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p-Adic Physics

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Year 2015

Indications for the new physics predicted by TGD

The recently reported 750 GeV bump at LHC seems to be more important than I though originally. This bump is only one instance of potential anomalies of the standard the model, which TGD could explain. TGD indeed predicts a lot of new physics at LHC energy scale. For this reason I decided to write a more organized version of the earlier posting.

  1. TGD suggests the existence of two scaled up copies of the ordinary hadron physics labelled by Mersenne prime M107=2107-1. The first copy would corresponds to M89 with mass spectrum of ordinary hadrons scale by factor 29= 512 and second one to Gaussian Mersenne MG,179=(1+i)79-1 with mass spectrum of ordinary hadrons scaled by 214. The signature of the this new physics is the existence of entire hadronic spectroscopy of new states rather than just a couple of exotic elementary particles. If this new physics is there it is eventually bound to become visible as more information is gathered.
  2. TGD also suggests the existence of copies of various gauge bosons analogous to higher fermion generations assisupgned to the genus g=0,1,2 of boundary topology of partonic 2-surface: genus is actually the of partonic 2-surface whose light-like orbit is the surface at which the induced metric changes its signature from Minkowskian to Euclidian. Copies of gauge bosons (electroweak bosons and gluons) and Higgs correspond to octet representations for the dynamical "generation color" group SU(3) assignable to 3 fermion generations. The 3 gauge bosons with vanishing "color" are expected to be the lightest ones: for them the opposite throats of wormhole contact have same genus. The orthogonality of charge matrices for bosons implies that the couplings of these gauge bosons (gluons and electroweak bosons) to fermions break universality meaning that they depend on fermion generations. There are indications for the breaking of the universality. TGD differs from minimal supersymmetric extension of standard model in that all these Higgses are almost eaten by weak gauge bosons so that only the neutral Higgses remain.

    One can ask whether the three lightest copies of weak and color physics for various boson families could correspond M89, MG,79 and M61.

  3. TGD SUSY is not N=1. Instead superpartners of particle is added by adding right handed neutrino or antineutrino or pair of them to the state. In quark sector one obtains leptoquark like states and the recent indications for the breaking of lepton universality has been also explained in terms of leptoquarks which indeed have quantum numbers of bound states of quark and right-handed neutrino also used to explain the indications for the breaking of lepton universality.
During last years several indications for the new physics suggested by TGD have emerged. Recently the first LHC Run 2 results were announced and there was a live webcast.
  1. The great news was the evidence for a two photon bump at 750 GeV about which there had been rumors. Lubos told earlier about indications for diphoton bump around 700 GeV. This mass differs only few percent from the naive calling estimate for the mass of ρ and ω mesons of M89 hadron physics for which masses for the simplest option are obtained by using p-adic length scale hypothesis by scaling with the factor 2(107-89)/2 =512 the masses of these mesons for ordinary M107 hadron physics.

    There is however a problem: these mesons do not decay to gamma pairs! The effective interaction Lagrangian for photon and ρ is product of Maxwell action with the divergence of ρ vector field. ρ is massive. Could the divergence be non-vanishing and could the large mass of ρ make the decay rate high enough? No. The problem is that the divergence should vanish for on mass shell states also for massive ρ. Also off mass shell states with unphysical polarization of ρ near resonance are excluded since the propagator should eliminate time-like polarizations in the amplitude. Scalar, pseudoscalar, or spin 2 resonance is the only option.

    If the scaling factor is the naive 512 so that M89 pion would have mass about 70 GeV, there are several meson candidates with relative angular momentum L=1 for quarks assignable to string degrees of freedom in the energy region considered. The inspection of the experimental meson spectrum shows that there is quite many resonances with desired quantum numbers. The scaled up variants of neutral scalar mesons η(1405) and η(1475) consisting of quark pair would have mases 702.5 GeV and 737.5 GeV and could explain both 700 GeV and 750 bump. There are also neutral exotic mesons, which cannot be quark pairs but pairs of quark pairs f0(400), f0(980), f2(1270), f0(1370), f0(1500), f2(1430), f2(1565), f2(1640), f?(1710) (the subscript tells the total spin and the number inside brackets gives mass in MeVs) would have naively scaled up masses 200, 490, 635, 685, 725, 750, 715, 782.5, 820, 855 GeV. The charged exotic meson a0(1450) scales up to 725 GeV state.

  2. There is a further mystery to be solved. Matt Strassler emphasizes the mysterious finding fact that the possible particle behind the bump does not seem to decay to jets: only 2-photon state is observed.

    Situation might of course change when data are analyzed. Jester in fact reports that 1 sigma evidence for Zγ decays has been observed around 730 GeV. The best fit to the bump has rather large width, which means that there must be many other decay channels than digamma channels. If they are strong as for TGD model, one can argue that they should have been observed.

    As if the particle would not have any direct decay modes to quarks, gluons and other elementary particles. If the particle consists of quarks of M89 hadron physics it could decay to mesons of M89 hadron physics but we cannot directly observe them. Is this enough to explain the absence of ordinary hadron jets: are M89 jets somehow smoothed out as they decay to ordinary hadrons? Or is something more required? Could they decay to M89 hadrons leaking out from the reactor volume before a transition to ordinary hadrons?

    The TGD inspired idea that M89 hadrons are produced at RHIC in heavy ion collisions and in proton heavy ion collisions at LHC as dark variants with large value of heff= n×h with scaled up Compton length of order hadron size or even nuclear size conforms with finding that the decay of string like objects identifiable as M89 hadrons in TGD framework explains the unexpected properties of what was expected to be simple quark gluon plasma analogous to blackbody radiation. Could dark M89 eta mesons decaying only via digamma annihilation to ordinary particles be in question? Large heff states are produced at quantum criticality (they are responsible for quantal long range correlations) and the criticality would correspond to the phase transition fron confined to de-confined phase (at criticality confinement in the same or larger scale but with much longer Compton wavelength!). They have life times which are scaled up by heff factor: could this imply the leak out? Note that in TGD inspired biology dark EEG photons would have energies in bio-photon energy range (visible and UV) and would be exactly analogous to dark M89 hadrons.

  3. Lubos mentions in his posting several excesses which could be assigned with the above mentioned states. The bump at 750 GeV could correspond to scaled up copy of η(1475)$ or - less probably - of f0(1500). Also the bump structure around 700 GeV for which there are indications could be explained as a scaled up copy of η(1405) with mass 702.5 GeV or - less plausibly - f0(1370) with mass around 685 GeV. Lubos mentions also a 662 GeV bump. If it turns out that there are several resonances in 700 TeV region (and also elsewhere) then the only reasonable explanation relies on hadron like states since one cannot expect a large number of Higgs like elementary particles. One can of course ask why the exotic states should be seen first.
  4. Remarkably, for the somewhat ad hoc scaling factor 2× 512∼ 103 one does not have any candidates so that the M89 neutral pion should have the naively predicted mass around 67.5 GeV. Old Aleph anomaly had mass 55 GeV. This anomaly did not survive. I found from my old writings that Delphi and L3 have also observed 4-jet anomaly with dijet invariant mass about 68 GeV: M89 pion? There is indeed an article about search of charged Higgs bosons in L3 telling about an excess in cs*τ-ν*τ production identified in terms of H++H- annihilation suggesting charged Higgs mass 68 GeV. TGD based interpretation would in terms of the annihilation of charged M89 pions.

    The gammas in 130-140 GeV range detected by Fermi telescope were the motivation for assuming that M89 pion has mass twice the naively scaled up mass. The digammas could have been produced in the annihilation of a state with mass 260 GeV. The particle would be the counterpart of the ordinary η meson η(548) with scaled up mass 274 GeV thus decaying to two gammas with energies 137 GeV. Also scaled up eta prime shold be there. Also an excess in the production of two-jets above 500 GeV dijet mass has been reported and could relate to the decays of η' (958) with scaled up mass of 479 GeV! Also digamma bump should be detected.

  5. What about M89 kaon? It would have scaled up mass 250 GeV and could also decay to digamma. There are indications for a Higgs like state with mass of 250 GeV from ATLAS! It would decay to 125 GeV photons - the energy happens to be equal to Higgs mass. There are thus indications for both pion, kaon, all three scaled up η mesons, kaon and η' with predicted masses! The lowest lying M89 meson spectroscopy could have been already seen!
  6. Lubos tells that ATLAS sees charged boson excess manifesting via decay to tb in the range 200-600 TeV. Here Lubos takes the artistic freedom to talk about charged Higgs boson excess since Lubos still believes in standard SUSY predicting copies several Higgs doublets. TGD does not allow them. In TGD framework the excess could be due to the presence of charged M89 mesons: pion, kaon, ρ, ω.
  7. A smoking gun evidence would be detection of production of pairs of M89 nucleons with masses predicted by naive scaling to be around 470 GeV. This would give rise to dijets above 940 GeV cm energy with jets having total quantum numbers of ordinary nucleons. Each M89 nucleon consisting of 3 quarks of M89 hadron physics could also transform to ordinary quarks producing 3 ordinary hadron jets.
Is there any evidence for MG,79 hadron physics? Tommaso Dorigo told about indications for a neutral di-boson bump at 2 TeV. The mass of M79 pion is predicted to be 2.16 TeV by a direct scaling of the mass 135 MeV of the ordinary neutral pion!

