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p-Adic Physics

Note: Newest contributions are at the top!



Year 2014

Large parity breaking effects at RHIC?

Ulla Matfolk reminded about an old Sciencedaily article (see this) telling about discovery of large parity breaking effects at RHIC studying collisions of relativistic heavy ions at energies at which QCD suggests the formation of quark gluon plasma. Somehing exotic is observed but it seems to be something different from quark gluon plasma in that long range correlations not characteristic for plasma phase are present and the particle production does not look like black body radiation. Similar findings are made also at LHC and also for proton-proton collisions. This suggests new physics and M89 hadron physics is the TGD inspired candidate for it. In any case, I took the article as a hype as I read it for four years ago.

Now I read the article again and started to wonder on what grounds authors claim large parity violation. What they claim to observed are magnetic fields in which u and d quarks with charges 2/3 and -1/3 move in opposite directions along the magnetic field lines (flux tubes in TGD). They assign these motions to the presence of strong parity breaking, much stronger than predicted by the standard model.

1. Instanton density as origin of parity breaking

What says TGD? In TGD magnetic fields would form flux tubes, even flux tubes carrying monopole flux are possible. The findings suggests that magnetic field was accompanied by electric field and that both were parallel to the flux tubes and each other in average sense. Helical magnetic and electric fields parallel in average sense could be associated with flux tubes in TGD.

The helical classical field patterns would break the parity of ground state. Instanton density for Kähler field, essentially E.B, measuring the non-orthogonality of E and B would serve as a measure for the strength of parity breaking occurring at the level of ground state and thus totally different from weak parity breaking. u and d quarks with opposite signs of em charges would move in opposite directions in the electric force.

2. The origin of instanton density in TGD Universe

What is the origin of these non-orthogonal magnetic and electric fields? Here I must dig down to a twenty years old archeological layer of TGD. Already at seventies an anomalous creation of anomalous e+e- pairs having axion-like properties in heavy ion collisions near Coulomb wall was observed. Effect was forgotten since it was not consistent with standard model. TGD explanation is in terms of pairs resulting from the decay of lepto-pion formed as bound states of color excited electron and positron and created in strong non-orthogonal electric and magnetic fields of colliding nuclei.

Objection: Color excited leptons do not conform with standard model view about color. In TGD this is not a problem since colored states correspond to partial waves in CP2 and both leptons and quarks can move in higher color partial waves but usually with much higher mass.

Non-vanishing instanton density would mean that the orthogonal E and B created by colliding protons appear at the *same* space-time sheet so that a coherent instanton density E.B is created and gives rise to the generation of pairs. Large value of E.B means large parity breaking at the level of ground state. One expects that in most collisions the fields of colliding nuclei stay at different space-time sheets and therefore do not interfere directly (only their effects on charged particles sum up) but that with some property the fields can enter to the same space-time sheet and generate the physics not allowed by standard model.

Objection: Standard model predicts extremely weak parity breaking effects: this is due to the massivation of weak bosons, for massless weak bosons the parity breaking would be large. Indeed, if the non-orthogonal E and B are at different space-time sheets, no instantons are generated.

Objection: The existence of new particle in MeV scale would change dramatically the decay widths of weak bosons. The TGD solution is that colored leptons are dark in TGD sense (heff=n×h,n>1). Large heff would make weak bosons effectively massless below scaled up Compton length of weak bosons proportional to heff and large parity breaking could be understood also the "conventional manner".

3. Strong parity breaking as signature of dark variant of M89 hadron physics

This picture would apply also now and also leads to an increased understanding of M89 hadron physics about which I have been talking for years and which is TGD prediction for LHC. Very strong non-orthogonal E and B fields would be most naturally associated with colliding protons rather than nuclei. The energy scale is of course much much higher than in the heavy ion experiment. Instanton-like space-time sheets, where the E and B of the colliding nuclei could be formed as magneto-electric flux tubes (a priori this of course need not occur since fields an remain at different space-time sheets).

The formation of axionlike states is expected to be possible as pairs color excited quarks. M89 hadron physics is a scaled up copy of the ordinary M107 hadron physics with mass scale which is by a factor 512 higher. The natural possibility is pions of M89 hadron physics but with large heff/h ≈ 512 so that the size of M89 pions could increase to a size scales of ordinary hadrons! This would explain why heavy ion collisions involve energies in TeV range appropriate for M89 hadrons and thus Compton scales of order weak scale whereas size scales are associated with QCD plasma of M107 hadron physics and is by a factor 1/512 smaller. Brings in mind a line from an biblical story: The hands are Esau's hands but the voice is Jacob's voice! Quite generally, the failure estimates based on Uncertainty Principle could serve as a signature for non-standard values of heff: two great energy scale for effect as compared to its length scale.

