What's new in

p-Adic Physics

Note: Newest contributions are at the top!

Year 2017

Further support for second generation of electroweak bosons

I found in FB a link to a highly interesting popular article "Dark matter exists? Chinese satellite detects mysterious signals while measuring cosmic rays". There is also an article in Nature with title Direct detection of a break in the teraelectronvolt cosmic-ray spectrum of electrons and positrons by DAMPE collaboration.

A Chinese satellite – Dark Matter Particle Explorer (DAMPE), also called Wukong or "Monkey King", is reported to have made a discovery. The energy spectrum of cosmic ray electrons and positrons is measured. The surprise was that there is a break at about .9 TeV and a strange spike at around 1.4 TeV. The conclusion is that the spike indicates a particle with a mass of about 1.4 TeV on the spectrum. To me a more natural conclusion would be that there is a particle with mass 2.8 TeV decaying to electron positron pair. Unfortunately, the popular article does not allow to conclude what is the precise finding.

In any case, TGD predicts scaled up variant of electroweak physics and there are several pieces of evidence for its existence coming from the violation of lepton and quark universality (see this). The mass scale for this physics would correspond to Gaussian Mersenne prime MG,79 = (1+i)79-1 and is obtained by scaling the mass scale of electroweak physics by a factor 32. This predicts the mass of Z boson of this physics to be 2.9 TeV. It would decay to electron positron pairs with members having energy 1.45 TeV in cm system. Also gluons could have scaled up variants and there is some evidence for this too from the breaking of the quark universality.

Cosmic ray electron and positron spectra are found to have peak at 1.4 TeV. Could they result in the decays of the second generation Z boson with mass 2.9 TeV? In TGD framework this boson would not however solve dark matter puzzle. In TGD Universe dark matter has explanation as heff/h=n phases of ordinary matter.

Could the spectral "break" at about .9 TeV (I am not quite sure what "break" really means) relate to massive photon of MG,79physics?

Article also mentions that the cosmic ray positron flux is higher than predicted above 70 GeV. That this energy corresponds to the mass of M89 pion, might not be an accident. The decay to gamma pairs dominates and gives a peak but the rate for the decay to gamma+ e+e- pair would be by factor of order &alpha ≈ 1/137 lower and would give a break rather than peak since the energy spectrum of pairs is continuous. Therefore support for both M89 and MG,79 physics emerges. Maybe the long-waited breakthrough of TGD might not be in too far future.

See the chapter New Physics Predicted by TGD: I or the updated article Indications for the breaking of Universality in B meson decays.

Encountering the inert neutrino once again

Sabine Hossenfelder had an interesting link to Quanta Magazine article "On a Hunt for a Ghost of a Particle" telling about the plans of particle physicist Janet Conrad to find the inert neutrino.

The attribute "sterile" or "inert" (I prefer the latter since it is more respectful) comes from the assumption this new kind of neutrino does not have even weak interactions and feels only gravitation. There are indications for the existence of inert neutrino from LSND experiments and some Mini-Boone experiments. In standard model it would be interpreted as fourth generation neutrino which would suggest also the existence of other fourth generation fermions. For this there is no experimental support.

The problem of inert neutrino is very interesting also from TGD point of view. TGD predicts also right handed neutrino with no electroweak couplings but mixes with left handed neutrino by a new interaction produced by the mixing of M4 and CP2 gamma matrices: this is a unique feature of induced spinor structure and serves as a signature of sub-manifold geometry and one signature distinguishing TGD from standard model. Only massive neutrino with both helicities remains and behaves in good approximation as a left handed neutrino.

There are indeed indications in both LSND and MiniBoone experiments for inert neutrino. But only in some of them. And not in the ICECUBE experiment performed at was South Pole. Special circumstances are required. "Special circumstances" need not mean bad experimentation. Why this strange behavior?

  1. The evidence for the existence of inert neutrino, call it νbar;I, came from antineutrino mixing νbar;μ→ νbar;&e; manifesting as mass squared difference between muonic and electronic antineutrinos. This difference was Δ m2(LSND)= 1-10 eV2 in the LSND experiment. The other two mass squared differences deduced from solar neutrino mixing and atmospheric neutrino mixing were Δ m2(sol)= 8×10-5 eV2 and Δ m2(atm)= 2.5×10-3 eV2 respectively.
  2. The inert neutrino interpretation would be that actually νbar;μ→ νbar;I takes place and the mass squared difference for νbar;μ and νbar;I determines the mixing.
1. The explanation based on several p-adic mass scales for neutrino

The first TGD inspired explanation proposed for a long time ago relies on p-adic length scale hypothesis predicting that neutrinos can exist in several p-adic length scales for which mass squared scale ratios come as powers of 2. Mass squared differences would also differ by a power of two. Indeed, the mass squared differences from solar and atmospheric experiments are in ratio 2-5 so that the model looks promising!

Writing Δ m2(LSND) = x eV2 the condition m2(LSND)/ m2(atm)= 2k has 2 possible solutions corresponding to k= 9, or 10 and x=2.5 and x=1.25. The corresponding mass squared differences 2.5 eV2 and 1.25 eV2.

The interpretation would be that the three measurement outcomes correspond to 3 neutrinos with nearly identical masses in given p-adic mass scale but having different p-adc mass scales. The atmospheric and solar p-adic length scales would comes as powers (L(atm),L(sol))= (2n/2, 2(n+10)/2)× L(k(LSND)) , n=9 or 10. For n=10 the mass squared scales would come as powers of 210.

How to estimate the value of k(LSND)?

  1. Empirical data and p-adic mass calculations suggest that neutrino mass is of order .1 eV . The most natural candidates for p-adic mass scales would correspond to k=163, 167 or 169. The first primes k=163, 167 correspond to Gaussian Mersenne primes MG,n= (1+i)n-1 and to p-adic length scales L(163) = 640 nm and L(167)= 2.56 μm.
  2. p-Adic mass calculations predict that the ratio x=Δ m2/m2 for μ-e system has upper bound x∼ .4. This does not take into account the mixing effects but should give upper bound for the mass squared difference affected by the mixing.
  3. The condition Δ m2/m2=.4× x, where x≤ 1 parametrizes the mass difference assuming Δ m(LSND)2= 2.5 eV2 gives m2(LSND) ∼ 6.25 eV2/x.

    x= 1/4 would give (k(LSND),k(atm),k(sol))=(157, 167, 177). k(LSND) and k(atm) label two Gaussian Mersenne primes MG,k= (1+i)k in the series k=151, 157, 163, 167 of Gaussian Mersennes. The scale L(151)=10 nm defines cell membrane thickness. All these scales could be relevant for DNA coiling. k(sol)=177 is not Mersenne prime nor even prime. The correspoding p-adic length scale is 82 μm perhaps assignable to neuron. Note that k=179 is prime.