What about higher generations of gauge bosons?

  1. There has been also a rumour about a bump at 4 TeV. By scaling Higgs mass 125 GeV by 32 one obtains 4 TeV! Maybe the Higgs is there but in different sense than in standard SUSY! Could one have copy of weak physics with scale up gauge boson masses and Higgs masses waiting for us! Higgs would be second generation Higgs associated with second generation of weak bosons analogous to that for fermions predicted by TGD? Actually one would have octet associated with dynamical "generation color" symmetry SU(3) but neutral members of the octet are expected to be the lightest states. This Higgs would have also only neutral member after massivation and differ from SUSY Higgs also in this respect. The scaled up weak boson masses would be by scaling with factor 32 from 80.4 GeV for W and 91 GeV for Z would be 2.6 TeV and 2.9 TeV respectively. Lubos mentions also 2.9 GeV dilepton event: decay of second generation Z0?!
  2. There is already evidence for second generation gauge bosons from the evidence for the breaking of lepton universality. The couplings of second generation weak bosos depend on fermion generation because their charge matrices must be orthogonal to those of the ordinary weak bosons. The outcome is breaking of universality in both lepton and quark sector. An alternative explanation would be in terms leptoquarks, which in TGD framework are super partners of quarks identifiable as pairs of right-handed neutrinos and quarks.
We are living exciting times! If TGD is right, experimenters and theorists are forced to change their paradigm completely. Instead of trying to desperately to identify elementary particle predicted by already excluded theories like SUSY they must realize that there is entire zoo of hadron resonances whose existence and masses are predicted by scaled up hadron physics. Finding a needle in haystack is difficult. In the recent situation one does not even know what one is searching for! Accepting TGD framework one would know precisely what to search for. The enormous institutional inertia of recent day particle physics community will not make the paradigm shift easy. The difficult problem is how to communicate bi-directionally with the elite of particle physics theorists, which refuses to take seriously anyone coming outside the circles.

See the article Indications for the new physics predicted by TGD and chapter New Particle Physics Predicted by TGD: Part I.

Could leptoquarks be squarks in TGD sense?

The basic problem of TGD inspired SUSY has been the lack of experimental information allowing to guess what might be the p-adic length scale associated with sparticles. The massivation as such is not a problem in TGD: the same mass formula would be obeyed by particles and sparticles and SUSY breaking would mean only different p-adic mass scales for stable particle states. One can even consider the possibility that particles and sparticles have identical masses but sparticles have non-standard value of heff behaving therefore like dark matter.

p> The solution of the problem could emerge from experiments in totally unexpected manner. Indications for the existence of leptoquarks have been accumulating gradually from LHC. Leptoquarks should have same quantum numbers as pairs of quark and right-handed neutrino and would thus correspond to squarks in N=2 SUSY of TGD.

Both Jester and Lubos have written about leptoquarks. Jester lists 3 B-meson potential anomalies, which leptoquarks could resolve :

  • A few sigma deviation in differential distribution of B → K*μ+- decays.
  • 2.6 sigma violation of lepton flavor universality in B → Dμ+μ- vs. K→ D e+e- decays.
  • 3.5 sigma violation of lepton flavor universality, but this time in B → Dτν vs. B → Dμν decays.
There is also a 3 sigma discrepancy of the experimentally measured muon magnetic moment, one of the victories of QED. One explanation has been in terms of SUSY, and I have also considered explanation in terms of N=2 SUSY strongly suggested by TGD. It has been is claimed that leptoquark with quantum numbers of D νR, where D denotes D type quark - actually s quark, which in TGD framework corresponds to genus g=1 for the corresponding partonic 2-surface - could explain all these anomalies.

TGD allows to consider two explanations for the observed breaking of leptonic universality in induced by quark self energy diagrams involving emission of virtual W- boson decaying normally to lepton pair.

The breaking of lepton universality for charged lepton pair production would be following. Penguin diagram involving self energy loop for b quark is involved. b quark transforms to t quark by emitting virtual W decaying to charged lepton and antineutrino. Antineutrino decays to leptoquark and s quark (say) and leptoquark fuses with top quark to charged antilepton. Charged lepton pairs is obtained and the presence of CKM matrix elements implies breaking of universality. Breaking of universality becomes possible also in the production of lepton-neutrino pairs. This option is discussed in an article and also in blog posting .

TGD allows also an alternative mechanism based on the (almost-)predicted existence of higher gauge boson generations, whose charged matrices are orthogonal to those of ordinary gauge bosons with charge matrix which in the 3-D state space associated with three families is unit matrix for the ordinary gauge bosons. For higher generations the charge matrices must break universality by orthogonality condition. Hence emission of virtual gauge boson of higher generation would explain the breaking of universality. For more details see the article and blog posting .

But what about TGD based SUSY, which should have N=2 and should be generated by adding right-handed neutrino or antineutrino to particle state assignable to a pair of wormhole contacts and basically to single wormhole throat as fermion line? Is there any hope that the p-adic mass scale corresponds to either k=89 (Mersenne) or more plausibly k=79 (Gaussian Mersenne)?

An interesting possibility is that light leptoquarks (using CP2 mass scale as unit) actually consist of quark and right-handed neutrino apart from possible mixing with left-handed antineutrino, whose addition to the one-particle state generates broken N=2 supersymmetry in TGD. The model for the breaking of universality is consistent with this interpretation since leptoquark is assumed to be scalar (squark!) and to consist of right-handed neutrino and quark. This would resolve the long-standing issue about the p-adic mass scale of sparticles in TGD. SUSY would be there - not N=1 SUSY of standard unifiers but N=2 SUSY of TGD reducing to CP2 geometry. I have made also other proposals - in particular the idea that sparticles could have same p-adic mass scales as particles but appear only as dark in TGD sense- that is having non-standard value of Planck constant.

With a lot of good luck both mechanisms are involved and leptoquarks are squarks in TGD sense. If also M89 and M79 hadron make themselves visible at LCH (there are several pieces of evidence for this), a breakthrough of TGD would be unavoidable. Or is it too optimistic to hope that the power of truth could overcome academic stupidity, which is after all the strongest force of Nature?

See the article Leptoquarks as first piece of evidence for TGD based view about SUSY? and chapters SUSY in TGD Universe and New Particle Physics Predicted by TGD: Part I.

Indications for the breaking of lepton universality from higher generations of weak bosons

Lepton and quark universality of weak interactions is basic tenet of the standard model. Now the first indications for the breaking of this symmetry have been found.

  1. Lubos tells that LHCb has released a preprint with title Measurement of the ratio of branching ratios (Bbar0→ Dbar *+ τ ντ)/ (Bbar0→ Dbar*+ μ νμ). The news is that the measured branching ratio is is about 33 per cent instead of 25 percent determined by mass ratios if standard model is correct. The outcome differs by 2.1 standard deviations from the prediction so that it might be a statistical fluke.
  2. There are also indications for second Bbar0 anomaly (see this). B mesons have to long and short-lived variants oscillating to their antiparticles and back - this relates to CP breaking. The surprise is that the second B meson - I could not figure out was it short- or long-lived - prefers to decay to eν instead of μnu;.
  3. There are also indications for the breaking of universality (see this) from B+ → K+e+ e- and B+ → K+μ+mu;- decays.

In TGD framework my first - and wrong - guess for an explanation was CKM mixing for leptons. TGD predicts that also leptons should suffer CKM mixing induced by the different mixings of topologies of the partonic 2-surfaces assignable to charged and neutral leptons. The experimental result would give valuable information about the values of leptonic CKM matrix. What new this brings is that the decays of W bosons to lepton pairs involve the mixing matrix and CKM matrix whose deviation from unit matrix brings effects anomalous in standard model framework.

The origin of the mixing would be topological - usually it is postulated in completely ad hoc manner for fermion fields. Particles correspond to partonic 2-surfaces- actually several of them but in case of fermions the standard model quantum numbers can be assigned to one of the partonic surfaces so that its topology becomes especially relevant. The topology of this partonic 2- surface at the end of causal diamond (CD) is characterized by its genus - the number of handles attached to sphere - and by its conformal equivalene class characterized by conformal moduli.

Electron and its muon correspond to spherical topology before mixing, muon and its neutrino to torus before mixing etc. Leptons are modelled assuming conformal invariance meaning that the leptons have wave functions - elementary particle vacuum functionals - in the moduli space of conformal equivalence classes known as Teichmueller space.

Contrary to the naive expection mixing alone does not explain the experimental finding. Taking into account mass corrections, the rates should be same to different charged leptons since neutrinos are not identified. That mixing does not have any implications follows from the unitary of the CKM matrix.

The next trial is based on the prediction of 3 generations of weak bosons suggested by TGD.

