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p-Adic Physics

Note: Newest contributions are at the top!



Year 2018

Still about quark gluon plasma and M89 physics

QCD predicts that quark gluon plasma (QGP) is is created in p-p, p-A, and A-A high energy collisions. Here p denotes proton and A heavy nucleus. In the first approximation the nuclei are expected to go through each other but for high enough collision the kinetic energy of the incoming beams is expected to materialize to quarks and gluons giving rise to QGP. Various signatures of QGP such as high density, strangeness production, and the failure of quark jets to propagate have been observed.

Also unexpected phenomena such as very small shear viscosity to entropy ratio η/s meaning that QGP behaves like ideal liquid and double ridge structure detected first in p-Pb collisions implying long range correlations suggesting emission of particles in opposite directions from a linear string like object. Also the predicted suppression of charmonium production seems to be absent for heavy nuclei.

I have already earlier proposed explanation in terms of a creation of dark pions (and possibly also heavier mesons) of M89 hadron physics with Planck constant heff=512× h. M89 pions would be flux tube like structures having mass 512 times that of ordinary pion but having the same Compton length as ordinary pion and being of the same size as heavy nuclei. The unexpected features of QGP, in particular long range correlations, would reflect quantum criticality. Double ridge structure would reflect the decay of dark mesons to ordinary hadrons. In this article this proposal is discussed in more detail.

See chapter New Particle Physics Predicted by TGD: Part I or the article Still about quark gluon plasma and M89 physics.



TGD view about ANITA anomalous events

I read an article (see this) telling about 2 anomalous cosmic ray events detected by ANITA (The Antarctic Impulsive Transient Antenna) collaboration. Also ICECUBE collaboration has observed 3 events of this kind. What makes the events anomalous is that the cosmic ray shower emanates from Earth: standard model does not allow the generation of this kind of showers. The article proposes super-partner of tau lepton known as stau as a possible solution of the puzzle.

Before continuing it is good to summarize the basic differences between TGD and standard model at the level of elementary particle physics. TGD differs from standard model by three basic new elements: p-adic length scale hypothesis predicting a fractal hierarchy of hadron physics and electroweak physics; topological explanation of family replication phenomenon; and TGD view about dark matter.

  1. p-Adic length scale hypothesis states that Mersenne primes Mn and Gaussian Mersennes MG,n give rise to scaled variants of ordinary hadron and electroweak physics with mass scale proportional to Mn1/2= 2n/2. M127 would correspond to electron and possibly also to what I have called lepto-hadron physics. Muon and nuclear physics would correspond to MG,113 and τ and hadron physics would correspond to M107. Electroweak gauge bosons would correspond to M89. nG= 73, 47, 29, 19, 11,7,5,3,2 would correspond to Gaussian Mersennes and n= 61,31,19,17,13,7,5,3,2 to ordinary Mersennes. There are four Gaussian Mersennes corresponding to nG∈{151,157,163,167} in biologically relevant length scale range 10 nm-2.5 μm (from cell membrane thickness to nucleus size): this can be said to be a number theoretical miracle.
  2. The basic assumption is that the family replication phenomenon reduces to the topology of partonic 2-surfaces serving as geometric correlates of particles. Orientable topology is characterized by genus - the number of handles attached to sphere to obtain the topology. 3 lowest genera are assumed to give rise to elementary particles. This would be due to the Z2 global conformal symmetry possible only for g=0,1,2. By this symmetry single handle behaves like particle and two handles like a bound state of 2 particles. Sphere corresponds to a ground state without particles. For the higher genera handles and handle pairs would behave like a many-particle states with mass continuum.
  3. The model of family replication is based on U(3) as dynamical "generation color" acts as a combinatorial dynamical symmetry assignable to the 3 generations so that fermions correspond to SU(3) multiplet and gauge bosons to U(3) octet with lowest generation associated with U(1). Cartan algebra of U(2) would correspond to two light generations with masses above intermediate boson mass scale.

    3 "generation neutral" (g-neutral) weak bosons (Cartan algebra) are assigned with n=89 (ordinary weak bosons), nG= 79 and nG=73 correspond to mass scales m(79) = 2.6 TeV and m(73) =20.8 TeV. I have earlier assigned third generation with n=61. The reason is that the predicted mass scale is same as for a bump detected at LHC and allowing interpretation as g-neutral weak boson with m(61)=1.3 PeV.

    3+3 g-charged weak bosons could correspond to n=61 with m(61)= 1.3 PeV (or nG=73 boson with m(73) =20.8 TeV) and to nG= 47,29, 19 and n= 31,19. The masses are m(47)= .16 EeV, m(31)=256× m(47)=40 EeV, m(29)=80 EeV, m(19)= 256 EeV, m(17)= .5× 103 EeV, and m(13)= 2× 103 EeV. This corresponds to the upper limit for the energies of cosmic rays detected at ANITA.

    In TGD framework the most natural identification of Planck length would be as CP2 length R which is about 103.5 times the Planck length as it is usually identified. Newton's constant would have spectrum and its ordinary value would correspond to G= R2/&bar;effeff which &bar;effeff∼ 107. UHE cosmic rays would allow to get information about physics near Planck length scale in TGD sense!

