), a collaboration of more than 190 scientists from the United States and Canada. (Reuters)

Month, a measure of time corresponding or nearly corresponding to the length of time required by the Moon to revolve once around the Earth.

• The synodic month, or complete cycle of phases of the Moon as seen from Earth, averages 29.530588 mean solar days in length (i.e., 29 days 12 hours 44 minutes 3 seconds); because of perturbations in the Moon’s orbit, the lengths of all astronomical months vary slightly.
• The sidereal month is the time needed for the Moon to return to the same place against the background of the stars, 27.321661 days (i.e., 27 days 7 hours 43 minutes 12 seconds); the difference between synodic and sidereal lengths is due to the orbital movement of the Earth–Moon system around the Sun.
• The tropical month, 27.321582 days (i.e., 27 days 7 hours 43 minutes 5 seconds), only 7 seconds shorter than the sidereal month, is the time between passages of the Moon through the same celestial longitude.
• The draconic, or nodical, month of 27.212220 days (i.e., 27 days 5 hours 5 minutes 35.8 seconds) is the time between the Moon’s passages through the same node, or intersection of its orbit with the ecliptic, the apparent pathway of the Sun.

As a calendrical period, the month is derived from the lunation—i.e., the time elapsing between successive new moons (or other phases of the moon). A total of 12 lunations amounts to 354 days and is, roughly, a year. (Britannica)

The described Multiverse expansion creates huge parallel Multiverse bubbles with periodic parallel +m matter and periodic –m antimatter clusters, distributed on the bubbles walls.

• Fig. 13a shows parallel Universes/Anti-universe W2n / W2n+1.
• Fig. 13b shows repulsive antigravity between all the nearest matter/antimatter waveguides, e.g. between W-1 (antimatter), W+1 (antimatter) and our matter W0 Galaxies.
• Fig. 13c shows attractive Рravitв betаeen the nearest “dark” waveguides (e.g. between W-2 Dark Matter, W+2 Dark Matter) and our Matter W0 Galaxies.

The visible W-1 (antimatter), W+1 (antimatter) Universes are adjacent to the W0 (our matter)-Universe and have two joint framing membranes M0 and M-1, carrying two joint electrostatic potentials. (Gribov_I_2013 - pdf)

Prof Stephen Hawking’s final research paper suggests that our Universe may be one of many similar (BBC News).

The 26-dimensional traceless subalgebra J3(O)o is arepresentation of the 26-dim Theory of Unoriented Closed Bosonic Strings produces a Bohm Quantum Theory with geometry of E6 / F4. The E6 of the can be represented in terms of:

• 3 copies of the 26-dimensional traceless subalgebra J3(O)o of the 27-dimensional J3(O) by using the of 78-dimensional E6 over 52-dimensional F4 and the structure of based on the 26-dimensional representation of.
• In this view, Lie algebra D4-D5-E6-E7-E8 VoDou Physics model Jordan algebra fibration E6/F4 F4 as doubled J3(O)o F4

In order to reproduce the known spectrum of weakly coupled bosonic string theory, bosonic M theory will have to contain an additional field besides the 27 dimensional gravitational field, namely a three-form potential CFT. (PhiloPhysics - pdf)

Leptons do not interact via the strong interaction.

• Their respective antiparticles are the antileptons, which are identical, except that they carry the opposite electric charge and lepton number.
• The antiparticle of an electron is an antielectron, which is almost always called a “positron” for historical reasons.
• There are six leptons in total; the three charged leptons are called “electron-like leptons”, while the neutral leptons are called “neutrinos”.
• Neutrinos are known to oscillate, so that neutrinos of definite flavor do not have definite mass, rather they exist in a superposition of mass eigenstates.

The hypothetical heavy right-handed neutrino, called a “sterile neutrino”, has been omitted. (Wikipedia)

There are 28 octonion Fano plane triangles that correspond directly to the 28 Trott quartic curve bitangents.