  1. TGD based explanation of family replication phenomenon in terms of genus-generation correspondence forces to ask whether gauge bosons identifiable as pairs of fermion and antifermion at opposite throats of wormhole contact could have bosonic counterpart for family replication. Dynamical SU(3) assignable to three lowest fermion generations/genera labelled by the genus of partonic 2-surface (wormhole throat) means that fermions are combinatorially SU(3) triplets. Could 2.9 TeV state - if it would exist - correspond to this kind of state in the tensor product of triplet and antitriplet? The mass of the state should depend besides p-adic mass scale also on the structure of SU(3) state so that the mass would be different. This difference should be very small.
  2. Dynamical SU(3) could be broken so that wormhole contacts with different genera for the throats would be more massive than those with the same genera. This would give SU(3) singlet and two neutral states, which are analogs of η′ and η and π0 in Gell-Mann's quark model. The masses of the analogs of η and π0 and the the analog of η′, which I have identified as standard weak boson would have different masses. But how large is the mass difference?
  3. These 3 states are expected to have identical mass for the same p-adic mass scale, if the mass comes mostly from the analog of hadronic string tension assignable to magnetic flux tube. connecting the two wormhole contacts associates with any elementary particle in TGD framework (this is forced by the condition that the flux tube carrying monopole flux is closed and makes a very flattened square shaped structure with the long sides of the square at different space-time sheets). p-Adic thermodynamics would give a very small contribution genus dependent contribution to mass if p-adic temperature is T=1/2 as one must assume for gauge bosons (T=1 for fermions). Hence 2.95 TeV state for which there are some indications could indeed correspond to second Z generation. W should have similar state at 2.5 TeV.
The orthogonality of the 3 weak bosons implies that their charge matrices are orthogonal. As a consequence, the higher generations of weak bosons do not have universal couplings to leptons and quarks. The breaking of universality implies a small breaking of universality in weak decays of hadrons due to the presence of virtual MG,79 boson decaying to lepton pair. These anomalies should be seen both in the weak decays of hadrons producing Lν pairs via the decay of virtual W or its partner WG,79 and via the decay of virtual Z of its partner Zg,79 to L+ L- . Also γG,79 could be involved.

This could explain the three anomalies associated with the neutral B mesons, which are analogs of neutral K mesons having long- and short-lived variants.

  1. The two anomalies involving W bosons could be understood if some fraction of decays takes place via the decay b→ c+WG,79 followed by WG,79→ L+ν . The charge matrix of WG,79 is not universal and since CP breaking is involved. Hence one could have interference effects, which increase the braching fraction to τν or eν relative to μν depending on whether the state is long- or shortlived B meson.
  2. The anomaly in decays producing charged lepton pairs in decayse of B+ does not involve CP breaking and would be due to the non-universality of ZG,79 charge matrix.
TGD allows also to consider leptoquarks as pairs of leptons and quarks and there is some evidence for them too! I wrote a blog posting about this too (for an article see this). Also indications for M89 and MG,79 hadron physics with scaled up mass scales are accumulating and QCD is shifting tot the verge of revolution (see this).

It seems that TGD is really there and nothing can prevent it showing up. I predict that next decades in physics will be a New Golden Age of both experimental and theoretical physics. I am eagerly and impatiently waiting that theoretical colleagues finally wake up from their 40 year long sleep and CERN will again be full of working physicists also during weekends (see this);-).

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

Indication for a scaled variant of Z boson

Both Tommaso Dorigo and Lubos Motl tell about a spectacular 2.9 TeV di-electron event not observed in previous LHC runs. Single event of this kind is of course most probably just a fluctuation but human mind is such that it tries to see something deeper in it - even if practically all trials of this kind are chasing of mirages.

Since the decay is leptonic, the typical question is whether the dreamed for state could be an exotic Z boson. This is also the reaction in TGD framework. The first question to ask is whether weak bosons assignable to Mersenne prime M89 have scaled up copies assignable to Gaussian Mersenne M79. The scaling factor for mass would be 2(89-89)/2= 32. When applied to Z mass equal to about .09 TeV one obtains 2.88 TeV, not far from 2.9 TeV. Eureka!? Looks like a direct scaled up version of Z!? W should have similar variant around 2.6 TeV.

TGD indeed predicts exotic weak bosons and also gluons. TGD based explanation of family replication phenomenon in terms of genus-generation correspondence forces to ask whether gauge bosons identifiable as pairs of fermion and antifermion at opposite throats of wormhole contact could have bosonic counterpart for family replication. Dynamical SU(3) assignable to three lowest fermion generations/genera labelled by the genus of partonic 2-surface (wormhole throat) means that fermions are combinatorially SU(3) triplets. Could 2.9 TeV state - if it would exist - correspond to this kind of state in the tensor product of triplet and antitriplet? The mass of the state should depend besides p-adic mass scale also on the structure of SU(3) state so that the mass would be different. This difference should be very small.

Dynamical SU(3) could be broken so that wormhole contacts with different genera for the throats would be more massive than those with the same genera. This would give SU(3) singlet and two neutral states, which are analogs of η′ and η and π0 in Gell-Mann's quark model. The masses of the analogs of η and π0 and the the analog of η′, which I have identified as standard weak boson would have different masses. But how large is the mass difference?

These 3 states are expected top have identical mass for the same p-adic mass scale, if the mass comes mostly from the analog of hadronic string tension assignable to magnetic flux tube. connecting the two wormhole contacts associates with any elementary particle in TGD framework (this is forced by the condition that the flux tube carrying monopole flux is closed and makes a very flattened square shaped structure with the long sides of the square at different space-time sheets). p-Adic thermodynamics would give a very small contribution genus dependent contribution to mass if p-adic temperature is T=1/2 as one must assume for gauge bosons (T=1 for fermions). Hence 2.95 TeV state could indeed correspond to this kind of state.

Can one imagine any pattern for the Mersennes and Gaussian Mersennes involved? Charged leptons correspond to electron (M127), muon (MG,113) and tau (M107): Mersenne- Gaussian Mersenne-Mersenne. Does one have similar pattern for gauge bosons too: M89- MG,79 - M61?

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

Does color deconfinement really occur?

Bee had a nice blog posting related to the origin of hadron masses and the phase transition from color confinement to quark-gluon plasma involving also restoration of chiral symmetry in the sigma model description. In the ideal situation the outcome should be a black body spectrum with no correlations between radiated particles.

The situation is however not this. Some kind of transition occurs and produces a phase, which has much lower viscosity than expected for quark-gluon plasma. Transition occurs also in much smoother manner than expected. And there are strong correlations between opposite charged particles - charge separation occurs. The simplest characterization for these events would be in terms of decaying strings emitting particles of opposite charge from their ends. Conventional models do not predict anything like this.

Some background

The masses of current quarks are very small - something like 5-20 MeV for u and d. These masses explain only a minor fraction of the mass of proton. The old fashioned quark model assumed that quark masses are much bigger: the mass scale was roughly one third of nucleon mass. These quarks were called constituent quarks and - if they are real - one can wonder how they relate to current quarks.

Sigma model provide a phenomenological decription for the massivation of hadrons in confined phase. The model is highly analogous to Higgs model. The fields are meson fields and baryon fields. Now neutral pion and sigma meson develop vacuum expectation values and this implies breaking of chiral symmetry so that nucleon become massive. The existence of sigma meson is still questionable.

In a transition to quark-gluon plasma one expects that mesons and protons disappear totally. Sigma model however suggests that pion and proton do not disappear but become massless. Hence the two descriptions might be inconsistent.

The authors of the article assumes that pion continues to exist as a massless particle in the transition to quark gluon plasma. The presence of massless pions would yield a small effect at the low energies at which massless pions have stronger interaction with magnetic field as massive ones. The existence of magnetic wave coherent in rather large length scale is an additional assumption of the model: it corresponds to the assumption about large heff in TGD framework, where color magnetic fields associated with M89 meson flux tubes replace the magnetic wave.

In TGD framework sigma model description is at best a phenomenological description as also Higgs mechanism. p-Adic thermodynamics replaces Higgs mechanism and the massivation of hadrons involves color magnetic flux tubes connecting valence quarks to color singles. Flux tubes have quark and antiquark at their ends and are mesonlike in this sense. Color magnetic energy contributes most of the mass of hadron. Constituent quark would correspond to valence quark identified as current quark plus the associated flux tube and its mass would be in good approximation the mass of color magnetic flux tube.

There is also an analogy with sigma model provided by twistorialization in TGD sense. One can assign to hadron (actually any particle) a light-like 8-momentum vector in tangent space M8=M4× E4 of M4× CP2 defining 8-momentum space. Massless implies that ordinary mass squared corresponds to constant E4 mass which translates to a localization to a 3-sphere in E4. This localization is analogous to symmetry breaking generating a constant value of π0 field proportional to its mass in sigma model.

An attempt to understand charge asymmetries in terms of charged magnetic wave and charge separation

One of the models trying to explain the charge asymmetries is in terms of what is called charged magnetic wave effect and charge separation effect related to it. The experiment discussed by Bee attempts to test this model.