  4. TGD predicts also a hierarchy of Planck constants heff=n× h0, h=6h0, labelling phases of ordinary matter identified as dark matter. The phases with different values of n are dark matter relative to each other but phase transitions changing the value of n are possible. The hypothesis would realize quantum criticality with long length scale quantum fluctuations and it follows from what I call adelic physics.

    n corresponds to the dimension of extension of rationals defining one level in the hierarchy of adelic physics defined by extensions of rationals inducing extensions of p-adic number fields serving as correlates for cognition in TGD inspired theory of consciousness. p-Adic physics would provide extremely simple but information rich cognitive representations of the real number based physics and the understanding of p-adic physics would be easy manner to understand the real physics. This idea was inspired by the amazing success of p-adic mass calculations, which initiated the progress leading to adelic physics.

It is natural to ask what TGD could say about the Anita anomaly serving as very strong (5 sigma) evidence for new physics beyond standard model. Consider first the basic empirical constraints on the model.
  1. According to the article. there are 2 anomalous events detected by ANITA collaboration and 3 such events detected by ICECUBE collaboration. For these events there is cosmic ray shower coming Earth's interior. Standard model does not allow this kind of events since the incoming particle - also neutrino - would dissipate its energy and never reach the detector.

    This serves as a motivation for the SUSY inspired model of the article proposing that stau, super-partner of tau lepton, is created and could have so weak interactions with the ordinary matter that it is able to propagate through the Earth. There must be however sufficiently strong interaction to make the detection possible. The mass of stau is restricted to the range .5-1.0 TeV by the constraints posed by LHC data on SUSY.

  2. The incoming cosmic rays associated with anomalous events have energies around εcr=.5× 1018 eV. A reasonable assumption is that the rest system of the source is at rest with respect to Earth in an energy resolution, which corresponds to a small energy EeV scale. No astrophysical mechanism producing higher energy cosmic rays about 1011 GeV based on standard physic is known, and here the p-adic hierarchy of hadron physics and electroweak physics suggests mechanisms.
In TGD framework the natural question is whether the energy scale correspond to some Mersenne or Gaussian Mersenne so that neutrino and corresponding lepton could have been produced in a decay of W boson labelled by this prime. By scaling of weak boson mass scale Gaussian Mersenne MG,47 =(1+i)47-1 would correspond to a weak boson mass scale m(47)= 2(89-47)/2× 80 GeV = .16 EeV. This mass scale is about roughly a factor 1/3 below the energy scale of the incoming cosmic ray. This would require that the temperature of the source is at least 6× m(47) at source if neutrino is produced in the decay of MG,47 W boson. This option does not look attractive to me.

Could cosmic rays be (possibly dark) protons of MG,47 hadron physics.

  1. The scaling of the mass of the ordinary proton about mp(107)≈ 1 GeV gives mp(47)= 2(107-47)/2 GeV ≈ 1 EeV! This is encouraging! Darkness in TGD sense could make for them possible to propagate through matter. In the interactions with matter neutrinos and leptons would be generated.

    The article tells that the energy εcr of the cosmic ray showers is εcr∼ .6 EeV, roughly 60 per cent the rest mass of cosmic ray proton. I do not how precise the determination of the energy of the shower is. The production of dark particles during the generation of shower could explain the discrepancy.

  2. What could one say about the interactions of dark M(47) proton with ordinary matter? Does p(47) transform to ordinary proton in stepwise manner as Mersenne prime is gradually reduced or in single step. What is the rate for the transformation to ordinary proton. The free path should be a considerable fraction of Earth radius by the argument of the article.

    The transformation to ordinary proton would generate a shower containing also tau leptons and tau neutrinos coming pion decays producing muons and electrons and their neutrinos. Neutrino oscillations would produce tau neutrinos: standard model predicts flavor ratio about 1:1:1.

  3. What could happen in the strong interactions of dark proton with nuclei? Suppose that dark proton is relativistic with Ep =x Mp= x EeV, x>1, say x∼ 2. The total cm energy Ecm in the rest system of ordinary proton is for a relativistic)!) EeV dark proton + ordinary proton about Ecm=(3/2)x1/2 (mpMp1/2= x1/2× 5 TeV, considerably above the rest energy mp(89)=512 mp=.48 TeV of M89 dark proton. The kinetic energy is transformed to rest energy of particles emanating from the collision of dark and ordinary proton.

    If the collision takes place with a quark of ordinary proton with mass mq= 5 MeV, Ecm is reduced by a factor of 51/210-3/2 giving E=x1/2 1.3 TeV, which is still above for the threshold for transforming the cosmic ray dark proton to M89 dark proton.

    This suggests that the interaction produce first dark relativistic M89 protons, which in further interactions transform to ordinary protons producing the shower and neutrinos. I have proposed already more than two decades ago that strange cosmic ray events such as Centauros generate hot spot involving M89 hadrons. At LHC quite a number of bumps with masses obtained by scaling from the masses of mesons of ordinary hadron physics are observed. I have proposed that they are associated with quantum critically assignable to a phase transition analogous to the generation of quark gluon plasma, and are dark in TGD sense having heff/h=512 so that their Compton wavelengths are same as for ordinary hadrons.

  4. The free path of (possibly) dark MG,47 proton in ordinary matter should be a considerable fraction of the Earth's radius since the process of tau regeneration based on standard physics cannot explain the findings. The interaction with ordinary matter possibly involving the transformation of the dark proton to ordinary one (or vice versa!) must be induced by the presence of ordinary matter rather than being spontaneous.

    Also the flux of cosmic ray protons at EeV energies must be high enough. It is known that UHE cosmic rays very probably are not gamma rays. Besides neutrinos dark MG,47 protons would be a natural candidate for them.

See chapter New Particle Physics Predicted by TGD: Part I, the article Topological description of family replication and evidence for higher gauge boson generations, or the shorter article TGD based explanation of two new neutrino anomalies.



