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Note: Newest contributions are at the top!
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.
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?
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)?
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.
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.
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.
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.
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.
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?
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.
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
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.
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.
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?
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.
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?
See the article About parity violation in hadron physics
For background see the chapters New Physics Predicted by TGD: Part I.
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.
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.
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.
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.
Consider next Lamb shift.
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?
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.
See the article Two different lifetimes for neutron as evidence for dark protons and chapter New Particle Physics Predicted by TGD: Part I.