  1. So called chiral magnetic wave effect and charge separation effects are proposed as an explanation for the the linear dependence of the asymmetry of so called elliptic flow on charge asymmetry. Conventional models explain neither the charge separation nor this dependence. Chiral magnetic wave would be a coherent magnetic field generated by the colliding nuclei in a relatively long scale, even the length scale of nuclei.
  2. Charged pions interact with this magnetic field. The interaction energy is roughly h× eB/E, where E is the energy of pion. In the phase with broken chiral symmetry the pion mass is non-vanishing and at low energy one has E=m in good approximation. In chirally symmetric phase pion is massless and magnetic interaction energy becomes large a low energies. This could serve as a signature distginguishing between chirally symmetric and asymmetric phases.
  3. The experimenters try to detect this difference and report slight evidence for it. This is change of the charge asymmetry of so called elliptic flow for positively and negatively charged pions interpreted in terms of charge separation fluctuation caused by the presence of strong magnetic field assumed to lead to separation of chiral charges (left/righ handedness). The average velocities of the pions are different and average velocity depends azimuthal angle in the collision plane: second harmonic is in question (say sin(2φ)).
In TGD framework the explanation of the un-expected behavior of should-be quark-gluon plasma is in terms of M89 hadron physics.
  1. A phase transition indeed occurs but means a phase transition transforming the quarks of the ordinary M107 hadron physics to those of M89 hadron physics. They are not free quarks but confined to form M89 mesons. M89 pion would have mass about 135 GeV. A naive scaling gives half of this mass but it seems unfeasible that pion like state with this mass could have escaped the attention - unless of course the unexpected behavior of quark gluon plasma demonstrates its existence! Should be easy for a professional to check. Thus a phase transition would yield a scaled up hadron physics with mass scale by a factor 512 higher than for the ordinary hadron physics.
  2. Stringy description applies to the decay of flux tubes assignable to the M89 mesons to ordinary hadrons. This explains charge separation effect and the deviation from the thermal spectrum.
  3. In the experiments discussed in the article the cm energy for nucleon-nucleon system associated with the colliding nuclei varied between 27-200 GeV so that the creation of even on mass shell M89 pion in single collision of this kind is possible at highest energies. If several nucleons participate simultaneosly even many-pion states are possible at the upper end of the interval.
  4. These hadrons must have large heff=n× h since collision time is roughly 5 femtoseconds, by a factor about 500 (not far from 512!) longer than the time scale associated with their masses if M89 pion has the proposed mass of 135 MeV for ordinary Planck constant and scaling factor 2× 512 instead of 512 in principle allowed by p-adic length scale hypothesis. There are some indications for a meson with this mass. The hierarchy of Planck constants allows at quantum criticality to zoom up the size of much more massive M89 hadrons to nuclear size! The phase transition to dark M89 hadron physics could take place in the scale of nucleus producing several M89 pions decaying to ordinary hadrons.
  5. The large value of heff would mean quantum coherence in the scale of nucleus explaining why the value of viscosity was much smaller than expected for quark gluon plasma. The expected phase transition was also much smoother than expected. Since nuclei are many-nucleon systems and the Compton wavelength of M89 pion would be of order nucleus size, one expects that the phase transition can take place in a wide collision energy range. At lower energies several nucleon pairs could provide energy to generate M89 pion. At higher energies even single nucleon pair could provide the energy. The number of M89 pions should therefore increase with nucleon-nucleon collision energy, and induce the increase of charge asymmetry and strength of the charge asymmery of the elliptic flow.
  6. Hydrodynamical behavior is essential in order to have low viscosity classically. Even more, the hydrodynamics had better to be that of an ideal liquid. In TGD framework the field equations have hydrodynamic character as conservation laws for currents associated with various isometries of imbedding space. The isometry currents define flow lines. Without further conditions the flow lines do not however integrate to a coherent flow: one has something analogous to gas phase rather than liquid so that the mixing induced by the flow cannot be described by a smooth map.

    To achieve this given isometry flow must make sense globally - that is to define coordinate lines of a globally defined coordinate ("time" along flow lines). In this case one can assign to the flow a continuous phase factor as an order parameter varying along the flow lines. Super-conductivity is an example of this. The so called Frobenius conditions guarantee this at least the preferred extremals could have this complete integrability property making TGD an integrable theory (see the appendix of the article at my homepage). In the recent case, the dark flux tubes with size scale of nucleus would carry ideal hydrodynamical flow with very low viscosity.

See the chapter New Particle Physics Predicted by TGD: Part I or article Does color deconfinement really occur?.

Could MG,79 hadron physics be seen at LHC?

Gaussian Mersennes MG,n=(1+i)n-1 (complex primes for complex integers) are much more abundant than ordinary Mersennes and corresponding p-adic time scales seem to define fundamental length scales of cosmology, astrophysics, biology, nuclear physics, and elementary physics. There are as many as 10 Gaussian Mersennes besides 9 Mersennes above LHC energy scale suggesting a lot of new physics in sharp contrast with the GUT dogma that nothing interesting happens above weak boson scale- perhaps copies of hadron physics or weak interaction physics. In the following I consider only those Gaussian Mersennes possibly interesting from the point of view of very high energy particle physics.

n∈{2, 3, 5, 7, 11, 19, 29, 47, 73} correspond to energies not accessible at LHC. n= 79 might define new copy of hadron physics above TeV range - something which I have not considered seriously before. The scaled variants of pion and proton masses (M107 hadron physics) are about 2.2 TeV and 16 TeV. Is it visible at LHC is a question mark to me.

Some weeks after writing the last sentence I saw the posting of Lubos suggesting that MG,79 pion might have been already seen! Lubos tells about a bump around 2(!)TeV energy observed already earlier at ATLAS and now also at CMS. See the article in Something goes bump in Symmetry Magazine. The local signficance is about 3.5 sigma and local significance about 2.5 sigma. Bump decays to weak bosons.

Many interpretations are possible. An interpretation as new Higgs like particle has been suggested. Second interpretation - favored by Lubos - is as right-handed W boson predicted by left-right- symmetric variants of the standard model. If this is correct interpretation, one can forget about TGD since the main victory of TGD is that the very strange looking symmmetries of standrad model have an elegant explanation in terms of CP2 geometry, which is also twistorially completely unique and geometrizes both electroweak and color quantum numbers.

Note that the masses masses of MG,79 weak physics would be obtained by scaling the masses of ordinary M89 weak bosons by factor 2(89-79)/2)= 512. This would give the masses about 2.6 TeV and 2.9 TeV.

There is however an objection. If one applies p-adic scaling 2(107-89)/2=29 of pion mass in the case of M89 hadron physics, M89 pion should have mass about 69 GeV (this brings in mind the old and forgotten anomaly known as Aleph anomaly at 55 GeV). I proposed that the mass is actually an octave higher and thus around 140 GeV: p-adic length scale hypothesis allows to consider octaves. Could it really be that a pion like state with this mass could have slipped through the sieve of particle physicists? Note that the proton of M89 hadron physics would have mass about .5 TeV.

I have proposed that M89 hadron physics has made itself visible already in heavy ion collisions at RHIC and in proton-heavy ion collisions at LHC as strong deviation from QCD plasma behavior meaning that charged particles tended to be accompanied by particles of opposite charged in opposite direction as if they would be an outcome of a decay of string like objects, perhaps M89 pions. There has been attempts - not very successful - to explain non-QCD type behavior in terms of AdS/CFT. Scaled up variant of QCD would explain them elegantly. Strings would be in D=10. The findings from LHC during this year probably clarify this issue.

Lubos is five days later more enthusiastic about superstring inspired explanation of the bump than the explanation relying on left-right symmetric variant of the standard model. The title of the posting of Lubos is The 2 TeV LHC excess could prove string theory. The superstringy model involves as many as six superstring phenomenologists as chefs and the soup contains intersecting branes and anomalies as ingredients.

The article gives further valuable information about the bump also for those who are not terribly interested on intersecting branes and addition of new anomalous factors to the standard model gauge group. The following arguments show that the information is qualitatively consistent with the TGD based model.

  1. Bump is consistent with both ZZ, WZ, and according to Lubos also Zγ final states and is in the range 1.8-2.1 TeV. Therefore bump could involve both charged and neutral states. If the bump corresponds to neutral elementary particle such as new spin 1 boson Z' as proposed by superstring sextet, the challenge is to explain ZZ and Zγ bumps. WZ pairs cannot result from primary decays.
  2. There is dijet excess, which is roughly by a factor of 20 larger than weak boson excesses. This would suggest that some state decays to quarks or their excitations and the large value of QCD coupling strength gives rise to a the larger excess. This also explains also why no lepton excess is observed.

    For the superstring inspired model the large branching fraction to hadronic dijets suggesting the presence of strong interactions is a challenge: Lubos does not comment this problem. Also the absence of leptonic pairs is problematic and model builders deduce that Z' suffers syndrome known as lepto-phobia.

  3. Neutral and charged MG,79 pions can decay to virtual MG,79 or M89 quark pair annihilating further to a pair of weak bosons (also γγ pair is predicted) or by exchange of gluon to MG,79, M89 (or M107) quark pair producing eventually the dijet. This would explain the observations qualitatively. If the order of magnitude for the relative mass splitting between neutral and charged MG,79 pion is same as for ordinary pion one, the relative splitting is of order Δ M/M≈ 1/14 - less that 10 per cent meaning Δ M<.2 TeV. The range for the position of the bump is about .3 TeV.
  4. The predictions of TGD model are in principle calculable. The only free parameter is the MG,79 color coupling strength so that the model is easy to test.
See the chapter New Particle Physics Predicted by TGD: Part I.