New indications for the third generation of weak bosons

There are indications (see this) that electron neutrinos appear observed by ICECUBE more often than other neutrinos. In particular, the seems to be a deficit of τ neutrinos. The results are very preliminary. In any case, there seems to be an inconsistency between two methods observing the neutrinos. The discrepancy seems to come from higher energy end of the energy range [13 TeV, 7.9 PeV] from energies above 1 PeV.

The article "Invisible Neutrino Decay Could Resolve IceCube's Track and Cascade Tension" by Peter Denton and Irene Tamborra tries to explain this problem by assuming that τ and μ neutrinos can decay to a superparticle called majoron (see this).

The standard model for the production of neutrinos is based on the decays of pions producing e+νe and μ+ νμ. Also μ+ can travel to the direction of Earth and decay to e+ νe νμ and double the electron neutrino fraction. The flavor ratio would be 2:1:0.

Remark: The article at (see this) claims that the flavor ratio is 1:2:0 in pion decays, which is wrong: the reason for the lapsus is left as an exercise for the reader.

Calculations taking into account also neutrino oscillations during the travel to Earth to be discussed below leads in good approximation to a predicted flavor ratio 1:1:1. The measurement teams suggest that measurements are consistent with this flavor ratio.

There are however big uncertainties involved. For instance, the energy range is rather wide [13 TeV, 7.9 PeV] and if neutrinos are produce in decay of third generation weak boson with mass about 1.5 PeV as TGD predicts, the averaging can destroy the information about branching fractions.

In TGD based model (see this) third generation weak bosons - something new predicted by TGD - at mass around 1.5 TeV corresponding to mass scale assignable to Mersenne prime M61 (they can have also energies above this energy) would produce neutrinos in the decays to antilepton neutrino pairs.

  1. The mass scale predicted by TGD for the third generation weak bosons is correct: it would differ by factor 2(89-61)/2= 214 from weak boson mass scale. LHC gives evidence also for the second generation corresponding to Mersenne prime M79: also now mass scale comes out correctly. Note that ordinary weak bosons would correspond to M89.
  2. The charge matrices of 3 generations must be orthogonal and this breaks the universality of weak interactions. The lowest generation has generation charge matrix proportional to (1,1,1) - this generation charge matrix describes couplings to different generations. Unit matrix codes for universality of ordinary electroweak and also color interactions. For higher generations of electro-weak bosons and also gluons universality is lost and the flavor ratio for the produced neutrinos in decays of higher generation weak bosons differs from 1:1:1.

    One example of charge matrices would be 3/21/2×(0,1,-1) for second generation and (2,-1,-1)/21/2 for the third generation. In this case electron neutrinos would be produced 2 times more than muon and tau neutrinos altogether. The flavor ratio would be 0:1:1 for the second generation and 4:1:1 for the third generation in this particular case.

  3. This changes the predictions of the pion decay mechanism. The neutrino energies are above the energy about 1.5 PeV in the range defined by the spectrum of energies for the decaying weak boson. If they are nearly at rest the energie are a peak around the rest mass of third generation weak boson. The experiments detect neutrinos at energy range [13 TeV, 7.9 PeV] having the energy of the neutrinos produced in the decay of third generation weak bosons in a range starting from 1.5 PeV and probably ending below 7.9 PeV. Therefore their experimental signature tends to be washed out if pion decays are responsible for the background.
These fractions are however not what is observed at Earth.
  1. Suppose that L+νL pair is produced. It can also happen that L+, say μ+ travels to the direction of Earth. It can decay to e+νμνe. Therefore one obtains both νμ and νe. From the decy to τ+ντ one obtains all three neutrinos. If the fractions of the neutrinos from the generation charge matrix are (Xe,Xμ,Xτ), the fractions travelling to each are proportional to

    xα↔ Xα=(Xe,Xμ,Xτ) =(xe +xμ+xτ,xμ+ xτ,xτ) .

    and the flavor ratio in the decays would be

    Xe:Xμ:Xτ =xe +xμ+xτ: xμ+xτ:xτ .

    The decays to lower neutrino generations tend to increase the fraction of electronic and muonic neutrinos in the beam.

  2. Also neutrino oscillations due to different masses of neutrinos (see this) affect the situation. The analog of CKM matrix describing the mixing of neutrinos, the mass squared differences, and the distance to Earth determines the oscillation dynamics.

    One can deduce the mixing probabilities from the analog of Schrödinger equation by using approximation E= p+m2/2p which is true for energies much larger than the rest mass of neutrinos. The masses of mass eigenstates, which are superpositions of flavour eigenstates, are different.

    The leptonic analog of CKM matrix Uα i (having in TGD interpretation in terms of different mixings of topologies of partonic 2-surfaces associated with different charge states of various lepton families allows to express the flavor eigenstates να as superpositions of mass eigenstates νi. As a consequence, one obtains the probabilities that flavor eigenstate να transforms to flavour eigenstate νβ during the travel. In the recent case the distance is very large and the dependence on the mass squared differences and distance disappears in the averaging over the source region.

    The matrix Pαβ telling the transformation probabilities α→β is given in Wikipedia article (see this) in the general case. It is easy to deduce the matrix at the limit of very long distances by taking average over source region to get exressions having no dependence

    Pαβ= δαβ- 2 ∑i>j Re[Uβ iUi αUα jU] .

    Note that ∑β Pαβ=1 holds true since in the summation second term vanishes due to unitary condition U†U=1 and i>j condition in the formula.