• These bitangents are directly related to the Legendre functions used in the Shroedinger spherical harmonic electron orbital probability densities.
• Shown below is a graphic of these overlaid onto the n=5, l=2, m=1 element, which is assigned to gold (Au).
• When using an algorithm based on the E8 positive algebra root assignments, the “flipped” Fano plane has E8 algebra root number 79 (the atomic number of Au) and split real even group number of 228 (in Clifford/Pascal triangle order).
• This matrix is shown to be useful in providing direct relationships between E8 and the lower dimensional Dynkin and Coxeter-Dynkin geometries contained within it, geometries that are visualized in the form of real and virtual 3 dimensional objects.
• A direct linkage between E8, the folding matrix, fundamental physics particles in an extended Standard Model Gravi GUT, quaternions, and octonions is introduced, and its importance is investigated and described.
• E8 and its 4D children, the 600-cell and 120-cell (pages on which I have some work, amongst others) and its grandkids (2 of the 3D 5 Platonic Solids, one of which is the 3D version of the 2D Pentagon) are all related to the Fibonacci numbers and the Golden Ratio.
• And finally, the {7, 8} dimensions in physics can be identified with quark color, as {7} preserves the blue quark positions, while {8} moves the dual concentric rings of quarks while preserving their relative positions within the rings. It is interesting t note that the dimensions {6, 7, 8} are appropriately labeled {r, g, b} in SRE coordinates, since in this projection the SRE math coordinates are located at the afforementioned 6 triple overlap points at center of the quark’s {r, g, ¯ g, b, ¯ ¯b} concentric rings (the intersection of the gluons triality lines)

So that kind of explains why most of my 2D art, 3D objects and sculptures (e.g. furniture like the dodecahedron table below), and 4D youtube animations all use the Golden Ratio theme. (E8 to H4 folding matrix - pdf)

The natural next step is to generalise this to D = 3, 4, 6, 10 and obtain a ‘magic pyramid’ with the D = 3 magic square at the base and Type II supergravity at the summit. On the basis of these results we speculate that the part played by octonions in string and M-theory may be more prominent than previously though. (Super Yang-Mills - pdf)

In this article, we investigated the phenomenology of triplet Higgs bosons in the simplest A4-symmetric version of the Higgs Triplet Model (A4HTM). The A4HTM is a four-Higgs- Triplet-Model (δ of 1 and (∆x, ∆y, ∆z) of 3).

• Four mass eigenstates of doubly charged Higgs bosons, H±±i, are obtained explicitly from the Higgs potential.
• We also obtained four mass eigenstates of the triplet-like singly charged Higgs bosons, H±T i, for which doublet components can be ignored because of small triplet vev’s.
• It was shown that the A4HTM gives unique predictions about their decay branching ratios into two leptons (H−−i → ℓℓ′ and H−iT → ℓν); for example, the leptonic decays of H−−2 are only into µµ and eτ because an approximate Z3 symmetry remains, and the ratio of the branching ratios is 2 : 1 as a consequence of the A4 symmetry in the original Lagrangian.
• Therefore, it will be possible to test the model at hadron colliders (Tevatron and LHC) if some of these Higgs bosons are light enough to be produced.
• Even if these Higgs bosons are too heavy to be produced at hadron colliders, they can affect the lepton flavor violating decays of charged leptons if the triplet Yukawa coupling constants are large enough.
• It was shown that there is no contribution of these Higgs bosonsto µ → eee ¯ and ℓ → ℓ′γ.
• Thus, we can naturally expect signals of τ → µee and τ → eµµ(which are possible in this model among six τ → ℓℓ′ℓ′′) in the future in collider experiments (Super-KEKB, super B factory, super flavor factory, and LHCb) without interfering with a stringent experimental bound on µ → eee ¯ . This model will be excluded if ℓ → ℓ ′γ is observed.