What really happens when neutrino characterised by p-adic length scale L(k1) transforms to a neutrino characterized by p-adic length scale L(k2).
  1. The simplest possibility would be that k1→ k2 corresponds to a 2-particle vertex. The conservation of energy and momentum however prevent this process unless one has Δ m2=0. The emission of weak boson is not kinematically possible since Z0 boson is so massive. For instance, solar neutrinos have energies in MeV range. The presence of classical Z0 field could make the transformation possible and TGD indeed predicts classical Z0 fields with long range. The simplest assumption is that all classical electroweak gauge fields except photon field vanish at string world sheets. This could in fact be guaranteed by gauge choice analogous to the the unitary gauge.
  2. The twistor lift of TGD however provides an alternative option. Twistor lift predicts that also M4 has the analog of Kähler structure characterized by the Kähler form J(M4) which is covariantly constant and self-dual and thus corresponds to parallel electric and magnetic components of equal strength. One expects that this gives rise to both classical and quantum field coupling to fermion number, call this U(1) gauge field U. The presence of J(M4) induces P, T, and CP breaking and could be responsible for CP breaking in both leptonic and quark sectors and also explain matter antimatter asymmetry (see this and this) as well as large parity violation in living matter (chiral selection). The coupling constant strength α1 is rather small due to the constraints coming from atomic physics (U couples to fermion number and this causes a small scaling of the energy levels). One has α1∼ 10-9, which is also the number characterizing matter antimatter asymmetry as ratio of the baryon density to CMB photon density.

    Already the classical long ranged U field could induce the neutrino transitions. k1→ k2 transition could become allowed by conservation laws also by the emission of massless U boson. The simplest situation corresponds to parallel momenta for neutrinos and U. Conservation laws of energy and momentum give E1= (p12+m12)1/2=E2+E(U)= (p22+m221/2+ E(U), p1=p2+p(U). Masslessness gives E(U)=p(U). This would give in good approximation p2/p1= m12/m22 and E(U)= p1-p2=p1(1-m12/m22).

    One can ask whether CKM mixing for quarks could involve similar mechanism explaining the CP breaking. Also the transitions changing heff/h=n could involve U boson emission.

This explanation looks rather nice because the mass squared difference ratios come as powers of two and one ends up to a detailed mechanism for the transition changing the p-adic length scale.

2. The explanation based on several p-adic mass scales for neutrinos

Second TGD inspired interpretation would be as a transformation of ordinary neutrino to a dark variant of ordinary neutrino with heff/h=n occurring only if the situation is quantum critical (what would this mean now?). Dark neutrino would behave like inert neutrino.

This proposal need not however be in conflict with the first one since the transition k(LSND)→ k1 could produce dark neutrino with different value of heff/h= 2Δ k scaling up the Compton scale by this factor. This transition could be followed by a transition back to a particle with p-adic length scale scaled up by 22k. I have proposed that p-adic phase transitions occurring at criticality requiring heff/h>1 are important in biology.

There is evidence for a similar effect exists in the case of neutron decays. Neutron lifetime is found to be considerably longer than predicted. The TGD explanation is that part of protons resulting in the beta decays of neutrino transform to dark protons and remain undetected so that lifetime looks longer than it really is. Note however that also now conservation laws give constraints and the emission of U photon might be involved also in this case. As a matter of fact, one can consider the possibility that the phase transition changing heff/h=n involve the emission of U photon too. The mere mixing of the ordinary and dark variants of particle would induce mass splitting and U photon would take care of energy momentum conservation.

See the chapter New Physics Predicted by TGD: I or the article Encountering the inert neutrino once again.

Newest indications for dark M89 hadrons

I received a link to a quite interesting popular article telling about surplus of antiprotons from cosmic rays interpreted in terms of dark matter particles decays to protons and antiprotons. The article mentions two articles summarizing essentially similar experimental findings.

The first article Novel Dark Matter Constraints from Antiprotons in Light of AMS-02 is published in Phys Rev Letters. The abstract is here.

We evaluate dark matter (DM) limits from cosmic-ray antiproton observations using the recent precise AMS-02 measurements. We properly take into account cosmic-ray propagation uncertainties, fitting DM and propagation parameters at the same time and marginalizing over the latter. We find a significant indication of a DM signal for DM masses near 80 GeV, with a hadronic annihilation cross section close to the thermal value, < σ v>∼ 2× 10-26 cm3/s. Intriguingly, this signal is compatible with the DM interpretation of the Galactic center gamma-ray excess. Confirmation of the signal will require a more accurate study of the systematic uncertainties, i.e., the antiproton production cross section, and the modeling of the effect of solar modulation. Interpreting the AMS-02 data in terms of upper limits on hadronic DM annihilation, we obtain strong constraints excluding a thermal annihilation cross section for DM masses below about 50 GeV and in the range between approximately 150 and 500 GeV, even for conservative propagation scenarios. Except for the range around ∼ 80 GeV, our limits are a factor of ∼ 4 stronger than the limits from gamma-ray observations of dwarf galaxies.

The second article Possible Dark Matter Annihilation Signal in the AMS-02 Antiproton Data is also published in Phys Rev Letters . The abstract is here.

Using the latest AMS-02 cosmic-ray antiproton flux data, we search for a potential dark matter annihilation signal. The background parameters about the propagation, source injection, and solar modulation are not assumed a priori but based on the results inferred from the recent B/C ratio and proton data measurements instead. The possible dark matter signal is incorporated into the model self-consistently under a Bayesian framework. Compared with the astrophysical background-only hypothesis, we find that a dark matter signal is favored. The rest mass of the dark matter particles is ∼ 20-80 GeV, and the velocity-averaged hadronic annihilation cross section is about (0.2-5) × 10-26 cm3/s, in agreement with that needed to account for the Galactic center GeV excess and/or the weak GeV emission from dwarf spheroidal galaxies Reticulum 2 and Tucana III. Tight constraints on the dark matter annihilation models are also set in a wide mass region.

The proposal is that decay of dark matter particles possibly arriwing from the Galactic center produce proton-antiproton pairs. The mass of the decaying particles would be between 40-80 GeV. I have been talking for years about M89 hadron physics - a scaled up copy of ordinary hadron physics with mass scale 512 times higher than that of ordinary hadron physics. The pion of this physics would have mass about 69 GeV (by scaling from the mass of ordinary pion by factor 512). There are indications for two handfuls of bumps with masses of mesons of ordinary hadron physics scaled up by 512 (see this).

These scaled up pions could be produced abundantly in collisions of cosmic rays in atmosphere (situation would be analogous to that at LHC). It would not be surprising if they would producealso proton and antiproton pairs in their decays? This view about the origin of the dark pions is different from the usual view about dark matter. Dark pions would be created by the cosmic rays arriving from galactic center and colliding with nuclear matter in the Earth's atmosphere rather than arriving from the galactic center.