  3. The observed flavor fraction is Ye:Yμ:Yτ, where one has

    Yα = PαβXβ .

    It is clear that if the generation charge matrix is of the above form, the fraction of electron neutrinos increases both the decays of τ and μ and by this mechanism. Of course, the third generation could have different charge matrix, say (3/21/2(0,1,-1). In this case the effects would tend to cancel.

See chapter New Particle Physics Predicted by TGD: Part I or the article Topological description of family replication and evidence for higher gauge boson generations.



How to describe family replication phenomenon gauge theoretically?

In TGD framework family replication phenomenon is described topologically (see this). The problem is to modify the gauge theory approach of the standard model to model to describe family replication phenomenon at QFT limit.

1. Identification of elementary particles

1.1 Original picture

The original view about family replication phenomenon assumed that fermions correspond to single boundary component of the space-time surface (liquid bubble is a good analogy) and thus characterized by genus g telling the number of handles attached to the sphere to obtain the bubble topology.

  1. Ordinary bosons would correspond to g=0 (spherical) topology and the absorption/emission of boson would correspond to 2-D topological sum in either time direction. This interpretation conforms with the universality of ordinary ew and color interactions.
  2. The genera of particle and antiparticle would have formally opposite sign and the total genus would be conserved in the reaction vertices. This makes sense if the annihilation of fermion and anti-fermion to g=0 boson means that fermion turns backwards in time emitting boson. The vertex is essentially 2-D topological sum at criticality between two manifold topologies. In the vertex 2-surface would be therefore singular manifold. The analogy to closed string emission in string model is obvious.
1.2 The recent vision

Later the original picture was replaced with a more complex identification.

  1. Fundamental particles - partons - serving as building bricks of elementary particles are partonic 2-surfaces identified as throats of wormhole contacts at which the Euclidian signature of the induced metric of the wormhole contact changes to Minkowskian one. The orbit of partonic 2-surface corresponds to a light-like 3-surface at which the Minkowskian signature of the induced metric changes to Euclidian, and carries fermion lines defining of boundaries of string world sheets. Strings connect different wormhole throats and mean generalization of the notion of point like particle leading to the notion of tensor network (see this).

    Elementary particles are pairs of two wormhole contacts. Both fermions and bosons are pairs of string like flux tubes at parallel space-time sheets and connected at their ends by CP2 sized wormhole contacts having Euclidian signature of induced metric. A non-vanishing monopole flux loop runs around the extrenely flattened rectangle loop connecting wormhole throats at both space-time sheets and traverses through the contacts.

  2. The throats of wormhole contacts are characterized by genus given by the number g of handles attached to sphere to get the topology. If the genera ga,gb of the opposite throats of given wormhole contact are same, one can assign genus to it : g=ga=gb. This can be defended by the fact, that the distance between the throats is given by CP2 length scale and thus extremely short so that ga≠ gb implies strong gradients and by Uncertainty Principle mass of order CP2 mass.

    If the genera of the two wormhole contacts are same: g1=g2, one one can assign genus g to the particle. This assumption is more questionable if the distance between contacts is of order of Compton length of the particle. The most general assumption is that all genera can be different.

  3. There is an argument for why only 3 lowest fermion generations are observed (see this). Assume that the genus g for all 4 throats is same. For g=0,1,2 the partonic 2-surfaces are always hyper-elliptic allowing thus a global conformal Z2 symmetry. Only these 3 2-topologies would be realized as elementary particles whereas higher generations would be either very heavy or analogous to many-particle states with a continuum mass spectrum. For the latter option g=0 and g=1 state could be seen as vacuum and single particle state whereas g=2 state could be regarded as 2-particle bound state. The absence of bound n-particle state with n>2 implies continuous mass spectrum.
  4. Fundamental particles would wave function in the conformal moduli space associated with its genus (Teichmueller space). For fundametal fermions the wave function would be strongly localized to single genus. For ordinary bosons one would have maximal mixing with the same amplitude for the appearance of wormhole throat topology for all genera g=0,1,2. For the two other u(3)g neutral bosons in octet one would have different mixing amplitudes and charge matrices would be orthogonal and universality for the couplings to ordinary fermions would be broken for them. The evidence for the breaking of the universality (see this) is indeed accumulating and exotic u(3)g neutral gauge bosons giving effectively rise to two additional boson families could explain this.
2. Two questions related to bosons and fermions

What about gauge bosons and Higgs, whose quantum numbers are carried by fermion and anti-fermion (or actually a superposition of fermion-anti-fermion pairs). There are two options.

  1. Option I: The fermion and anti-fermion for elementary boson are located at opposite throats of wormhole contact as indeed assumed hitherto. This would explain the point-likeness of elementary bosons. u(3) charged bosons having different genera at opposite throats would have vanishing couplings to ordinary fermions and bosons. Together with large mass of ga≠ gb wormhole contacts this could explain why ga≠ gb bosons and fermions are not observed and would put the Cartan algebra of u(3)g in physically preferred position. Ordinary fermions would effectively behave as u(3)g triplet.
  2. Option II: The fermion and anti-fermion for elementary boson are located at throats of different wormhole contacts making them non-point like string like objects. For hadron like stringy objects, in particular graviton, the quantum numbers would necessarily reside at both ends of the wormhole contact if one assumes that single wormhole throats carries at most one fermion or anti-fermion. For this option also ordinary fermions could couple to (probably very massive) exotic bosons different genera at the second end of the flux tube.
There are also two options concerning the representation of u(3)g assignal to fermions corresponding ot su(3)g triplet 3 and 8⊕ 1.