We considered current experimental constraints on the model and prospects of the measurement of the non-standard neutrino interactions (NSI) in the neutrino factory. If H±±2 or H±±3 is lighter enough than other H±±i, effects of the NSI can be around the expected sensitivity in the neutrino factory. (Triplet Higgs bosons - pdf)

The discovery of neutrino oscillations indicates that the Standard Model is incomplete, but there is currently no clear evidence that nature is described by any Grand Unified Theory. Neutrino oscillations have led to renewed interest toward certain GUT such as SO(10). (Wikipedia)

This paper seeks to examine several extended SUSY Yang-Mills Theories on the 0-Brane by obtaining the L and R matrices, generate the corresponding adinkra, and studying their correlators.

• The transformation laws of the on-shell 10D, N=1 Super Yang-Mills Theory are given, and the SUSY algebra is shown to exhibit closure when the equations of motion are satisfied.
• The closure of the algebra for the 4D N=4 theory was calculated using new computational methods.

The resulting adinkra matrices and SUSY algebra structure are investigated for these theories, and from this comparisons are made.

Supersymmetry (SUSY) is a space-time symmetry which relates fermions and bosons. It predicts superpartners for every known particle with identical quantum numbers except the spin which differs by 1/2 and thus offers a solution to several open problems of the standard model (SM).

• As no superpartners with SM mass has been observed, SUSY must be broken. The Minimal Supersymmetric Standard Model (MSSM) with the most general SUSY breaking potential adds more than 100 new parameters.
• To decrease the number of parameters, specific SUSY breaking scenarios are considered assuming that spontaneous symmetry breaking in a hidden sector is mediated by some interaction to the visible sector.

When the mediators are gauge interactions, we arrive to Gauge Mediated Supersymmetry Breaking models (GMSB, 5 parameters) or to its generalization, General Gauge Mediation (GGM, 8 parameters)

In this paper, we have extended our previous discussions about using HYMNs (height-yielding matrix numbers) which are the eigenvalues [14] of functions of the adjacency matrices associated with the L-matrics and R-matrices derived from adinkras. (Properties of HYMNs - pdf)

Only then may we obtain the L and R matrices, which we use to generate adinkras. The adinkra that is generated from a set of adinkra matrices in Super Yang-Mills Theory is shown below

Inspired by the history of how Einstein constructed General Relativity, we study the linearized Nordstrom supergravity in 10- and 11-dimensional superspaces.

• Valise adinkras, although an important subclass, do not encode all information present when a 4D supermultiplet is reduced to 1D. We extend this to non-valise adinkras providing a complete eigenvalue classification via Python code.
• We found no obstacles to applying the lessons we learned in 4D to higher dimensions. We also derive infinitesimal 10D superspace Weyl transformation laws. The identification of all off-shell ten-dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions.
• We realize that Lie Algebra techniques, in particular branching rules, Plethysm, and tensor product, provide the key to deciphering the complete list of independent fields that describe a supersymmetric multiplet in arbitrary spacetime dimensions efficiently.
• Thus, adinkra-based arguments suggest the surprising possibility that the 11D, N=1 scalar superfield alone might describe a Poincare supergravity prepotential or semi-prepotential in analogy to one of the off-shell versions of 4D, N=1.
• All of these results strongly suggest adynkras are pointing in the direction of using series expansion in terms of Young Tableaux (YT’s) as a tool to gain the most fundamental mathematical understanding of this class of problems.

We show the explicit one-to-one correspondence between Lorentz irreps and field variables, leading to an adynkrafield formalism in which the traditional ζ (theta)-monomials are replaced by YT’s as shown below. (YangruiHu.com)

All of these results strongly suggest adynkras are pointing in the direction of using series expansion in terms of YT’s as a tool to gain the most fundamental mathematical understanding of this class of problems. (Higher-Dimensional Supergravity - Pdf)

The similarity between Adinkra in supersymmetry and Adinkra symbols is that they are both graphical representations with hidden meanings (Prof. Sylvester James Gates Jr.). (Adinkra Alphabet)

We have shown that the SU(2)L triplet Higgs suggested by the CDF W -boson mass anomaly, significantly improve the gauge coupling unification compared to the SM case if the triplet Higgs is a complex field and exists around the TeV scale.