Can one say that they represent dark matter and in what sense? The TGD based proposal explaining various bumps observed at LHC and having masses 512 times those of ordinary mesons assumes that they are produced at quantum criticality and are dark in TGD sense meaning that the value of effective Planck constant for them is heff=n× h, n=512. Scaled up Compton length would realize long range quantum correlations at criticality. Dark mesons at criticality would be hybrids of ordinary and scaled up mesons: Compton length would same as for ordinary mesons but mass would 512 times higher: Esau's hands and Jacob's voice. This would give a precise meaning to what it means for two phases to be same at quantum criticality: half of both.

See the article M89 Hadron Physics and Quantum Criticality or the chapter New Physics Predicted by TGD: I

Anomalous J/Ψ production and TGD

A new anomaly has been discovered by LHCb collaboration. The production of J/Ψ mesons in proton-proton collisions in the Large Hadron Collider (LHC) at CERN does not agree with the predictions made by a widely used computer simulation, Pythia. The result comes from CERN's LHCb experiment studying the jets of hadrons created as protons collide at 13 TeV cm energy.

These jets contain large numbers of J/Ψ mesons consisting of charmed quark and a charmed anti-quark. The LHCb measured the ratio of the momentum carried by the J/Ψ mesons to the momentum carried by the entire jet. They were also able to discriminate between J/Ψ mesons created promptly (direct/prompt production) in the collision and J/Ψ mesons that were created after the collision by the decay of charmed hadrons produced by jets (jet production).

Analysis of the data demonstrates that PYTHIA - a Monte Carlo simulation used to model high-energy particle collisions - does not predict correctly the momentum fraction carried by prompt J/Ψ mesons. The conclusion is that the apparent shortcomings of PYTHIA could have a significant effect on how particle physics is done because the simulation is used both in the design of collider detectors and also to determine which measurements are most likely to reveal information about physics beyond the Standard Model of particle physics. Heretic could go further and ask whether the problem is really with Pythia: could it be with QCD?

The TGD explanation for the finding is same as that for strangeness enhancement in p-p collisions in the same energy range at which the de-confinement phase transition is predicted to occur in QCD. In TGD one would have quantum criticality for a phase transition from the ordinary M107 hadron physics to M89 hadron physics with hadronic mass scale by a factor 512 higher than for ordinary hadrons. The gluons and quarks at quantum criticality would be dark in the sense of having heff/h=n=512. Also 1/n-fractional quarks and gluons are possible.

TGD predicts besides ordinary bosons two additional boson generations, whose family charge matrices in the space of fermion families are hermitian, diagonal and orthogonal to each other to the unit charge matrix for ordinary bosons, and most naturally same for all bosons. The charge matrices for higher generations necessarily break the universality of fermion couplings. The model for strangeness enhancement and the violation of lepton universality in B-meson decays predicts that the bosonic family charge matrix for second generation favours decays to third generation quarks and dis-favors decays to quarks of first and second generation. This predicts that the rate for prompt production of J/Ψ is lower and jet production rate from b-hadron decays is higher than predicted by QCD.

See the chapter New Physics predicted by TGD: I and the article Phase transition from M107 hadron physics to M89 hadron physics as counterpart for de-confinement phase transition? .

Phase transition from M107 hadron physics to M89 hadron physics as counterpart for de-confinement phase transition?

Quark gluon plasma assigned to de-confinement phase transition predicted by QCD has turned out to be a problematic notion. The original expectation was that quark gluon plasma (QGP) would be created in heavy ion collisions. A candidate for QGP was discovered already at RHIC but did not have quite the expected properties such as black body spectrum behaving like an ideal liquid with long range correlations between charged particle pairs created in the collision. Then LHC discovered that this phase is created even in proton-heavy nucleus collisions. Now this phase have been discovered even in proton-proton collisions. This is something unexpected and both a challenge and opportunity to TGD.

In TGD framework QGP is replaced with quantum critical state appearing in the transition from ordinary hadron physics characterized by Mersenne prime M107 to dark variant of M89 hadron physics characterized by heff/h=n=512. At criticality partons are hybrids of M89 and M107 partons with Compton length of ordinary partons and mass m(89)≤ 512× m(107). Inequality follows from possible 1/512 fractionization of mass and other quantum numbers. The observed strangeness enhancement can be understood as a violation of quark universality if the gluons of M89 hadron physics correspond to second generation of gluons whose couplings necessarily break quark universality.

The violation of quark universality would be counterpart for the violation of lepton universality and the simplest hypothesis that the charge matrices acting on family triplets are same for quarks and leptons allows to understand also the strangeness enhancement qualitatively.

See the chapter New Physics predicted by TGD: I and the article Phase transition from M107 hadron physics to M89 hadron physics as counterpart for de-confinement phase transition? .

Breaking of lepton universality seems to be real

The evidence for the violation of lepton number universality is accumulating at LHC. I have written about the violation of lepton number universality in the decays of B and K mesons already earlier explaining it in terms of two higher generations of electroweak bosons. The existence of free fermion generations having topological explanation in TGD can be regarded formally as SU(3) triplet. One can speak of family-SU(3).

Electroweak bosons and gluons belong to singlet and octet of family-SU(3) and the natural assumption is that only singlet (ordinary gauge bosons) and two SU(3) neutral states of octet are light. One would have effectively 3 generations of electroweak bosons and gluons. There charge matrices would be orthogonal with respect to the inner product defined by trace so that both quark and lepton universality would be broken in the same manner. The strongest assumption is that the charge matrices in flavor space are same for all weak bosons. The CKM mixing for neutrinos complicates this picture by affecting the branching rations of charged weak bosons.

I learned quite recently about new data concerning B meson anomalies. The experimental ideas are explained here. It is interesting to look at the results in more detail from TGD point of view..

  1. There is about 4.0 σ deviation from $τ/l$ universality (l=μ,e) in b→ c transitions. In terms of branching ratios ones has:

    R(D*)=Br(B→ D*→τντ)/Br(B→ D*l) =0.316+/- 0.016+/- 0.010 ,

    R(D) =Br(B→ Dτντ)/Br(B→ lνl) =0.397+/- 0.040+/- 0.028 ,

    The corresponding SM values are R(D*)|SM= 0.252+/- 0.003 and R(D)|SM=.300+/- .008. My understanding is that the normalization factor in the ratio involves total rate to D*l, l=μ, e involving only single neutrino in final state whereas the τν decays involve 3 neutrinos due to the neutrino pair from τ implying broad distribution for the missing mass.

    The decays to τ ντ are clearly preferred as if there were an exotic W boson preferring to decay τν over lν , l=e,μ. In TGD it could be second generation W boson. Note that CKM mizing of neutrinos could also affect the branching ratios.