Option I: Since only the wormhole throat carrying fermionic quantum numbers is active and since fundamental fermions naturally correspond to u(3)g triplets, one can argue that the wormhole throat carrying fermion quantum number determines the fermionic u(3)g representation and should be therefore 3 for fermion and 3bar anti-fermion.

At fundamental level also bosons would in the tensor products of these representations and many-sheeted description would use these representations. Also the description of graviton-like states involving fermions at all 4 wormhole throats would be natural in this framework. At gauge theory limit sheets would be identified and in the most general case one would need U(3)g× U(3)g× U(3)g× U(3)g with factors assignable to the 4 throats.

  1. The description of weak massivation as weak confinement based on the neutralization of weak isospin requires a pair of left and right handed neutrino located with νL and νbarR or their CP conjugates located at opposite throats of the passive wormhole contact associated with fermion. Already this in principle requires 4 throats at fundamental level. Right-handed neutrino however carries vanishing electro-weak quantum numbers so that it is effectively absent at QFT limit.
  2. Why should fermions be localized and su(3)g neutral bosons delocalized with respect to genus? If g labels for states of color triplet 3 the localization of fermions looks natural, and the mixing for bosons occurs only in the Cartan algebra in u(3)g framework: only u(3)g neutral states an mix.
Option II: Also elementary fermions belong to 8+1. The simplest assumption is that both fermions and boson having g1≠ g2 have large mass. In any case, g1≠ g2 fermions would couple only to u(3)g charged bosons. Also for this option ordinary bosons with unit charge matrix for u(3)g would couple in a universal manner.
  1. The model for CKM mixing (see this) would be modified in trivial manner. The mixing of ordinary fermions would correspond to different topological mixings of the three states su(3)-neutral fermionic states for U and D type quarks and charged leptons and neutrinos. One could reduce the model to the original one by assuming that fermions do not correspond to generators Id, Y, and I3 for su(3)g but their linear combinations giving localization to single valued of g in good approximation: they would correspond to diagonal elements eaa, a=1,2,3 corresponding to g=0,1,2.
  2. p-Adic mass calculations (see this) assuming fixed genus for fermion predict an exponential sensitivity on the genus of fermion. In the general case this prediction would be lost since one would have weighted average over the masses of different genera with g=2 dominating exponentially. The above recipe would cure also this problem. Therefore it seems that one cannot distinguish between the two options allowing g1≠ g2. The differences emerge only when all 4 wormhole throats are dynamical and this is the case for graviton-like states (spin 2 requires all 4 throats to be active).
The conclusion seems to be that the two options are more or less equivalent for light fermions. In the case of exotic fermions expected to be extremely heavy the 8+1 option looks more natural. At this limit however QFT limit need not make sense anymore.

3. Reaction vertices

Consider next the reaction vertices for the option in which particles correspond to string like objects identifiable as pairs of flux tubes at opposite space-time sheets and carrying monopole magnetic fluxes and with ends connected by wormhole contacts.

  1. Reaction vertex looks like a simultaneous fusing of two open strings along their ends at given space-time sheets. The string ends correspond to wormhole contacts which fuse together completely. The vertex is a generalization of a Y-shaped 3-vertex of Feynman diagram. Also 3-surfaces assignable to particles meet in the same manner in the vertex. The partonic 2-surface at the vertex would be non-singular manifold whereas the partonic orbit would be singular manifold in analogy with Y shaped portion of Feynman diagram.
  2. In the most general case the genera of all four throats involved can be different. Since the reaction vertex corresponds to a fusion of wormhole contacts characterized in the general case by (g1,g2), one must have (g1,g2)=(g3,g4). The rule would correspond in gauge theory description to the condition that the quark and antiquark su(3)g charges are opposite at both throats in order to guarantee charge conservation as the wormhole contact disappears.
  3. One has effectively pairs of open string fusing along their and and the situation is analogous to that in open string theory and described in terms of Chan-Paton factors. This suggests that gauge theory description makes sense at QFT limit.
    1. If g is same for all 4 throats, one can characterize the particle by its genus. The intuitive idea is that fermions form a triplet representation of u(3)g assignable to the family replication. In the bosonic sector one would have only u(3)g neutral bosons. This approximation is expected to be excellent.
    2. One could allow g1≠ g2 for the wormhole contacts but assume same g for opposite throats. In this case one would have U(3)g× U(3)g as dynamical gauge group with U(3)g associated with different wormhole contacts. String like bosonic objects (hadron like states) could be therefore seen as a nonet for u(3)g. Fermions could be seen as a triplet.

      Apart from topological mixing inducing CKM mixing fermions correspond in good approximation to single genus so that the neutral members of u(3)g nonet, which are superpositions over several genera must mix to produce states for which mixing of genera is small. One might perhaps say that the topological mixing of genera and mixing of u3(g) neutral bosons are anti-dual.

    3. If all throats can have different genus one would have U(3)g× U(3)g× U(3)g× U(3)g as dynamical gauge group U(3)g associated with different wormhole throats. This option is probably rather academic. Also fermions could be seen as nonets.
4. What would the gauge theory description of family replication phenomenon look like?

For the most plausible option bosonic states would involve a pair of fermion and anti-fermion at opposite throats of wormhole contact. Bosons would be characterized by adjoint representation of u(3)g=su(3)g× u(1)g obtained as the tensor product of fermionic triplet representations 3 and 3bar.