Criticality of Higgs: is Planck length dogmatics physically feasible?

While studying the materials related to Convergence conference running during this week at Perimeter institute I ended up with a problem related to the fact that the mass Mh= 125.5+/- .24 GeV implies that Higgs as described by standard model (now new physics at higher energies) is at the border of metastability and stability - one might say near criticality (see this and this), and I decided to look from TGD perspective what is really involved.

Absolute stability would mean that the Higgs potential becomes zero at Planck length scale assumed to be the scale at which QFT description fails: this would require Mh>129.4 GeV somewhat larger that the experimentally determined Higgs mass in standard model framework. Metastability means that a new deep minimum is developed at large energies and the standard model Higgs vacuum does not anymore correspond to a minimum energy configuration and is near to a phase transition to the vacuum with lower vacuum energy. Strangely enough, Higgs is indeed in the metastable region in absence of any new physics.

Since the vacuum expectation of Higgs is large at high energies the potential is in a reasonable approximation of form V= λ h4, where h is the vacuum expectation in the high energy scale considered and λ is dimensionless running coupling parameter. Absolute stability would mean λ=0 at Planck scale. This condition cannot however hold true as follows from the input provided by top quark mass and Higgs mass to which λ at LHC energies is highly sensitive. Rather, the value of λ at Planck scale is small and negative: λ(MPl)=-0.0129 is the estimate to be compared with λ(Mt)=0.12577 at top quark mass. This implies that the potential defining energy density associated with the vacuum expectation value of Higgs becomes negative at high enough energies.The energy at which λ becomes negative is in the range 1010-1012 GeV, which is considerably lower than Planck mass about 1019 GeV. This estimate of course assumes that there is no new physics involved.

The plane defined by top and Higgs masses can be decomposed to regions (see figure 5 of this), where perturbative approach fails (λ too large), there is only single minimum of Higgs potential (stability), there is no minimum of Higgs potential (λ<0, instability) and new minima with smaller energy is present (metastability). This metastability can lead to a transition to a lower energy state and could be relevant in early cosmology and also in future cosmology.

The value of λ turns out to be rather small at Planck mass. λ however vanishes and changes sign in a much lower energy range 1010-1012 GeV. Is this a signal that something interesting takes place considerably below Planck scale? Could Planck length dogmatics is wrong? Is criticality only an artefact of standard model physics and as such a signal for a new physics?

How could this relate to TGD? Planck length is one of the unchallenged notions of modern physics but in TGD p-adic mass calculations force to challenge this dogma. Planck length is replaced with CP2 length scale which is roughly 104 longer than Planck length and determined by the condition that electron corresponds to the largest Mersenne prime (M127), which does not define completely super-astrophysical p-adic length scale, and by the condition that electron mass comes out correctly. Also many other elementary particles correspond to Mersenne primes. In biological relevant scales there are several (4) Gaussian Mersennes.

In CP2 length scale the QFT approximation to quantum TGD must fail since the the replacement of the many-sheeted space-time with GRT space-time with Minkowskian signature of the metric fails, and space-time regions with Euclidian signature of the induced metric defining the lines of generalized Feynman diagrams cannot be anymore approximated as lines of ordinary Feynman diagrams or twistor diagrams. From electron mass formula and electron mass of .5 MeV one deduces that CP2 mass scale is 2.53× 1015 GeV - roughly three orders of magnitudes above 1012 GeV obtained if there is no new physics emerges above TeV scale.

TGD "almost-predicts" several copies of hadron physics corresponding to Mersenne primes Mn, n=89, 61, 31,.. and these copies of hadron physics are expected to affect the evolution of λ and maybe raise the energy 1012 GeV to about 1015 GeV. For M31 the electronic p-adic mass scale happens to be 2.2× 1010 GeV. The decoupling of Higgs by the vanishing of λ could be natural at CP2 scale since the very notion of Higgs vacuum expectation makes sense only at QFT limit becoming non-sensical in CP2 scale. In fact, the description of physics in terms of elementary particles belonging to three generations might fail above this scale. Standard model quantum numbers make still sense but the notion of family replication becomes questionable since in TGD framework the families correspond to different boundary topologies of wormhole throats and the relevant physics is above this mass scale inside the wormhole contacts: there would be only single fermion generation below CP2 scale.

This raises questions. Could one interpret the strange criticality of the Higgs as a signal about the fact that CP2 mass scale is the fundamental mass scale and Newton's constant might be only a macroscopic parameter. This would add one more nail to the coffin of superstring theory and of all theories relying on Planck length scale dogmatics. One can also wonder whether the criticality might somehow relate to the quantum criticality of TGD Universe. My highly non-educated guess is that it is only an artefact of standard model description. Note however that below CP2 scale the transition from the phase dominated by cosmic strings to a phase in which space-time sheets emerge and leading to the radiation dominated cosmology would take place: this period would be the TGD counterpart for the inflationary period and also involve a rapid expansion.

See the chapter Higgs or Something Else.

Have lepto-quarks been observed in the decays of B mesons?

Jester told in his blog "Resonaances" about an evidence for anomalies in the decays of B meson to K meson and lepton pair. There exist several anomalies.

  1. The 3.7 sigma deviation from standard model predictions in the differential distribution of the B→ K*μ+μ- decay products.
  2. The 2.6 sigma violation of lepton flavor universality in B+→ K+l+l- decays.
The reported violation of lepton universality (, which need not be real) is especially interesting. The branching ratio B(B+→ K+e+e-)/B(B+→ K+μ+μ-)≈ .75 holds true. Standard model expectation is very near to unity.

Scalar lepto-quark has been proposed as an explanation of the anomaly. The lowest order diagram for lepton pair production in standard model is penguin diagram obtained from the self energy diagram for b quark involving tW- intermediate in which W emits γ/Z decaying to lepton pair. Lepton universality is obvious. The penguin diagram involves 4 vertices and 4 propagators and the product of CKM matrix elements VtbV*st. The diagram involving leptoquark is obtained from this diagram by a modification.

The diagram would induce an effective four-fermion coupling bbarLγ μsL μ+Lγμ μ-L representing neutral current breaking universality. Authors propose a heavy scalar boson exchanges with quantum numbers of lepto-quark and mass of order 10 TeV to explain why no anomalous weak interactions between leptons and quarks by lepto-quark exchange have not been observed. Scalar nature would suggest Higgs type coupling proportional to mass of the lepton and this could explain why the effect of exchange is smaller in the case of electron pair. The effective left-handed couplings would however suggest vector lepto-quarks with couplings analogous to W boson coupling. Note that the effect should reduce the rate: the measured rate for Bs → μ-μ+ is .79+/- .20: reduction would be due to destructive interference of amplitudes.

General ideas

Some general ideas about TGD are needed in the model and are listed in order to avoid the impression that the model is just ad hoc construct.

  1. In TGD all elementary particle can be regarded as pairs of wormhole contacts through which monopole magnetic flux flows: two wormhole contacts are necessary to get closed magnetic field lines. Monopole flux in turn guarantees the stability of the wormhole contact. In the case of weak bosons second wormhole contact carries fermion and antifermion at opposite throats giving rise to the net charges of the boson. The neutrino pair at the second wormhole contact neutralize the weak charges and guarantees short range of weak interactions.
  2. The TGD inspired explanation of family replication phenomenon is in terms of the genus of the partonic 2-surfaces (wormhole throat) at the end of causal diamond. There is topological mixing of partonic topologies which depend on weak quantum numbers of the wormhole throat leading to CKM mixing. Lepton and quark families obvious correspond to each other: L(g)↔ q(g) and this is important in the model to be considered.

    The genera of the opposite wormhole throats are assumed to be identical for bosonic wormhole contacts. This can be assumed also for fermionic wormhole contacts for which only second throat carries fermion number. The universality of standard model couplings inspires the hypothesis that bosons are superpositions of the three lowest genera forming singlets with respect effective symmetry group SU(3)g associated with the 3 lowest genera. Gauge bosons involve also superpositions of various fermion pairs with coefficients determined by the charge matrix.

  3. p-Adic length scale hierarchy is one of the key predictions of TGD. p-Adic length scale hypothesis (to be used in the sequel) stating that p-adic primes are near powers of of 2: p≈ 2k, k integer, relies on the success of p-adic mass calculations. p-Adic length scale hypothesis poses strong constraints on particle mass scales and one can readily estimate the mass of possible p-adically scaled up variants of masses of known elementary particles.

    One of the basic predictions is the possibility of p-adically scaled up variants of ordinary hadron physics and also of weak interaction physics. One such prediction is M89 ~ hadron physics, which is scaled up variant of the ordinary M107 hadron physics with mass scale which is by a factor 512 higher and corresponds to the energy scale relevant at LHC. Hence LHC might eventually demonstrate the feasibility of TGD.