  2. Since these decays are mediated at tree level in the SM, relatively large new physics contributions are necessary to explain these deviations. Observation of 2.6 σ deviation of μ/e universality in the dilepton invariant mass bin 1 GeV2≤ q2≤ 6 GeV2 in b→ s transitions:

    R(K)=Br(B→ Kμ+μ-)/Br(B→ K e+e-) =0.745+0.090/-0.074+/- 0.038

    deviate from the SM prediction R(K)|SM=1.0003+/- 0.0001.

    This suggests the existence of the analog of Z boson preferring to decay to e+e- rather than μ+μ- pairs.

    If the charge matrices acting on dynamical family-SU(3) fermion triplet do not depend on electroweak bosons and neutrino CKM mixing is neglected for the decays of second generation W, the data for branching ratios of D bosons implies that the decays to e+e- and τ+τ- should be favored over the decays to μ+μ-. Orthogonality of the charge matrices plus the above data could allow to fix them rather precisely from data. It might be that one must take into account the CKM mixing.

  3. CMS recently also searched for the decay h→ τμ and found a non-zero result of Br(h→ τμ)=0.84+0.39/-0.37 , which disagrees by about 2.4 σ from 0, the SM value. I have proposed an explanation for this finding in terms of CKM mixing for leptons. h would decay to W+W- pair, which would exchange neutrino transforming to τμ pair by neutrino CKM mixing.
  4. According to the reference, for Z, the lower bound for the mass is 2.9 TeV, just the TGD prediction if it corresponds to Gaussian Mersenne MG,79=(1+i)79 so that the mass would be 32 times the mass of ordinary Z boson! It seem that we are at the verge of the verification of one key prediction of TGD.
For background see the chapter New Physics predicted by TGD: I of "p-Adic length scale hypothesis".

Getting even more quantitative about CP violation

The twistor lift of TGD forces to introduce the analog of Kähler form for M4, call it J. J is covariantly constant self-dual 2-form, whose square is the negative of the metric. There is a moduli space for these Kähler forms parametrized by the direction of the constant and parallel magnetic and electric fields defined by J. J partially characterizes the causal diamond (CD): hence the notation J(CD) and can be interpreted as a geometric correlate for fixing quantization axis of energy (rest system) and spin.

Kähler form defines classical U(1) gauge field and there are excellent reasons to expect that it gives rise to U(1) quanta coupling to the difference of B-L of baryon and lepton numbers. There is coupling strength α1 associated with this interaction. The first guess that it could be just Kähler coupling strength leads to unphysical predictions: α1 must be much smaller. Here I do not yet completely understand the situation. One can however check whether the simplest guess is consistent with the empirical inputs from CP breaking of mesons and antimatter asymmetry. This turns out to be the case.

One must specify the value of α1 and the scaling factor transforming J(CD) having dimension length squared as tensor square root of metric to dimensionless U(1) gauge field F= J(CD)/S. This leads to a series of questions.

How to fix the scaling parameter S?

  1. The scaling parameter relating J(CD) and F is fixed by flux quantization implying that the flux of J(CD) is the area of sphere S2 for the twistor space M4× S2. The gauge field is obtained as F=J/S, where S= 4π R2(S2) is the area of S2.
  2. Note that in Minkowski coordinates the length dimension is by convention shifted from the metric to linear Minkowski coordinates so that the magnetic field B1 has dimension of inverse length squared and corresponds to J(CD)/SL2, where L is naturally be taken to the size scale of CD defining the unit length in Minkowski coordinates. The U(1) magnetic flux would the signed area using L2 as a unit.
How R(S2) relates to Planck length lP? lP is either the radius lP=R of the twistor sphere S2 of the twistor space T=M4× S2 or the circumference lP= 2π R(S2) of the geodesic of S2. Circumference is a more natural identification since it can be measured in Riemann geometry whereas the operational definition of the radius requires imbedding to Euclidian 3-space.

How can one fix the value of U(1) coupling strength α1? As a guideline one can use CP breaking in K and B meson systems and the parameter characterizing matter-antimatter symmetry.

  1. The recent experimental estimate for so called Jarlskog parameter characterizing the CP breaking in kaon system is J≈ 3.0× 10-5. For B mesons CP breading is about 50 times larger than for kaons and it is clear that Jarlskog invariant does not distinguish between different meson so that it is better to talk about orders of magnitude only.
  2. Matter-antimatter asymmetry is characterized by the number r=nB/nγ ∼ 10-10 telling the ratio of the baryon density after annihilation to the original density. There is about one baryon 10 billion photons of CMB left in the recent Universe.
Consider now the identification of α1.
  1. Since the action is obtained by dimensional reduction from the 6-D Kähler action, one could argue α1= αK. This proposal leads to unphysical predictions in atomic physics since neutron-electron U(1) interaction scales up binding energies dramatically.

    U(1) part of action can be however regarded a small perturbation characterized by the parameter ε= R2(S2)/R2(CP2), the ratio of the areas of twistor spheres of T(M4) and T(CP2). One can however argue that since the relative magnitude of U(1) term and ordinary Kähler action is given by ε, one has α1=ε× αK so that the coupling constant evolution for α1 and αK would be identical.

  2. ε indeed serves in the role of coupling constant strength at classical level. αK disappears from classical field equations at the space-time level and appears only in the conditions for the super-symplectic algebra but ε appears in field equations since the Kähler forms of J resp. CP2 Kähler form is proportional to R2(S2) resp. R2(CP2) times the corresponding U(1) gauge field. R(S2) appears in the definition of 2-bein for R2(S2) and therefore in the modified gamma matrices and modified Dirac equation. Therefore ε1/2=R(S2)/R(CP2) appears in modified Dirac equation as required by CP breaking manifesting itself in CKM matrix.

    NTU for the field equations in the regions, where the volume term and Kähler action couple to each other demands that ε and ε1/2 are rational numbers, hopefully as simple as possible. Otherwise there is no hope about extremals with parameters of the polynomials appearing in the solution in an arbitrary extension of rationals and NTU is lost. Transcendental values of ε are definitely excluded. The most stringent condition ε=1 is also unphysical. ε= 22r is favoured number theoretically.

Concerning the estimate for ε it is best to use the constraints coming from p-adic mass calculations.
  1. p-Adic mass calculations predict electron mass as

    me= hbar/R(CP2)(5+Y)1/2 .

    Expressing me in terms of Planck mass mP and assuming Y=0 (Y∈ (0,1)) gives an estimate for lP/R(CP2) as

    lPR(CP2) ≈ 2.0× 10-4 .

  2. From lP= 2π R(S2) one obtains estimate for ε, α1, g1=(4πα1)1/2 assuming αK≈ α≈ 1/137 in electron length scale.

    ε = 2-30 ≈ 1.0× 10-9 ,

    α1=εαK ≈ 6.8× 10-12 ,

    g1= (4πα11/2 ≈ 9.24 × 10-6 .