  1. u(1)g would correspond to the ordinary gauge bosons bosons coupling to ordinary fermion generations in the same universal manner giving rise to the universality of electroweak and color interactions.
  2. The remaining gauge bosons would belong to the adjoint representation of su(3)g. One indeed expects symmetry breaking: the two neutral gauge bosons would be light whereas charged bosons would be extremely heavy so that it is not clear whether QFT limit makes sense for them.

    Their charge matrices Qgi would be orthogonal with each other (Tr(QgiQgj)=0, i≠ j) and with the unit charge matrix u(1)g charge matrix Q0∝ Id (Tr(Qgi)=0) assignable to the ordinary gauge bosons.These charge matrices act on fermions and correspond to the fundamental representation of su(3)g. They are expressible in terms of the Gell-Mann matrices λi (see this).

How to describe family replication for gauge bosons in gauge theory framework? A minimal extension of the gauge group containing the product of standard model gauge group and U(3)g does not look promising since it would bring in additional generators and additional exotic bosons with no physical interpretation. This extension would be analogous to the extension of the product SU(2)× SU(3) of the spin group SU(2) and Gell-Mann's SU(3) to SU(6)). Same is true about the separate extensions of U(2)ew and SU(3)c.
  1. One could start from an algebra formed as a tensor product of standard model gauge algebra g= su(3)c× u(2)ew and algebraic structure formed somehow from the generators of u(3)g. The generators would be

    Ji,a= Ti ⊗ Ta ,

    where i labels the standard model Lie-algebra generators and a labels the generators of u(3)g.

    This algebra should be Lie-algebra and reduce to the same as associated with standard model gauge group with generators Tb replacing effectively complex numbers as coefficients. Mathematician would probably say, that standard model Lie algebra is extended to a module with coefficients given by u(3)g Lie algebra generators in fermionic representation but with Lie algebra product for u(3)g replaced with a product consistent with the standard model Lie-algebra structure, in particular with the Jacobi-identities.

  2. By writing explicitly commutators and Jacobi identifies one obtains that the product must be symmetric: Ta• Tb= Tb• Ta and must satisfy the conditions Ta• (Tb• Tc)= Tb• (Tc• Ta)= Tc• (Ta• Tb) since these terms appear as coefficients of the double commutators appearing in Jacobi-identities

    [Ji,a,[Jj,b],Jk,c]]+[Jj,b,[Jk,c],Ji,a]] + [Jk,c,[Ji,a],Jj,b]]=0 .

    Commutativity reduces the conditions to associativity condition for the product •. For the sub-algebra u(1)3g these conditions are trivially satisfied.

  3. In order to understand the conditions in the fundamental representation of su(3), one can consider the product the su(3)g product defined by the anti-commutator in the matrix representation provided by Gell-Mann matrices λa (see this and this):

    ab}= 43δa,b Id + 4dabcλc , & Tr(λaλb) =2δab , & dabc= Tr(λaλbc)

    dabc is totally symmetric under exchange of any pair of indices so that the product defined by the anti-commutator is both commutative and associative. The product extends to u(3)g by defining the anti-commutator of Id with λa in terms of matrix product. The product is consistent with su(3)g symmetries so that these dynamical charges are conserved. For complexified generators this means that generator and its conjugate have non-vanishing coefficient of Id.

    Remark: The direct sum u(n)⊕ u(n)s formed by Lie-algebra u(n) and its copy u(n)s endowed with the anti-commutator product • defines super-algebra when one interprets anti-commutator of u(n)s elements as an element of u(n).

  4. Could su(3) associated with 3 fermion families be somehow special? This is not the case. The conditions can be satisfied for all groups SU(n), n≥ 3 in the fundamental representation since they all allow completely symmetric structure constants dabc as also higher completely symmetric higher structure constants dabc... up to n indices. This follows from the associativity of the symmetrized tensor product: ((Adj⊗ Adj)S⊗ Adj)S =(Adj⊗ (Adj⊗ Adj)S)S for the adjoint representation.
To sum up, the QFT description of family replication phenomenon with the extension of the standard model gauge group would bring to the theory the commutative and associative algebra of u(3)g as a new mathematical element. In the case of ordinary fermions and bosons and also in the case of u(3)g neutral bosons the formalism would be however rather trivial modification of the intuitive picture.

See chapter New Particle Physics Predicted by TGD: Part I.



Further evidence for the third generation of weak bosons

Matt Strassler had a blog posting about an interesting finding from old IceCube data revealed at thursday (July 12, 2018) by IceCube team. The conclusion supports the view that so called blasars, thin jets of high energy particles suggested to emerge as matter falls into giant black hole, might be sources of high energy neutrinos. In TGD framework one could also think that blazars originate from cosmic strings containing dark matter and energy. Blazars themselves could be associated with cosmic strings thickened to magnetic flux tubes. The channeling to flux tubes would make possible observation of the particles emerging from the source whatever it might be.

Only the highest energy cosmic neutrinos can enter the IceCube detector located deep under the ice. IceCube has already earlier discovered a new class of cosmic neutrinos with extremely high energy: Matt Strassler has written a posting also about this two years ago (see this): the energies of these neutrinos were around PeV. I have commented this finding from TGD point of view (see this).

Last year one of these blazars flared brightly producing high energy neutrinos and photons: neutrinos and photons came from the same position in the sky and occurred during the same period. IceCube detector detected a collision of one (!) ultrahigh energy neutrino with proton generating muon. The debris produced in the collision contained also photons, which were detected. IceCube team decided to check whether old data could contain earlier neutrino events assignable to the same blasar and found a dramatic burst of neutrinos in 2014-2015 data during period of 150 days associated with the same flare; the number of neutrinos was 20 instead of the expected 6-7. Therefore it seems that the ultrahigh energy neutrinos can be associated with blazars.