    Quite generally, one can argue that one should speak about M89 physics in which exotic variants of weak bosons and scaled up variants of hadrons appear. There would be no deep distinction between weak bosons and M89 hadrons and elementary particles in general: all of them would correspond to string like objects involving both magnetic flux tubes carrying monopole flux between two wormhole throats and string world sheets connecting the light-like orbits of wormhole throats at which the signature of the induced metric changes.

  4. TGD predicts dark matter hierarchy based on phases with non-standard value heff=n× h of Planck constant. The basic applications are to living matter but I have considered also particle physics applications.
    1. Dark matter in TGD sense provides a possible explanation for the experimental absence of super partners of ordinary particles: sparticles would be dark and would be characterized by the same p-adic mass scales as sparticles
    2. TGD predicts also colored leptons and there is evidence for meson like bound states of colored leptons. Light colored leptons are however excluded by the decay widths of weak bosons but also now darkness could save the situation.
    3. I have also proposed that RHIC anomaly observed in heavy ion collisions and its variant for proton heavy ion collisions at LHC suggesting string like structures can be interpreted in terms of low energy M89 hadron physics but with large value of heff meaning that the M89 p-adic length scale increases to M107 p-adic length scale (ordinary hadronic length scale).
    One can consider also the adventurous possibility that vector lepto-quarks are dark in TGD sense.
  5. TGD view about gauge bosons allows to consider also lepto-quark type states. These bosons would have quark and lepton at opposite wormhole throats. One can consider bosons which are SU(3)g singlets defined by superpositions of L(g)q(g) or L(g)qbar(g). These states can be either M4 vectors or scalars (all bosons are vectors in 8-D sense in TGD by 8-D chiral symmetry guaranteeing separate conservation of B and L). Left handed couplings to quarks and leptons analogous to those of W bosons are suggested by the model for the anomalies. Vector lepto-quarks can be consistent with what is known about weak interactions only if they are dark in TGD sense. Scalar lepto-quarks could have ordinary value of Planck constant.
A TGD based model for the B anomaly in terms of lepto-quarks

It is natural to approach also the anomaly under discussion by assuming the basic framework just described. The anomaly in the decay amplitude of B→ Kμ-μ+ could be due to an additional contribution based on a simple modification for the standard model amplitude.

  1. In TGD framework, and very probably also in the model studied in the article, the starting point is the penguin diagram for lepton pair production in B→ Kμ-μ+ decay involving only the decay b→ sl+l- by virtual tW state emitting virtual γ/Z decaying to lepton pair and combining with t to form s.
    1. The diagram for lepton pair production involving virtual lepto-quark is obtained from the tW- self-energy loop for b. One can go around the W- branch of the loop to see what must happen. The loop starts with b→ tW- followed by W-→ l-(g1) νbar(g1) producing on mass shell lepton l-(g1). This is followed by νbar(g1)→ s X(Dbarνbar) producing on mass shell s. The genus of the virtual neutrino must ge g=1 unless leptonic CKM mixing is allow in the W decay vertex.

      After this one has X=∑Dbar(g)νbar(g) → Dbar(g2)νbar(g2). Any value of g2 is possible. Finally, one has tDbar→ W+ and W+ νbar(g2)) → l+(g2). There are two loops involved and four lines contain a heavy particle (two W bosons, t, and X). The diagram contains 6 electroweak vertices whereas the standard model diagram has 4 vertices.

    2. All possible lepton pairs can be produced. The amplitude is proportional to the product VtbV*tD(g2) implying breaking of lepton universality. The amplitude for production of e+μ- pair is considerably smaller than that for μ+μ- and τ+μ- as the experimental findings suggest. If neutrino CKM mixing is taken into account, there is also a proportional to the matrix element VLl(g1g=1.

      In absence of leptonic CKM mixing (mixing explains the recently reported production of μ+e- pairs in the decays of Higgs) only μ-l+(g) pairs are produced. The possibility to have g≠ 1 is also a characteristic of lepton non-universality, which is however induced by the hadronic CKM mixing: lepto-quark couplings are universal.

      Note that the flavour universality of the gauge couplings means in the case of lepto-quarks that Lq pairs superpose to single SU(3)g singlet as for ordinary gauge bosons. If L(g)q(g) would appear as separate particles, only μ+μ- pairs would be produced in absence of leptonic CKM mixing.

  2. A rough estimate for the ratio r of lepto-quark amplitude A(b→ sl- (g1)l+ (g2) to the amplitude A(b→ sl-(g)l+(g) involving virtual photon decaying to l+l- pair is

    z =[X1/X2]× [F1(xX,xt)/F2(xt)],

    X1=VLl1ν(g=1) [∑gVLl(g2)ν(g) V*D(g)t]VtD(g2)g X2gW2 ,

    X2=V*dte2 ,

    xX= m2(X)/m2(W) , xt= m2(t)/m2(W) .

    The functions Fi correspond come from the loop integral and depend on mass ratios appearing as the argument. The factors Xi collect various coupling parameters together.

  3. The objection is that the model predicts a contribution to the scattering of leptons and quarks of the same family (L(g)-q(g) scattering) by the exchange of lepto-quark, which is of the same order of magnitude as for ordinary weak interactions. This should have been observed in high precision experiments testing standard model if the mass of the lepto-quark is of the same magnitude as weak boson mass. 10 TeV mass scale for lepto-quarks should guarantee that this is not the case and is probably the basic motivation for the estimate of the article. This requires that the ratio of the loop integrals appearing in z is of the order of unity. For a processional it should be easy to check this. Since the loop integral in the case of scalar lepto-quark studied in the article has the desired property and should not depend on the spin of the particles in the loops, one has good reasons to expect that the same holds true also for vector lepto-quarks.

    Without precise numerical calculation one cannot be sure that the loop integral ratio is not too large. In this case one could reduce the gauge coupling to lepto-quarks (expected to be rather near to weak coupling constant strength) but this looks like ad hoc trick. A more adventurous manner to overcome the problem would be to assume that lepto-quarks represent dark matter in TGD sense having effective Planck constant heff=n× h. Therefore they would not be visible in the experiments, which do not produce dark matter in elementary particle length scales.

  4. The proposal of the article is that lepto-quark is scalar so that its coupling strength to leptons and quarks increases with mass scale. If I have understood correctly, the motivation for this assumption is that only in this manner the effect on the rate for e+e- production is smaller than in the case of μ+μ- pair. As found, the presence of CKM matrix elements in lepto-quark emission vertices at which quark charge changes, guarantees that both anomalous contributions to the amplitude are for electron pair considerably smaller than for muon pair.
  5. Consider first a mass estimate for dark vector lepto-quark assumed to have weak boson mass scale. Even the estimate m(X)∼ m(W) is much higher than the very naive estimate as a sum of μ- and s masses would suggest. Quite generally, if weak bosons, lepto-quarks, and M89 hadrons are all basic entities of same M89 physics, the mass scale is expected to be that of M89 hadron physics and of the order of weak mass scale. A very naive scaling estimate for the mass would be by factor 512 and give an estimate around 50 GeV. If μ- mass is scaled by the same factor 512, one obtains mass of order 100 GeV consistent with the estimate for the magnitude of the anomaly.

    Second p-adic mass scale estimate assumes vector or scalar lepto-quark with mass scale not far from 10 TeV. Ordinary μ- corresponds to Gaussian Mersenne MG,k, k=113. If p-adically scaled up variant of lepton physics is involved, the electron of the p-adically scaled up lepton physics could correspond to M89. If muons correspond to Gaussian primes then the scaled up muon would correspond to the smallest Gaussian Mersenne prime below M89, which is MG,79. The mass of the scaled up muon would be obtained from muon mass by scaling by a factor 2(113-79)/2 =217=1.28× 105 giving mass of order 10 TeV, which happens to be consistent with the conservative estimate of the article.

See the chapter New Particle Physics Predicted by TGD or the article Have lepto-quarks been observed in the decays of B mesons?.

What could be the TGD counterpart of SUSY

Supersymmetry is very beautiful generalization of the ordinary symmetry concept by generalizing Lie-algebra by allowing grading such that ordinary Lie algebra generators are accompanied by super-generators transforming in some representation of the Lie algebra for which Lie-algebra commutators are replaced with anti-commutators. In the case of Poincare group the super-generators would transform like spinors. Clifford algebras are actually super-algebras. Gamma matrices anti-commute to metric tensor and transform like vectors under the vielbein group (SO(n) in Euclidian signature). In supersymmetric gauge theories one introduced super translations anti-commuting to ordinary translations.

Supersymmetry algebras defined in this manner are characterized by the number of super-generators and in the simplest situation their number is one: one speaks about N=1 SUSY and minimal super-symmetric extension of standard model (MSSM) in this case. These models are most studied because they are the simplest ones. They have however the strange property that the spinors generating SUSY are Majorana spinors- real in well-defined sense unlike Dirac spinors. This implies that fermion number is conserved only modulo two: this has not been observed experimentally. A second problem is that the proposed mechanisms for the breaking of SUSY do not look feasible.

LHC results suggest MSSM does not become visible at LHC energies. This does not exclude more complex scenarios hiding simplest N=1 to higher energies but the number of real believers is decreasing. Something is definitely wrong and one must be ready to consider more complex options or totally new view abot SUSY.