• This leads to the three SM gauge couplings unifying rather precisely at around 1014 GeV. The light SU(2)L triplet Higgs required by the gauge coupling unification can be realized consistently within the framework of SU(5) grand unified theory (see Appendix B).
• This complex triplet Higgs contains one CP-even Heavy Higgs, one CP-odd Higgs and two charged Higgs bosons, which could be the smoking gun single of this scenario.
• Although the unification scale around 1014 GeV is too low, in the usual sense, leading to significant proton decay constraints, we have shown that the constrains can be avoided by introducing additional vector-like fermions which mix with the SM fermions through an SU(5) breaking mass term.
• Importantly, the minimal requirement is quite simple and only requires the addition of a single pair of 10 and 10 fermions to mix with the first generation 10 matter multiplet.
• To get enough suppression in the proton decay rate, the SU(2)L singlet quark should have significant mixing with the vector-like fermion while SU(2) doublet quark should have almost zero mixing with it (or vice versa).
• Interestingly, this leads to a suppression in the proton decay mediated by X gauge bosons but leads to a significant enhancement in the proton decay through the colored Higgs boson. This means that if nature is realized by this minimal model, it is bound to show up in proton decay experiments eventually.
• Although this model has some additional fine tuning, the fine-tuning of the fermion masses is similar in nature to the doublet-triplet splitting present in all GUT models.

Since the fine-tuning for all the fields in our model, including the light complex SU(2)L triplet, are similar in design to the doublet-triplet splitting, it is possible that all the required tuning of this GUT theory is solved by a single lmechanism, e.g. product group unification scenarios. (W boson mass anomaly and grand unification - pdf)

In addition, the Standard Model involves gauge bosons (photons for the electromagnetic interaction, W and Z for the weak interaction, and eight (8) gluons for the strong interaction), plus the (scalar) Higgs particle. This is what all known matter in the Universe consists of. (Netrinos)

Recently, the CMS and ATLAS Collaborations reported observations of the Higgs boson produced in association with a top quark pair thus representing the first direct measurements of the Higgs boson coupling to quarks. - This week the CMS Collaboration announces another major achievement and reports the observation of Higgs boson decay to bottom quarks (H→ bb)

• A precise measurement of the rate of the H→ bb process directly tests the Yukawa coupling of the Higgs boson to a down-type quark, and is necessary to solidify the Higgs boson as the possible sole source of mass generation in the fermion sector of the Standard Model (SM).
• While the decay of the Higgs boson to bottom quarks is the most frequent of all Higgs boson decays, it has been a real experimental challenge to observe it. This is on account of the overwhelmingly large background contribution from a number of other SM processes that can mimic its experimental signature characterized by the appearance of a bottom and an anti-bottom quark.

The CMS Collaboration overcame this challenge by deploying modern sophisticated analysis tools and by focusing on particular signatures where a Higgs boson is produced in association with a vector boson V (a W or Z particle), a weak interaction process known as VH(bb), shown in the figure below, leading to a significant reduction in the background. (CERN)

Since right-handed neutrinos appear naturally in the grand unified model based on the group SO(10) [5], it is of interest to discuss leptogenesis under the constraints suggested by such a model.

• It turns out, however, that such constraints render a successful leptogenesis extremely difficult to obtain.
• This happens because, unless a fine tuning on the neutrino mass parameters is introduced, the right-handed neutrinos become very hierarchical in mass, with the lowest mass being too small to allow for leptogenesis.

A compactness in the right-handed neutrino mass spectrum is, however, able to overcome this difficulty and achieve a consistent leptogenesis. (Neutrino Phenomenology and Leptogenesis - pdf)

Our framework features the minimum of three (and maximum of five) light Higgs doublets at the electroweak scale providing a Cabibbo mixing consistent with the top-charm and bottom-strange mass hierarchies as well as massless first-generation quarks at tree-level. (Prospects for new physics)

The present particle physics or standard model based on the “unreal gauge transformation symmetry” and meaningless math cannot explain any actual physical mechanism at all (biglobe.ne.jp)

All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold. (An Exceptionally Simple Theory of Everything - pdf)

Supersymmetry and more specifically supergravity grand unification allow one to extrapolate physics from the electroweak scale up to the grand unification scale consistent with electroweak data.