There are two options corresponding to lP= R(S2) and lP =2π R(S2). Only the length of the geodesic of S2 has meaning in the Riemann geometry of S2 whereas the radius of S2 has operational meaning only if S2 is imbedded to E3. Hence lP= 2π R(S2) is more plausible option.

For ε=2-30 the value of lP2/R2(CP2) is lP2/R2(CP2)=(2π)2 × R2(S2)/R2(CP2) ≈ 3.7× 10-8. lP/R(S2) would be a transcendental number but since it would not be a fundamental constant but appear only at the QFT-GRT limit of TGD, this would not be a problem.

One can make order of magnitude estimates for the Jarlskog parameter J and the fraction r= n(B)/n(γ). Here it is not however clear whether one should use ε or α1 as the basis of the estimate

  1. The estimate based on ε gives J∼ ε1/2 ≈ 3.2× 10-5 ,

    r∼ ε ≈ 1.0× 10-9 .

    The estimate for J happens to be very near to the recent experimental value J≈ 3.0× 10-5. The estimate for r is by order of magnitude smaller than the empirical value.

  2. The estimate based on α1 gives J∼ g1 ≈ 0.92× 10-5 ,

    r∼ α1 ≈ .68× 10-11 .

    The estimate for J is excellent but the estimate for r by more than order of magnitude smaller than the empirical value. One explanation is that αK has discrete coupling constant evolution and increases in short scales and could have been considerably larger in the scale characterizing the situation in which matter-antimatter asymmetry was generated.

Atomic nuclei have baryon number equal the sum B= Z+N of proton and neutron numbers and neutral atoms have B= N. Only hydrogen atom would be also U(1) neutral. The dramatic prediction of U(1) force is that neutrinos might not be so weakly interacting particles as has been thought. If the quanta of U(1) force are not massive, a new long range force is in question. U(1) quanta could become massive via U(1) super-conductivity causing Meissner effect. As found, U(1) part of action can be however regarded a small perturbation characterized by the parameter ε= R2(S2)/R2(CP2). One can however argue that since the relative magnitude of U(1) term and ordinary Kähler action is given by ε, one has α1=ε× αK.

Quantal U(1) force must be also consistent with atomic physics. The value of the parameter α1 consistent with the size of CP breaking of K mesons and with matter antimatter asymmetry is α1= εαK = 2-30αK.

  1. Electrons and baryons would have attractive interaction, which effectively transforms the em charge Z of atom Zeff= rZ, r=1+(N/Z)ε1, ε11/α=ε × αK/α≈ ε for αK≈ α predicted to hold true in electron length scale. The parameter

    s=(1 + (N/Z)ε)2 -1= 2(N/Z)ε +(N/Z)2ε2

    would characterize the isotope dependent relative shift of the binding energy scale.

    The comparison of the binding energies of hydrogen isotopes could provide a stringent bounds of the value of α1. For lP= 2π R(S2) option one would have α1=2-30αK ≈ .68× 10-11 and s≈ 1.4× 10-10. s is by order of magnitude smaller than α4≈ 2.9× 10-9 corrections from QED (see this). The predicted differences between the binding energy scales of isotopes of hydrogen might allow to test the proposal.

  2. B=N would be neutralized by the neutrinos of the cosmic background. Could this occur even at the level of single atom or does one have a plasma like state? The ground state binding energy of neutrino atoms would be α12mν/2 ∼ 10-24 eV for mν =.1 eV! This is many many orders of magnitude below the thermal energy of cosmic neutrino background estimated to be about 1.95× 10-4 eV (see this). The Bohr radius would be hbar/(α1mν) ∼ 106 meters and same order of magnitude as Earth radius. Matter should be U(1) plasma. U(1) superconductor would be second option.
See the new chapter New physics predicted by TGD: I or the article About parity violation in hadron physics.

How the QFT-GRT limit of TGD differs from QFT and GRT?

In the sequel I discuss an interesting idea related to both the definition and conservation of gauge charges in non-Abelian theories. First the idea popped in QCD context but immediately generalized to electro-weak and gravitational sectors. It might not be entirely correct: I have not yet checked the calculations.

QCD sector

I have been working with possible TGD counterparts of so called chiral magnetic effect (CME) and chiral separation effect (CSE) proposed in QCD to describe observations at LHC and RHIC suggesting relatively large P and CP violations in hadronic physics associated with the deconfinement phase transition. See the recent article About parity violation in hadron physics).

The QCD based model for CME and CSE is not convincing as such. The model assumes that the theta parameter of QCD is non-vanishing and position dependent. It is however known that theta parameter is extremal small and seems to be zero: this is so called strong CP problem of QCD caused by the possibility of istantons. The axion hypothesis could make θ(x) a dynamical field and θ parameter would be eliminated from the theory. Axion has not however been however found: various candidates have been gradually eliminated from consideration!

What is the situation in TGD? In TGD instantons are impossible at the fundamental space-time level. This is due to the induced space-time concept. What this means for the QFT limit of TGD?

  1. Obviously one must add to the action density a constraint term equal to Lagrange multiple θ times instanton density. If θ is constant the variation with respect to it gives just the vanishing of instanton number.
  2. A stronger condition is local and states that instanton density vanishes. This differs from the axion option in that there is no kinetic term for θ so that it does not propagate and does not appear in propagators.
Consider the latter option in more detail.
  1. The variation with respect to θ(x) gives the condition that instanton density rather than only instanton number vanishes for the allowed field configurations. This guarantees that axial current having instanton term as divergence is conserved if fermions are massless. There is no breaking of chiral symmetry at the massless limit and no chiral anomaly which is mathematically problematic.
  2. The field equations are however changed. The field equations reduce to the statement that the covariant divergence of YM current - sum of bosonic and fermionic contributions - equals to the covariant divergence of color current associated with the constraint term. The classical gauge potentials are affected by this source term and they in turn affect fermionic dynamics via Dirac equation. Therefore also the perturbation theory is affected.
  3. The following is however still uncertain: This term seems to have vanishing ordinary total divergence by Bianchi identities - one has topological color current proportional to the contraction of the gradient of θ and gauge field with 4-D permutation symbol! I have however not checked yet the details.

    If this is really true then the sum of fermionic and bosonic gauge currents not conserved in the usual sense equals to a opological color current conserved in the usual sense! This would give conserved total color charges as topological charges - in spirit with "Topological" in TGD! This would also solve a problem of non-abelian gauge theories usually put under the rug: the gauge total gauge current is not conserved and a rigorous definition of gauge charges is lost.