By looking the article of IceCube team (see this) one learns that neutrino energies are of order few PeV (Peta electron Volt), which makes 1 million GeV (proton has mass .1 GeV). What kind of mechanism could create these monsters in TGD Universe? TGD suggests scaled variants of both electroweak physics and QCD and the obvious candidate would be decays of weak bosons of a scaled variant of ew physics. I have already earlier considere a possible explanation interms of weak bosons of scaled up variant of weak physics characterizes by Mersenne prime $M_{61}=2^{61}-1}$ (see this).

  1. TGD "almost-predicts" the existence of three families of ew bosons and gluons. Their coupling matrices to fermions must be orthogonal. This breaks the universality of both ew and color interactions. Only the ordinary ew bosons can couple in the same manner to 3 fermion generations. There are indeed indications for the breaking of the universality in both quark and leptons sector coming from several sources such as B meson decays, muon anomalous anomalous (this is not a typo!) magnetic moment, and the the finding that the value of proton radius is different depending on whether ordinary atoms or muonic atoms are used to deduce it (see this).
  2. The scaled variant of W boson could decay to electron and monster neutrino having same energies in excellent approximation. Also Z0 boson could decay to neutrino-antineutrino pair. The essentially mono-chromatic energy spectrum for the neutrinos would serve as a unique signature of the decaying weak boson. One might hope of observing two kinds of monster neutrinos with mass difference of the order of the scaled up W-Z mass difference. Relative mass difference would same as for ordinary W and Z - about 10 per cent - and thus of order .1 PeV.
One can look the situation quantitatively using p-adic length scale hypothesis and assumption that Mersenne primes and Gaussian Mersennes define preferred p-adic length scales assignable to copies of hadron physics and electroweak physics.
  1. Ordinary ew gauge bosons correspond in TGD framework to Mersenne prime Mk= 2k-1, k=89. The mass scale is 90 GeV, roughly 90 proton masses.
  2. Next generation corresponds to Gaussian Mersenne Gaussian Mersenne prime MG,79= (1+i)79-1. There is indeed has evidence for a second generation weak boson corresponding to MG,79 (see this). The predicted mass scale is obtained by scaling the weak boson mass scale of about 100 GeV with the factor 2(89-79/2=32 and is correct.
  3. The next generation would correspond to Mersenne prime M61. The mass scale 90 GeV of ordinary weak physics is now scaled up by a factor 2(89-61)/2= 214 ≈ 64,000. This gives a mass scale 1.5 PeV, which is the observed mass scale for the neutrino mosters detected by Ice-Cube. Also the earlier monster neutrinos have the same mass scale. This suggests that the PeV neutrinos are indeed produced in decays of W(61) or Z(61).
See chapter New Particle Physics Predicted by TGD: Part I.



LSND anomaly is here again!

Sabine Hossenfelder told about the finding of MinibooNe collaboration described in arXiv.org preprint Observation of a Significant Excess of Electron-Like Events in the MiniBooNE Short-Baseline Neutrino Experiment.

The findings give strong support for old and forgotten LSND anomaly - forgotten because it is in so blatant conflict with the standard model wisdom. The significance level of the anomaly is 6.1 sigmas in the new experiment. 5 sigma is regarded as the threshold for a discovery. It is nice to see this fellow again: anomalies are the theoreticians best friends.

To me this seems like a very important event from the point of view of standard model and even theoretical particle physics: this anomaly with other anomalies raises hopes that the patient could leave the sickbed after illness that has lasted for more than four decades after it became a victim of the GUT infection.

LSND as also other experiments are consistent with neutrino mixing model. LSND however produces electron excess as compared to other neutrino experiments. Anomaly means that the parameters of the neutrino mixing matrix (masses, mixing angles, phases) are not enough to explain all experiments.

One manner to explain the anomaly would be fourth "inert" neutrino having no couplings to electroweak bosons. TGD predicts both right and left-handed neutrinos and right-handed ones would not couple electroweakly. In massivation they would however combine to single massive neutrino just like in Higgs massivation Higgs gives components for massive gauge bosons and only neutral Higgs having no coupling to photon remains. Therefore this line of thought does not seem terribly promising in TGD framework.

For many years ago I explained the LSND neutrino anomaly in TGD framework as being due to the fact that neutrinos can correspond to several p-adic mass scales. p-Adic mass scale coming as power of 21/2 would bring in the needed additional parameter. The new particles could be ordinary neutrinos with different p-adic mass scales. The neutrinos used in experiment would have p-adic length scale depending on their origin. Lab, Earth's atmosphere, Sun, ... It is possible that the neutrinos transform during their travel to less massive neutrinos.

What is intriguing that the p-adic length scale range that can be considered as candidates for neutrino Compton lengths is biologically extremely interesting. This range could correspond to the p-adic length scales L(k)∼ 2(k-151)/2L(151), k= 151,157, 163, 167, varying from cell membrane thickness 10 nm to 2.5 μm. These length scales correspond to Gaussian Mersennes MG,k=(1+i)k-1. The appearance of four of 4 Gaussian Mersennes in such a short length scale interval is a number theoretic miracle. Could neutrinos or their dark variants with heff= n× h0 (h= 6× h0 is the most plausible option at this moment, see this and this) together with dark variants weak bosons effectively massless below their Compton length have a fundamental role in quantum biology?

For the TGD based new physics and also for LSND anomaly see chapter New Particle Physics Predicted by TGD: Part I of "p-Adic physics".