• Here we give a brief overview of their current status and show that the case for supersymmetry is stronger as a result of the Higgs boson discovery with a mass measurement at ∼ 125 GeV consistent with the supergravity grand unification prediction that the Higgs boson mass lie below 130 GeV. Thus the discovery of the Higgs boson and the measurement of its mass provide a further impetus for the search for sparticles to continue at the current and future colliders.
• The group SO(10) as the framework for grand unification appears preferred over SU(5). The group SO(10) contains both G(4, 2, 2) and SU(5)⊗U(1) as subgroups, i.e., SO(10) has the branchings SO(10) → SU(4)C ⊗ SU(2)L ⊗ SU(2)R and SO(10) → SU(5) ⊗ U(1).
• It possesses a spinor representation which is 2⁵ = 32 dimensional and which splits into 16 ⊕ 16. A full generation of quarks and leptons can be accommodated in a single 16 plet representation. Thus the 16 plet has the decomposition in SU(5) ⊗ U(1) so that 16 =10(−1) ⊕ 5(3) ⊕ 1(−5).
• As noted the combination 5 ⊕ 10 in SU(5) is anomaly free and further 1(−5) in the 16-plet decomposition is a right handed neutrino which is a singlet of the standard model gauge group and thus the 16-plet of matter in SO(10) is anomaly free.
• The absence of anomaly in this case is the consequence of a more general result for SO(N) gauge theories. Thus in general anomalies arise due to the non-vanishing of the trace over the product of three group generators in some given group representation Tr ({Ta, Tb}Tc).
• For SO(10) one will have Tr ({Σµν, Σαβ}Σλρ). However, there is no invariant tensor to which the above quantity can be proportional which then automatically guarantees vanishing of the anomaly for SO(10). This analysis extends to other SO(N) groups.
• One exception is SO(6) where there does exist a six index invariant tensor ǫµναβλρ and so in this case vanishing of the anomaly is not automatic.
• The group SO(10) is rank 5 where as the standard model gauge group is rank 4. The rank of the group can be reduced by either using 16 ⊕ 16 of Higgs fields or 126 ⊕ 126 of Higgs.
• Since under SU(5) ⊗ U(1) one has 16 ⊃ 1(−5) we see that a VEV formation for the singlet will reduce the rank of the group. Similarly 126 ⊃ 1(−10) under the above decomposition. Thus when the singlets in 16 ⊕ 16 of Higgs or 126 ⊕ 126 get VEVs, the SO(10) gauge symmetry will break reducing its rank.
• However, we still need to reduce the remaining group symmetry to the Standard Model gauge group. For this we need to have additional Higgs fields such as 45, 54, 210. Further to get the residual gauge group SU(3)C ⊗ U(1)em we need to have 10 -plet of Higgs fields.
• Thus the breaking of SO(10) down to SU(3)C ⊗ U(1)em requires at least three (3) sets of Higgs representations: one to reduce the rank, the second to break the rest of the gauge group to the Standard Model gauge group and then at least one 10-plet to break the electroweak symmetry.
• As discussed above one can do this by a combination of fields from the set: 10, 16 ⊕ 16, 45, 54, 120, 126 ⊕ 126, 210.
• To generate quark and lepton masses we need to couple two 16-plets of matter with Higgs fields. To see which Higgs fields couple we expand the product 16⊗16 as a sum over the irreducible representations of SO(10).

Here we have 16 ⊗ 16 = 10s ⊕ 120a ⊕ 126s, where the s(a) refer to symmetric (anti-symmetric) under the interchange of the two 16-plets. The array of Higgs bosons available lead to a large number of possible SO(10) models. (Superunification - pdf)

I am pleased to announce the availability of splitFano.pdf, a 321 page pdf file with the 3840=480*8 split octonion permutations (with Fano planes and multiplication tables).