  4. What the equations of motion of ordinary QCD would mean in this framework? First of all the color magnetic and electric fields can be said to be orthogonal with respect to the natural inner product. One can have also solutions for which θ is constant. This case gives just the ordinary QCD but without instantons and strong CP breaking. The total color current vanishes and one would have local color confinement classically! This is true irrespective of whether the ordinary divergence of color currents vanishes.
  5. This also allows to understand CME and CSE believed to occur in the deconfinement phase transition. Now regions with non-constant θ(x) but vanishing instanton density are generated. The sum of the conserved color charges for these regions - droplets of quark-gluon plasma - however vanish by the conservation of color charges. One would indeed have non-vanishing local color charge densities and deconfinement in accordance with the physical intuition and experimental evidence. This could occur in proton-nucleon and nucleon-nucleon collisions at both RHIC and LHC and give rise to CME and CSE effects. This picture is however essentially TGD based. QCD in standard form does not give it and in QCD there are no motivations to demand that instanton density vanishes.
Electroweak sector

The analog of θ (x) is present also at the QFT limit of TGD in electroweak sector since instantons must be absent also now. One would have conserved total electroweak currents - also Abelian U(1) current reducing to topological currents, which vanish for θ(x)= constant but are non-vanishing otherwise. In TGD the conservation of em charge and possibly also Z0 charge is understood if strong form of holography (SH) is accepted: it implies that only electromagnetic and possibly also Z0 current are conserved and are assignable to the string world sheets carrying fermions. At QFT limit one would obtain reduction of electroweak currents to topological currents if the above argument is correct. The proper understanding of W currents at fundamental level is however still lacking.

It is now however not necessary to demand the vanishing of instanton term for the U(1) factor and chiral anomaly for pion suggest that one cannot demand this. Also the TGD inspired model for so called leptohadrons is based on the non-vanishing elecromagnetic instanton density. In TGD also M4 Kähler form J(CD) is present and same would apply to it. If one applies the condition empty Minkowski space ceases to be an extremal.

Gravitational sector

Could this generalize also the GRT limit of TGD? In GRT momentum conservation is lost - this one of the basic problems of GRT put under the rug. At fundamental level Poincare charges are conserved in TGD by the hypothesis that the space-time is 4-surface in M4 × CP2. Space-time symmetries are lifted to those of M4.

What happens at the GRT limit of TGD? The proposal has been that covariant conservation of energy momentum tensor is a remnant of Poincare symmetry. But could one obtain also now ordinary conservation of 4- momentum currents by adding to the standard Einstein-YM action a Lagrange multiplier term guaranteing that the gravitational analog of instanton term vanishes?

  1. First objection: This makes sense only if vier-bein is defined in the M4 coordinates applying only at GRT limit for which space-time surface is representable as a graph of a map from M4 to CP2.
  2. Second objection: If metric tensor is regarded as a primary dynamical variable, one obtains a current which is symmetry 2-tensor like T and G. This cannot give rise to a conserved charges.
  3. Third objection: Taking vielbein vectors eAμ as fundamental variable could give rise to a conserved vector with vanishing covariant divergence. Could this give rise to conserved currents labelled by A and having interpretation as momentum components? This does not work. Since eAμ is only covariantly constant one does not obtain genuine conservation law except at the limit of empty Minkowski space since in this case vielbein vectors can be taken to be constant.
Despite this the addition of the constraint term changes the interpretation of GRT profoundly.
  1. Curvature tensor is indeed essentially a gauge field in tangent space rotation group when contracted suitably by two vielbein vectors eAμ and the instanton term is formally completely analogous to that in gauge theory.
  2. The situation is now more complex than in gauge theories due to the fact that second derivatives of the metric and - as it seems - also of vielbein vectors are involved. They however appear linearly and do not give third order derivatives in Einstein's equations. Since the physics should not depend on whether one uses metric or vielbein as dynamical variables, the conjecture is that the variation states that the contraction of T-kG with vielbein vector equals to the topological current coming from instanton term and proportional to the gradient of θ

    (T-kG)μν eAν =j.

    The conserved current j would be contraction of the instanton term with respect to eAμ with the gradient of θ suitably covariantized. The variation of the action with respect to the the gradient of eAμ would give it. The resulting current has only vanishing covariant divergence to which vielbein contributes.

The multiplier term guaranteing the vanishing of the gravitational instanton density would have however highly non-trivial and positive consequences.
  1. The covariantly conserved energy momentum current would be sum of parts corresponding to matter and gravitational field unlike in GRT where the field equations say that the energy momentum tensors of gravitational field and matter field are identical. This conforms with TGD view at the level of many-sheeted space-time.
  2. In GRT one has the problem that in absence of matter (pure gravitational radiation) one obtains G=0 and thus vacuum solution. This follows also from conformal invariance for solutions representing gravitational radiation. Thanks to LIGO we however now know that gravitational radiation carries energy! Situation for TGD limit would be different: at QFT limit one can have classical gravitational radiation with non-vanishing energy momentum density thanks the vanishing of instanton term.

See the article About parity violation in hadron physics

For background see the chapters New Physics Predicted by TGD: Part I.

About parity violation in hadron physics

Strong interactions involve small CP violation revealing in the physics of neutral kaon and B meson. An interesting question is whether CP violation and also P violation could be seen also in hadronic reactions. QCD allows strong CP violation due to instantons. No strong CP breaking is observed, and Peccei-Quinn mechanism involving axion as a new but not yet detected particle is hoped to save the situation.

The de-confinement phase transition is believed to occur in heavy nucleus collisions and be accompanied by a phase transition in which chiral symmetry is restored. It has been conjectured that this phase transition involves large P violation assignable to so called chiral magnetic effect (CME) involving separation of charge along the axis of magnetic field generated in collision, chiral separation effect (CSE), and chiral magnetic wave (CMW). There is some evidence for CME and CSE in heavy nucleus collisions at RHIC and LHC. There is however also evidence for CME in proton-nucleus collisions, where it should not occur.

In TGD instantons and strong CP violation are absent at fundamental level. The twistor lift of TGD however predicts weak CP, T, and P violations in all scales and it is tempting to model matter-anti-matter asymmetry, the generation of preferred arrow of time, and parity breaking suggested by CBM anomalies in terms of these violations. The reason for the violation is the analog of self-dual covariantly constant Kähler form J(CD) for causal diamonds CD⊂ M4 defining parallel constant electric and magnetic fields. Lorentz invariance is not lost since one has moduli space containing Lorentz boosts of CD and J(CD). J(CD) induced to the space-time surface gives rise to a new U(1) gauge field coupling to fermion number. Correct order of magnitude for the violation for K and B mesons is predicted under natural assumptions. In this article the possible TGD counterparts of CME, CSE, and CMW are considered: the motivation is the presence of parallel E and B essential for CME.

See the article About parity violation in hadron physics

For background see the chapters New Physics Predicted by TGD: Part I.