What is the situation in TGD? Here I must admit that I am still fighting to gain understanding of SUSY in TGD framework. That I can still imagine several scenarios shows that I have not yet completely understood the problem and am working hardly to avoid falling to the sin of sloppying myself. In the following I summarize the situation as it seems just now.

  1. In TGD framework N=1 SUSY is excluded since B and L and conserved separately and imbedding space spinors are not Majorana spinors. The possible analog of space-time SUSY should be a remnant of a much larger super-conformal symmetry in which the Clifford algebra generated by fermionic oscillator operators giving also rise to the Clifford algebra generated by the gamma matrices of the "world of classical worlds" (WCW) and assignable with string world sheets. This algebra is indeed part of infinite-D super-conformal algebra behind quantum TGD. One can construct explicitly the conserved super conformal charges accompanying ordinary charges and one obtains something analogous to N=∞ super algebra. This SUSY is however badly broken by electroweak interactions.
  2. The localization of induced spinors to string world sheets emerges from the condition that electromagnetic charge is well-defined for the modes of induced spinor fields. There is however an exception: covariantly constant right handed neutrino spinor νR: it can be de-localized along entire space-time surface. Right-handed neutrino has no couplings to electroweak fields. It couples however to the left handed neutrino by induced gamma matrices except when it is covariantly constant. Note that standard model does not predict νR but its existence is necessary if neutrinos develop Dirac mass. νR is indeed something which must be considered carefully in any generalization of standard model.

Could covariantly constant right handed neutrinos generate SUSY?

Could covariantly constant right-handed spinors generate exact N=2 SUSY? There are two spin directions for them meaning the analog N=2 Poincare SUSY. Could these spin directions correspond to right-handed neutrino and antineutrino. This SUSY would not look like Poincare SUSY for which anticommutator of super generators would be proportional to four-momentum. The problem is that four-momentum vanishes for covariantly constant spinors! Does this mean that the sparticles generated by covariantly constant νR are zero norm states and represent super gauge degrees of freedom? This might well be the case although I have considered also alternative scenarios.

What about non-covariantly constant right-handed neutrinos?

Both imbedding space spinor harmonics and the modified Dirac equation have also right-handed neutrino spinor modes not constant in M4. If these are responsible for SUSY then SUSY is broken.

  1. Consider first the situation at space-time level. Both induced gamma matrices and their generalizations to modified gamma matrices defined as contractions of imbedding space gamma matrices with the canonical momentum currents for Kähler action are superpositions of M4 and CP2 parts. This gives rise to the mixing of right-handed and left-handed neutrinos. Note that non-covariantly constant right-handed neutrinos must be localized at string world sheets.

    This in turn leads neutrino massivation and SUSY breaking. Given particle would be accompanied by sparticles containing varying number of right-handed neutrinos and antineutrinos localized at partonic 2-surfaces.

  2. One an consider also the SUSY breaking at imbedding space level. The ground states of the representations of extended conformal algebras are constructed in terms of spinor harmonics of the imbedding space and form the addition of right handed neutrino with non-vanishing four-momentum would make sense. But the non-vanishing four-momentum means that the members of the super-multiplet cannot have same masses. This is one manner to state what SUSY breaking is.

What one can say about the masses of sparticles?

The simplest form of massivation would be that all members of the super- multiplet obey the same mass formula but that the p-adic length scales associated with them are different. This could allow very heavy sparticles. What fixes the p-adic mass scales of sparticles? If this scale is CP2 mass scale SUSY would be experimentally unreachable. The estimate below does not support this option.

One can even consider the possibility that SUSY breaking makes sparticles unstable against phase transition to their dark variants with heff =n× h. Sparticles could have same mass but be non-observable as dark matter not appearing in same vertices as ordinary matter! Geometrically the addition of right-handed neutrino to the state would induce many-sheeted covering in this case with right handed neutrino perhaps associated with different space-time sheet of the covering.

This idea need not be so outlandish at it looks first.

  1. The generation of many-sheeted covering has interpretation in terms of breaking of conformal invariance. The sub-algebra for which conformal weights are n-tuples of integers becomes the algebra of conformal transformations and the remaining conformal generators do note represent gauge degrees of freedom anymore. They could however represent conserved conformal charges still.
  2. This generalization of conformal symmetry breaking gives rise to infinite number of fractal hierarchies formed by sub-algebras of conformal algebra and is also something new and a fruit of an attempt to avoid sloppy thinking. The breaking of conformal symmetry is indeed expected in massivation related to the SUSY breaking.
The following poor man's estimate supports the idea about dark sfermions and the view that sfermions cannot be very heavy.
  1. Neutrino mixing rate should correspond to the mass scale of neutrinos known to be in eV range for ordinary value of Planck constant. For heff/h=n it is reduced by factor 1/n, when mass kept constant. Hence sfermions could be stabilized by making them dark.
  2. A very rough order of magnitude estimate for sfermion mass scale is obtained from Uncertainty Principle: particle mass should be higher than its decay rate. Therefore an estimate for the decay rate of sfermion could give a lower bound for its mass scale.
  3. Assume the transformation νR→ νL makes sfermion unstable against the decay to fermion and ordinary neutrino. If so, the decay rate would be dictated by the mixing rate and therefore to neutrino mass scale for the ordinary value of Planck constant. Particles and sparticles would have the same p-adic mass scale. Large heff could however make sfermion dark, stable, and non-observable.
A rough model for the neutrino mixing in TGD framework

The mixing of right- and left handed neutrinos would be the basic mechanism in the decays of sfermions. The mixing mechanism is mystery in standard model framework but in TGD it is implied by both induced and modified gamma matrices. The following argument tries to capture what is essential in this process.

  1. Conformal invariance requires that the string ends at which fermions are localized at wormhole throats are light-like curves. In fact, light-likeness gives rise to Virasosoro conditions.
  2. Mixing is described by a vertex residing at partonic surface at which two partonic orbits join. Localization of fermions to string boundaries reduces the problem to a problem completely analogous to the coupling of point particle coupled to external gauge field. What is new that orbit of the particle has corner at partonic 2-surface. Corner breaks conformal invariance since one cannot say that curve is light-like at the corner. At the corner neutrino transforms from right-handed to left handed one.
  3. In complete analogy with Ψbar;γtAtΨ vertex for the point-like particle with spin in external field, the amplitude describing nuRL transition involves matrix elements of form νbarRΓt(CP2)ZtνL at the vertex of the CP2 part of the modified gamma matrix and classical Z0 field.

    How Γt is identified? The modified gamma matrices associated with the interior need not be well-defined at the light-like surface and light-like curve. One basis of weak form of electric magnetic duality the modified gamma matrix corresponds to the canonical momentum density associated with the Chern-Simons term for Kähler action. This gamma matrix contains only the CP2 part.

The following provides as more detailed view.
  1. Let us denote by ΓtCP2(in/out) the CP2 part of the modified gamma matrix at string at at partonic 2-surface and by Z0t the value of Z0 gauge potential along boundary of string world sheet. The direction of string line in imbedding space changes at the partonic 2-surface. The question is what happens to the modified Dirac action at the vertex.
  2. For incoming and outgoing lines the equation

    D(in/out)Ψ(in/out)= pk(in,out)γk Ψ(in/out) ,

    where the modified Dirac operator is D(in/out)=Γt(in/out)Dt, is assumed. νR corresponds to "in" and νR to "out". It implies that lines corresponds to massless M4 Dirac propagator and one obtains something resembling ordinary perturbation theory.

    It also implies that the residue integration over fermionic internal momenta gives as a residue massless fermion lines with non-physical helicities as one can expect in twistor approach. For physical particles the four-momenta are massless but in complex sense and the imaginary part comes classical from four-momenta assignable to the lines of generalized Feynman diagram possessing Euclidian signature of induced metric so that the square root of the metric determinant differs by imaginary unit from that in Minkowskian regions.

  3. In the vertex D(in/out) could act in Ψ(out/in) and the natural idea is that νRL mixing is due to this so that it would be described the classical weak current couplings νbarR ΓtCP2(out)Z0t(in)νL and νbarR ΓtCP2(out)Z0t(in)νL.
To get some idea about orders of magnitude assume that the CP2 projection of string boundary is geodesic circle thus describable as Φ= ω t, where Φ is angle coordinate for the circle and t is Minkowski time coordinate. The contribution of CP2 to the induced metric gtt is Δ gtt =-R2ω2.
  1. In the first approximation string end is a light-like curve in Minkowski space meaning that CP2 contribution to the induced metric vanishes. Neutrino mixing vanishes at this limit.
  2. For a non-vanishing value of ω R the mixing and the order of magnitude for mixing rate and neutrino mass is expected to be R∼ ω and m∼ ω/h. p-Adic length scale hypothesis and the experimental value of neutrino mass allows to estimate m to correspond to p-adic mass to be of order eV so that the corresponding p-adic prime p could be p≈ 2167. Note that k=127 defines largest of the four Gaussian Mersennes MG,k= (1+i)k-1 appearing in the length scale range 10 nm - 2.5 μm. Hence the decay rate for ordinary Planck constant would be of order R∼ 1014/s but large value of Planck constant could reduced it dramatically. In living matter reductions by a factor 10-12 can be considered.