• There are 30 canonical sets of 7 triads indexed with a Fano plane index (fpi) in (16). As in E8 with 16 of the 2⁸ = 256 binary representations excluded from the group, there are 32 excluded octonions from the 2⁹ = 512.
• As in E8, excluded particles are associated with the color=0, generation=0 (bosons) which are the positive (and negative) generators commonly associated with the 8-orthoplex with 16 permutations of {±1, 0, 0, 0, 0, 0, 0, 0}.
• These are organized into “flipped” and “non-flipped” pairs associated with the 240 assigned particles to E8 vertices (sorted by Fano plane index or fPi).
• They are assigned to the 30 canonical sets of 7 triples using the maskList: {5, 8, 4, 3, 7, 6, 3, 2, 6, 5, 1, 4, 6, 7, 3, 3, 8, 6, 3, 1, 6, 6, 2, 3, 5, 8, 4, 3, 7, 6}
• There are 7 sets of split octonions for each of the 480 “parent” octonions (each of which is defined by 30 sets of 7 triads and 16 7 bit “sign masks” which reverse the direction of the triad multiplication). The 7 split octonions are identified by selecting a triad.
• The complement of {1,2,3,4,5,6,7} and the triad list leaves 4 elements which are the rows/colums corresponding to the negated elements in the multiplication table (highlighted with yellow background).
• The red arrows in the Fano Plane indicate the potential reversal due to this negation that defines the split octonions. The selected triad nodes are yellow, and the other 4 are cyan (25MB).
• These allow for the simplification of Maxwell’s four equations which define electromagnetism (aka.light) into a single equation.

Below is the first page of the comprehensive split octonion list of all 3840 Split Fano Planes with their multiplication tables available. (8×16×30 Split Fano)

The breaking chains of SO(10) to G SM are shown along with their terrestrial and cosmological signatures, where G x represents either G 3221 or G 421 . Defects with only cosmic strings (including cosmic strings generated from preserved discrete symmetries) are denoted as blue solid arrows. Those including unwanted topological defects (monopoles or domain walls) are indicated by red dotted arrows. The instability of embedded strings is not considered. Removing an intermediate symmetry may change the type of unwanted topological defect but will not eliminate them. The highest possible scale of inflation, which removes unwanted defects, is assumed in this diagram. (Gravitational Waves and Proton Decay - pdf)

It has been found recently that the expansion of N = 8 supergravity in terms of Feynman diagrams has shown that N = 8 supergravity is in some ways [1] a product of two N = 4 super Yang–Mills theories.

• This is written schematically as: N = 8 supergravity = (N = 4 super Yang–Mills) × (N = 4 super Yang–Mills). This is not surprising, as N = 8 supergravity contains six independent representations of N = 4 super Yang–Mills.
• The theory contains 1 graviton (spin 2), 8 gravitinos (spin 3/2), 28 vector bosons (spin 1), 56 fermions (spin 1/2), 70 scalar fields (spin 0) where we don’t distinguish particles with negative spin.
• These numbers are simple combinatorial numbers that come from Pascal’s Triangle and also the number of ways of writing n as a sum of 8 nonnegative cubes A173681.
• The only theories with spins higher than 2 which are consistent involve an infinite number of particles (such as String Theory and Higher-Spin Theories). Stephen Hawking in his Brief History of Time speculated that this theory could be the Theory of Everything.
• One reason why the theory was abandoned was that the 28 vector bosons which form an O(8) gauge group is too small to contain the standard model U(1) x SU(2) x SU(3) gauge group, which can only fit within the orthogonal group O(10).

For model building, it has been assumed that almost all the supersymmetries would be broken in nature,[why?] leaving just one supersymmetry (N = 1), although nowadays because of the lack of evidence for N = 1 supersymmetry higher supersymmetries are now being considered such as N = 2. (Wikipedia)