Could second generation of weak bosons explain the reduction of proton charge radius?

The discovery by Pohl et al (2010) was that the charge radius of proton deduced from the muonic version of hydrogen atom - is .842 fm and about 4 per cent smaller than .875 fm than the charge radius deduced from hydrogen atom is in complete conflict with the cherished belief that atomic physics belongs to the museum of science (for details see the Wikipedia article). The title of the article Quantum electrodynamics-a chink in the armour? of the article published in Nature expresses well the possible implications, which might actually go well extend beyond QED.

Quite recently (2016) new more precise data has emerged from Pohl et al (see this). Now the reduction of charge radius of muonic variant of deuterium is measured. The charge radius is reduced from 2.1424 fm to 2.1256 fm and the reduction is .012 fm, which is about .8 per cent (see this). The charge radius of proton deduced from it is reported to be consistent with the charge radius deduced from deuterium. The anomaly seems therefore to be real. Deuterium data provide a further challenge for various models.

The finding is a problem of QED or to the standard view about what proton is. Lamb shift is the effect distinguishing between the states hydrogen atom having otherwise the same energy but different angular momentum. The effect is due to the quantum fluctuations of the electromagnetic field. The energy shift factorizes to a product of two expressions. The first one describes the effect of these zero point fluctuations on the position of electron or muon and the second one characterizes the average of nuclear charge density as "seen" by electron or muon. The latter one should be same as in the case of ordinary hydrogen atom but it is not. Does this mean that the presence of muon reduces the charge radius of proton as determined from muon wave function? This of course looks implausible since the radius of proton is so small. Note that the compression of the muon's wave function has the same effect.

Before continuing it is good to recall that QED and quantum field theories in general have difficulties with the description of bound states: something which has not received too much attention. For instance, van der Waals force at molecular scales is a problem. A possible TGD based explanation and a possible solution of difficulties proposed for two decades ago is that for bound states the two charged particles (say nucleus and electron or two atoms) correspond to two 3-D surfaces glued by flux tubes rather than being idealized to points of Minkowski space. This would make the non-relativistic description based on Schrödinger amplitude natural and replace the description based on Bethe-Salpeter equation having horrible mathematical properties.

The basic idea of the original model of the anomaly (see this) is that muon has some probability to end up to the magnetic flux tubes assignable to proton. In this state it would not contribute to the ordinary Schrödinger amplitude. The effect of this would be reduction of |Ψ|2 near origin and apparent reduction of the charge radius of proton. The weakness of the model is that it cannot make quantitative prediction for the size of the effect. Even the sign is questionable. Only S-wave binding energy is affected considerably but does the binding energy really increase by the interaction of muon with the quarks at magnetic flux tubes? Is the average of the charge density seen by muon in S wave state larger, in other words does it spend more time near proton or do the quarks spend more time at the flux tubes?

In the following a new model for the anomaly will be discussed.

  1. The model is inspired by data about breaking of universality of weak interactions in neutral B decays possibly manifesting itself also in the anomaly in the magnetic moment of muon. Also the different values of the charge radius deduced from hydrogen atom and muonium could reflect the breaking of universality. In the original model the breaking of universality is only effective.
  2. TGD indeed predicts a dynamical U(3) gauge symmetry whose 8+1 gauge bosons correspond to pairs of fermion and anti-fermion at opposite throats of wormhole contact. Throats are characterized by genus g=0,1,2, so that bosons are superpositions of states labelled by (g1,g2). Fermions correspond to single wormhole throat carrying fermion number and behave as U(3) triplet labelled by g.

    The charged gauge bosons with different genera for wormhole throats are expected to be very massive. The 3 neutral gauge bosons with same genus at both throats are superpositions of states (g,g) are expected to be lighter. Their charge matrices are orthogonal and necessarily break the universality of electroweak interactions. For the lowest boson family - ordinary gauge bosons - the charge matrix is proportional to unit matrix. The exchange of second generation bosons Z01 and γ1 would give rise to Yukawa potential increasing the binding energies of S-wave states. Therefore Lamb shift defined as difference between energies of S and P waves is increased and the charge radius deduced from Lamb shift becomes smaller.

  3. The model thus predicts a correct sign for the effect but the size of the effect from naive estimate assuming only γ2 and α21== α for M=2.9 TeV is almost by an order of magnitude too small. The values of the gauge couplings α2 and αZ,2 are free parameters as also the mixing angles between states (g,g). The effect is also proportional to the ratio (mμ/M(boson)2. It turns out that the inclusion of Z01 contribution and assumption α1 and αZ,1 are near color coupling strength αs gives a correct prediction.
Motivations for the breaking of electroweak universality

The anomaly of charge radius could be explained also as breaking of the universality of weak interactions. Also other anomalies challenging the universality exists. The decays of neutral B-meson to lepton pairs should be same apart from corrections coming from different lepton masses by universality but this does not seem to be the case (see this). There is also anomaly in muon's magnetic moment discussed briefly here. This leads to ask whether the breaking of universality could be due to the failure of universality of electroweak interactions.

The proposal for the explanation of the muon's anomalous magnetic moment and anomaly in the decays of B-meson is inspired by a recent very special di-electron event and involves higher generations of weak bosons predicted by TGD leading to a breaking of lepton universality. Both Tommaso Dorigo (see this) and Lubos Motl (see this) 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(89-79)/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.

  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 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 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.
The sign of the effect is predicted correctly and the order of magnitude come out correctly

Could the exchange of massive MG,79 photon and Z0 give rise to additional electromagnetic interaction inducing the breaking of Universality? The first observation is that the binding energy of S-wave state increases but there is practically no change in the energy of P wave state. Hence the effective charge radius rp as deduced from the parameterization of binding energy different terms of proton charge radius indeed decreases.

Also the order of magnitude for the effect must come out correctly.

  1. The additional contribution in the effective Coulomb potential is Yukawa potential. In S-wave state this would give a contribution to the binding energy in a good approximation given by the expectation value of the Yukawa potential, which can be parameterized as

    V(r)= g2 e-Mr/r ,&g2 = 4π kα .

    The expectation differs from zero significantly only in S-wave state characterized by principal quantum number n. Since the exponent function goes exponentially to zero in the p-adic length scale associated with 2.9 TeV mass, which is roughly by a factor 32 times shorter than intermediate boson mass scale, hydrogen atom wave function is constant in excellent approximation in the effective integration volume. This gives for the energy shift

    Δ E= g2| Ψ(0)|2 × I ,

    Ψ(0) 2 =[22/n2]×(1/a03) ,

    a0= 1/(mα) ,

    I= ∫ (e-Mr/r) r2drdΩ =4π/3M2.

    For the energy shift and its ratio to ground state energy

    En= α2/2n2× m

    one obtains the expression

    Δ En= 64π2 α/n2 α3 (m/M)2 × m ,

    Δ En/En= (27/3) π2α2 k2(m/M)2 .