Strange spin asymmetry at RHIC

The popular article Surprising result shocks scientists studying spin tells about a peculiar effect in p-p and p-N (N for nucleus) observed at Relativistic Heavy Ion Collider (RHIC). In p-p scattering with polarized incoming proton there is asymmetry in the sense that the protons with vertical polarization with respect to scattering plane give rise to more neutrons slightly deflected to right than to left (see the figure of the article). In p-N scattering of vertically polarized protons the effect is also observed for neutrons but is stronger and has opposite sign for heavier nuclei! The effect came as a total surprise and is not understood. It seems however that the effects for proton and nuclear targets must have different origin since otherwise it is difficult to understand the change of the sign.

The abstract of the original article summarizes what has been observed.

During 2015 the Relativistic Heavy Ion Collider (RHIC) provided collisions of transversely polarized protons with Au and Al nuclei for the first time, enabling the exploration of transverse-single-spin asymmetries with heavy nuclei. Large single-spin asymmetries in very forward neutron production have been previously observed in transversely polarized p+p collisions at RHIC, and the existing theoretical framework that was successful in describing the single-spin asymmetry in p+p collisions predicts only a moderate atomic-mass-number (A) dependence. In contrast, the asymmetries observed at RHIC in p+A collisions showed a surprisingly strong A dependence in inclusive forward neutron production. The observed asymmetry in p+Al collisions is much smaller, while the asymmetry in p+Au collisions is a factor of three larger in absolute value and of opposite sign. The interplay of different neutron production mechanisms is discussed as a possible explanation of the observed A dependence.

Since diffractive effect in forward direction is in question, one can ask whether strong interactions have anything to do with the effect. This effect can take place at the level of nucleons and a quark level and these two effects should have different signs. Could electromagnetic spin orbit coupling cause the effect both at the level of nucleons in p-N collisions and at the level of quarks in p-p collisions?

  1. Spin-orbit interaction effect is relativistic effect: the magnetic field of target nucleus in the reference frame of projectile proton is nonvanishing: B= -γ v× E, γ= 1/(1-v2)1/2. The spin-orbit interaction Hamiltonian is

    HL-S = -μB ,

    where

    μ= gp μNS , μN= e/2mp

    is the magnetic moment of polarized proton proportional to spin S, which no has definite direction due to the polarization of incoming proton beam. The gyromagnetic factor gp equals to gp=2.79284734462(82) holds true for proton.

  2. Only the component of E orthogonal to v is involved and the coordinates in this direction are unaffected by the Lorentz transformations. One can express the transversal component of electric field as gradient

    Er= - ∂rV r/r .

    Velocity v can be expressed as v=p/mp so that the spin-orbit interaction Hamiltonian reads as

    HL-S= γ gp (e/2mp) (1/mp)LS [∂rV/r ] .

    For polarised proton the effect of this interaction could cause the left-right asymmetry. The reason is that the sign of the interaction Hamiltonia is opposite at left and right sides of the target since the sign of L=r× p is opposite at left- and right-hand sides. One can argue as in non-relativistic case that this potential generates a force which is radial and proportional to ∂r[(∂rV(r))/r)].

Consider first the scattering on nucleus.
  1. Inside the target nucleus one can assume that the potential is of the form V= kr2/2: the force vanishes! Hence the effect must indeed come from peripheral collisions. At the periphery responsible for almost forward scattering one as V(r)=Ze/r and one has ∂r(∂rV(r))/r)= 3Ze/r4, r=R, R the nuclear radius. One has R = kA1/3 for a constant density nucleus so that one has ∂r(∂rV(r))/r)= 3k-4eZA-4/3.

    The force decreases with A roughly like A-1/3 but the scattering proton can give its momentum to a larger number of nucleons inside the target nucleus. If all neutrons get their share of the transversal momentum, the effect is proportional to neutron number N=A-Z one would obtain the dependence Z(A-Z)A-4/3 ∼ A2/3. If no other effects are involved one would have for the ratio r of Al and Au asymmetries

    r=Al/Au ∼ Z(Al)N(Al)/Z(Au)A(u) × [A(Au)/A(Al)]4/3 .

    Using (Z,A)=(13,27) for Al and (Z,A)=(79,197) for Au one obtains the prediction r=.28. The actual value is r≈ .3 by estimating from Fig. 4 of the article is not far from this.

  2. This effect takes place only for protons but it deviates proton at either side to the interior of nucleus. One expects that the proton gives its transversal momentum components to other nucleons - also neutrons. This implies that sign of the effect is same as it would be for the spin-orbit coupling when the projectile is neutron. This could be the basic reason for the strange sign of the effect.
Consider next what could happen in p-p scattering.
  1. One must explain why neutrons with R-L asymmetry with respect to the scattering axis are created. This requires quark level consideration.
  2. The first guess is that one must consider spin orbit interaction for the quarks of the polarized proton scattering from the quarks of the unpolarized proton. What comes in mind is that one could in a reasonable approximation treat the unpolarized proton as single coherent entity. In this picture u and d quarks of polarized proton would have asymmetric diffractive scattering tending to go to the opposite sides of the scattering axis.
  3. The effect for d quarks would be opposite to that for u quarks. Since one has n=udd and and p=uud, the side which has more d quarks gives rise to neutron excess in the recombination of quarks to hadrons. This effect would have opposite sign than the effect in the case of nuclear target. This quark level effect would be present also for nuclear targets.
See the chapter New Particle Physics Predicted by TGD: Part II.



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