See the chapter Does the QFT Limit of TGD Have Space-Time Super-Symmetry? or the article What went wrong with symmetries?.

Some comments about τ-μ anomaly of Higgs decays and anomalies of B meson decays

Lubos mentions 2.5 sigma anomaly (that is something to be not taken seriously) in the decay of Higgs to τ-μ pair or its charge conjugate not allowed by standard model. Lubos mentions a model explaining the anomaly and also other anomalies related to semileptonic decays of neutral B meson in terms of double Higgs sector and gauged Lμ-Lτ symmetry. In a more recent posting Lubos mentions another paper explaining the anomaly in terms of a frightingly complex E6 gauge model inspired by heterotic strings.

TGD suggests however an amazingly simple explanation of the τ-μ anomaly in terms of neutrino mixing. As a matter fact, after writing the first hasty summary of the childishly simple idea discussed below but still managing to make mistakes;-), I became skeptic: perhaps I have misunderstood what is meant by anomaly. Perhaps the production of τ-μ pairs is not the anomaly after all. Perhaps the anomaly is the deviation from the prediction based on the model below. It however seems that my hasty interpretation was correct. This brings in my mind a dirty joke about string theorists told only at late hours when superstring theorists have already gone to bed. How many super string theorists it takes to change the light bulb? Two. The first one holds the light bulb and the second one rotates the multiverse.

Model for the h→ μ-τc anomaly in terms of neutrino mixing

To my humble opinion both models mentioned by Lubos are highly artificial and bring in a lot of new parameters since new particles are introduced. Also a direct Yukawa coupling of Higgs to τ-μ pair is assumed. This would however break the universality since lepton numbers for charged lepton generations would not be conserved. This does not look attractive and one can ask whether the allowance of transformation of neutrinos to each other by mixing known to occur could be enough to explain the findings assuming that there are no primary flavor changing currents and without introducing any new particles or new parameters. In the hadronic sector the mixing for quarks D type quarks indeed explains this kind of decays producing charged quark pair of say type cuc. In TGD framework, where CKM mixing reduces to topological mixing of topologies of partonic 2-surfaces, this option is especially attractive.

  1. In standard model neutrinos are massless and have no direct coupling to Higgs. Neutrinos are however known to have non-vanishing masses and neutrino mixing analogous to CKM mixing is also known to occur. Neutrino mixing is enough to induce the anomalous decays and the rate is predicted completely in terms of neutrino mixing parameters and known standard physics parameters so that for a professional it should be easy to made the little computer calculations to kill the model;-).
  2. In absence of flavor changing currents only WLiνj vertices can produce the anomaly. The h→ μ-τc or its charge conjugate would proceed by several diagrams but the lowest order diagram comes from the decay of Higgs to W pair. If Higgs vacuum expectation value is non-vanishing as in standard model then Higgs could decay to a virtual W+W- pair decaying to τμ pair by neutrino exchange. Decay to Z pair does not produce the desired final state in accordance with the absence of flavor changing neutral currents in standard model. Triangle diagram would describe the decay. Any lepton pair is possible as final state. Neutrino mixing would occur in either W vertex. The rates for the decays to different lepton pairs differ due to different mass values of leptons which are however rather small using Higgs mass as as scale. Therefore decays to all lepton pairs are expected.
  3. In higher order Higgs could decay lepton pair to lepton pair decaying by neutrino exchange to W pair in turn decaying by neutrino exchange to lepton pair. As as special case one obtains diagrams Higgs decays τ pair with final state preferentially ντ exchange to W+W- pair decaying by τ neutrino exchange to μ-τc pair. The CKM mixing parameter for neutrino mixing would in either the upper vertices of the box. Note that Z0 pair as intermediate state does not contribute since neutral flavor changing currents are absent.
The proposed mechanism should be at work in any generalization of standard model claiming to explain neutrino masses and their mixing without flavor changing neutral currents. If the observed anomaly is different from this prediction, one can start to search for new physics explanations but before this brane constructions in multiverse are not perhaps the best possible strategy.

What about the anomalies related to B meson decays?

The model that Lubos refers to tries to explain also the anomalies related to semileptonic decays of neutral B meson. Neutrino mixing is certainly not a natural candidate if one wants to explain the 2.5 sigma anomalies reported for the decays of B meson to K meson plus muon pair. Lubos has a nice posting about surprisingly many anomalies related to the leptonic and pion and kaon decays of neutral B meson. Tommaso Dorigo tells about 4-sigma evidence for new physics in rare G boson decays. There is also an anomaly related to the decay of neutral B meson to muon pair reported by Jester. In the latter case the the decay can proceed via W or Higgs pair as intermediate state. The coupling h→ bsc resulting through CKM mixing for quarks by the same mechanism as in the case of leptons must have been taken into account since it is standard model process.

TGD predicts M89 hadron physics as a p-adically scaled up variant of ordinary M107 hadron physics with hadron mass scale scaled up by factor 512 which corresponds to LHC energies. Could it be that the loops involve also quarks of M89 hadron physics. A quantitative modelling would require precise formulation for the phase transition changing the p-adic prime characterizing quarks and gluons.

One can however ask whether one might understand these anomalies qualitatively in a simple manner in TGD framework. Since both leptons and quarks are involved, the anomaly must related to W-quark couplings. If M89 physics is there, there must be radiatively generated couplings representing the decay of W to a pair of ordinary M107 quark and M89 quark. A quark of M89 hadron physics appearing as a quark exchange between W+ and W- in box diagram would affect the rates of B meson to kaon and pion. This would affect also the semileptonic decays since the the photon or Z decaying to a lepton pair could be emitted from M89 quark.

But doesn't Higgs vacuum expectation vanish in TGD?

While polishing this posting I discovered an objection against TGD approach that I have not noticed earlier. This objection allows to clarify TGD based view about particles so that I discuss it here.

  1. In standard model the decay of Higgs decays to gauge bosons is described quite well by the lowest order diagrams and the decay amplitude is proportional to Higgs vacuum expectation. In TGD p-adic mass calculations describe fermion massivation and Higgs vacuum expectation vanishes at the fundamental level but must make sense at the QFT limit of TGD involving the replacement of many-sheeted space-time with single slightly curved region of Minkowski space defining GRT space-time. Various gauge fields are sums of induced gauge fields at the sheets.
  2. Note that the decays of Higgs to W pairs with a rate predicted in good approximation by the lowest order diagrams involving Higgs vacuum expectation have been observed. Hence Higgs vacuum expectation must appear as a calculable parameter in the TGD approach based on generalized Feynman diagrams. In this approach the vertices of Feynman diagrams are replaced with 3-D vertices describing splitting of 3-D surface, in particular that of partonic 2-surfaces associated with it and carrying elementary particle quantum numbers by strong form of holography. The condition that em charge is well-defined requires that the modes of the induced spinor fields are localized at string world sheets at which induced W fields vanish. Also induced Z fields should vanish above weak scale at string world sheets. Thus the description of the decays reduces at microscopic level to string model with strings moving in space-time and having their boundaries at wormhole contacts and having interpretation as world lines of fundamental point-like fermions.
  3. Elementary particles are constructed as pairs of wormhole contacts with throats carrying effective Kähler magnetic charge. Monopole flux runs along first space-time sheet, flows to another space-time sheet along contact and returns back along second space-time sheet and through the first wormhole contact so that closed magnetic flux tube is obtains. Both sheets carry string world sheets and their ends at the light-like orbits of wormhole throats are carriers of fermion number.
  4. This description gives non-vanishing amplitudes for the decays of Higgs to gauge boson pairs and fermion pairs. Also the couplings of gauge bosons to fermions can be calculated from this description so that both the gauge coupling strengths and Weinberg angle are predicted. The non-vanishing value of the coupling of Higgs to gauge boson defines the Higgs vacuum expectation which can be used in gauge theory limit. The breaking of weak gauge symmetry reflects the fact that weak gauge group acts as holonomies of CP2 and is not a genuine symmetry of the action. Since weak gauge bosons correspond classical to gauge potentials, the natural conjecture is that the couplings are consistent with gauge symmetry.
  5. Massivation of particles follows from the fact that physical particles are composites of massless fundamental fermions whose light-like momenta are in general non-parallel. It seems however possible to regarded particles as massless in 8-D sense. At classical level this is realized rather elegantly: Minkowskian and Euclidian regions give both a contribution to four-momentum and the contribution from the lines of generalized Feynman diagrams is imaginary due to the Euclidian signature of the induced metric. This gives rise to complex momenta and twistor approach suggests that these momenta are light-like allow real mass squared to be non-vanishing. Also the massivation of light particles could be described in this manner.

    This description would conform with M8-H duality at momentum space level: at imbedding space level one would have color representations and at space-time level representations of SO(4) associated with mass squared=constant sphere in Euclidian three space: this would correspond to the SU(2)L×SU(2)R dynamical symmetry group of low energy hadronic physics.

See the chapter New Particle Physics Predicted by TGD: Part I or the article Some comments about τμ anomaly of Higgs decays and anomalies of B meson decays.

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