    For k=1 and M=2.9 one has Δ En/En ≈ 3× 10-11 for muon.

Consider next Lamb shift.

  1. Lamb shift as difference of energies between S and P wave states (see this) is approximately given by

    Δn (Lamb)/En= 13α3/2n .

    For n=2 this gives Δ2 (Lamb)/E2= 4.9× 10-7.

  2. The parameterization for the Lamb shift reads as

    Δ E(rp) =a - brp2 +crp3 = 209.968(5) - 5.2248 × r2p + 0.0347 × r3p meV ,

    where the charge radius rp=.8750 is expressed in femtometers and energy in meVs.

  3. The reduction of rp by 3.3 per cent allows to estimate the reduction of Lamb shift (attractive additional potential reduces it). The relative change of the Lamb shift is

    x=[Δ E(rp))-Δ E(rp(exp))]/Δ E(rp)

    = [- 5.2248 × (r2p- r2p(exp)) + 0.0347 × ( r3p-r3p(exp))]/[209.968(5) - 5.2248 × r2p + 0.0347 × r3p(th)] .

    The estimate gives x= 1.2× 10-3.

This value can be compared with the prediction. For n=2 ratio of Δ En/Δ En(Lamb) is

x=Δ En/Δ En (Lamb)= k2 × [29π2/3×13α] × (m/M)2 .

For M=2.9 TeV the numerical estimate gives x≈ (1/3)×k2 × 10-4. The value of x deduced from experimental data is x≈ 1.2× 10-3. There is discrepancy of one order of magnitude. For k≈ 5 a correct order of magnitude is obtained. There are thus good hopes that the model works.

The contribution of Z01 exchange is neglected in the above estimate. Is it present and can it explain the discrepancy?

  1. In the case of deuterium the weak isospins of proton and deuterium are opposite so that their contributions to the Z01 vector potential cancel. If Z01 contribution for proton can be neglected, one has Δ rp=Δ rd.

    One however has Δ rp≈ 2.75 Δ rd. Hence Z01 contribution to Δ rp should satisfy Δ rp(Z01)≈ 1.75×Δ rp1). This requires αZ,11, which is true also for the ordinary gauge bosons. The weak isospins of electron and proton are opposite so that the atom is weak isospin singlet in Abelian sense, and one has I3pI3μ= -1/4 and attractive interaction. The condition relating rp and rZ suggests

    αZ,11≈ 286=4+13 .

    In standard model one has αZ/α= 1/[sin2W)cos2W)] =5.6 for sin2W)=.23 . One has upper bound αZ,11 ≥ 4 saturated for sin2W,1) =1/2. Weinberg angle can be expressed as

    sin2W,1)= (1/2)[1 - (1-4( α1Z,1)1/2] .

    αZ,11≈ 28/6 gives sin2W,1) = (1/2)[1 -(1/7)1/2] ≈ .31.

    The contribution to the axial part of the potential depending on spin need not cancel and could give a spin dependent contribution for both proton and deuteron.

  2. If the scale of α1 and αZ,1 is that of αs and if the factor 2.75 emerges in the proposed manner, one has k2≈ 2.75× 10= 27.5 rather near to the rough estimate k2≈ 27 from data for proton.

    Note however than there are mixing angles involved corresponding to the diagonal hermitian family charge matrix Q= (a,b,c) satisfying a2+b2+c2=1 and the condition a+b+c=0 expressing the orthogonality with the electromagnetic charge matrix (1,1,1)/31/2 expressing electroweak universality for ordinary electroweak bosons. For instance, one could have (a,b,c)= (0,1,-1)/21/2 for the second generation and (a,b,c)= (2,-1,-1)/61/2 for the third generation. In this case the above estimate would would be scaled down: α1→ 2α1/3≈ 1/20.5.

To sum up, the proposed model is successful at quantitative level allowing to understand the different changes for charge radius for proton and deuteron and estimate the values of electroweak couplings of the second generation of weak bosons apart from the uncertainty due to the family charge matrix. Muon's magnetic moment anomaly and decays of neutral B allow to test the model and perhaps fix the remaining two mixing angles.

See the article Could second generation of weak bosons explain the reduction of proton charge radius?

For background see the chapters New Physics Predicted by TGD: Part I and New Physics Predicted by TGD: Part II.

Two different lifetimes for neutron as evidence for dark protons

I found a popular article about very interesting finding related to neutron lifetime (see this). Neutron lifetime turns out tobe by about 8 seconds shorter, when measured by looking what fraction of neutrons disappears via decays in box than by measuring the number of protons produced in beta decays for a neutron beam travelling through a given volume. The life time of neutron is about 15 minutes so that relative lifetime difference is about 8/15×60 ≈ .8 per cent. The statistical signficance is 4 sigma: 5 sigma is accepted as the significance for a finding acceptable as discovery.

How could one explain the finding? The difference between the methods is that the beam experiment measures only the disappearences of neutrons via beta decays producing protons whereas box measurement detects the outcome from all possible decay modes. The experiment suggests two alternative explanations.

  1. Neutron has some other decay mode or modes, which are not detected in the box method since one measures the number of neutrons in initial and final state. For instance, in TGD framework one could think that the neutrons can transform to dark neutrons with some rate. But it is extremely unprobable that the rate could be just about 1 per cent of the decay rate. Why not 1 millionth? Beta decay must be involved with the process.

    Could some fraction of neutrons decay to dark proton, electron, and neutrino: this mode would not be detected in beam experiment? No, if one takes seriously the basic assumption that particles with different value of heff/h= n do not appear in the same vertex. Neutron should first transform to dark proton but then also the disappearance could take place also without the beta decay of dark proton and the discrepancy would be much larger.

  2. The proton produced in the ordinary beta decay of proton can however transform to dark proton not detected in the beam experiment! This would automatically predict that the rate is some reasonable fraction of the beta decay rate. About 1 percent of the resulting protons would transform to dark protons. This makes sense!
What is so nice is that the transformation of protons to dark protons is indeed the basic mechanism of TGD inspired quantum biology! For instance, it would occur in Pollack effect in with irradiation of water bounded by gel phase generates so called exclusion zone, which is negatively charged. TGD explanation is that some fraction of protons transforms to dark protons at magnetic flux tubes outside the system. Negative charge of DNA and cell could be due to this mechanism. One also ends up to a model of genetic code with the analogs of DNA, RNA, tRNA and amino-acids represented as triplets of dark protons. The model predicts correctly the numbers of DNAs coding given amino-acid. Besides biology the model has applications to cold fusion, and various free energy phenomena.

See the article Two different lifetimes for neutron as evidence for dark protons and chapter New Particle Physics Predicted by TGD: Part I.

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