To sum up, the strange findings about heavy ion and proton proton collisions at LHC for which I suggested M89 physics as an explanation would indeed make sense and one also ends up to a concrete mechanism for the emergence of dark variants of weak physics. The magnetic flux tubes playing key role in TGD inspired quantum biology would carry also electric fields not-orthonal to magnetic fields and the two fields would be twisted. As a mattter of fact, the observed strong parity breaking would be very analogous to that observed in biology if one accepts TGD based explanation of chiral selection in living matter.

4. Could this relate to non-observed SUSY somehow?

Dark matter and spartners have something in common: it is very difficult to observe them! I cannot resist typing a fleeting crazy idea, which I have managed to forfend several times but is popping up again and again from the murky depths of subconscious to tease me. TGD predicts also SUSY albeit different from the standard one: for instance, separate conservation of lepton and baryon numbers is predicted and fermions are not Majorana fermions. Whether covariantly constant right-handed neutrino mode which carries no quantum numbers except spin could be seen as a Majorana lepton is an open question.

One can however assume that covariantly constant right-handed neutrino, call it νR, and its antineutrino span N=2 SUSY representation. Particles would appear as SUSY 4-plets: particle, particle+νR,particle + antiνR, particle+ νR+antiνR. Covariantly constant right-handed neutrinos and antineutrino would generate the least broken sub-SUSY. Sparticles should obey the same mass formula as particles but with possibly different p-adic mass scale.

But how the mass scales of particles and its spartners can be so different if right handed does not have any weak interactions? Could it be that sparticles have same p-adic mass scale as particles but are dark having heff=n×h so that the observation of sparticle would mean observation of dark matter!?;-). Particle cannot of course transform to its spartner directly: already angular momentum conservation prevents this. For N=2 SUSY one can however consider the transformation of particle to the state particle +X, where X is νR+antiνR representing a dark variant of particle and having same quantum numbers. It would have non-standard value heff =n×h of Planck constant. The resulting dark particles could interact and generate also states in dark SUSY 4-plet. Dark photons could be spartners of photons and decay to biophotons. SUSY would be essential for living matter!

Critical reader asks whether leptopions could be actually pairs of (possibly color excited) N=2 SUSY partners of selectron and spositron. The masses of (color) excitations making up electropion must be indeed identical with electron and positron masses. Should one give up the assumption that color octet excitations of leptons are in question? But if color force is not present, what would bind the spartners together for form electropion? Coulomb attraction so that dark susy analog of positronium would be in question? But why not positronium? If spartner of electron is color excited, one can argue that its mass need not be the same as that of electron and could be of order CP2! The answer comes out only by calculating and I am too old to start this business again;-). But what happens to leptohadron model if color excitation is not in question? Nothing dramatic, the mathematical structure of leptohadron model is not affected since the calculations involve only the assumption that electropion couples to electromagnetic "instanton" term fixed by anomaly considerations.

If this makes sense, the answers to four questions: What is behind chiral selection in biology?; What dark matter is? ; What spartners are and why they are not seemingly observed?; What is behind various forgotten axion/pion-like states? would have a lot in common!

For the new physics predicted by TGD see the chapter "New Particle Physics Predicted by TGD: Part I" of "TGD and p-Adic numbers".



Higgs and p-adic mass calculations

In the earlier blog posting I told that the boundary condition for the Kähler-Dirac equation is massless Dirac equation with the analog of Higgs term added. The interpretation in terms of Higgs mechanism however fails since the term can be also tachyonic. Intriguingly, p-adic mass calculations require the ground state conformal weight to be negative half odd integer. This raises the question whether the the boundary condition for Kähler-Dirac equation could be equivalent for the mass formulation given by the condition that the scaling generator L0 annihilates the physical states for Super Virasoro representations. This equivalence is suggested by quantum classical correspondence.

If this is the case, the two mass shell conditions would be equivalent. This possibility is discussed more precisely below.

  1. The boundary condition for K-D equation reads as

    (pkγk+ Γn)Ψ=0 .

    (pkγk is algebraic Dirac operator in Minkowski space and Γn is Kähler Dirac gamma matrix defined as contraction of the canonical energy momentum current of Kähler action with imbedding space gamma matrices.

    Mass shell condition corresponds to the vanishing of the square of the algebraic Dirac operator and should be equivalent with the mass shell condition given by the vanishing of the action of L0:

    pkpk== p2= m02× (hgr +n) ==mn2 .

    m0 is CP2 mass scale dictated by CP2 size scale and analogous to that given by string tension. m0 is evaluated for the standard value of Planck constant. hgr is ground state conformal weight and n is the conformal weight assignable to the Super-Virasoro generators creating the state.

    p-Adic mass calculations require that hgr is negative and half odd integer valued so that ground state would be tachyonic. The first principle explanation for this could be the presence of Minkowskian time-like contribution in Γn coming from the canonical momentum density for Kähler action. One cannot exclude a p-adically small deviation of hgr from the negative half odd integer value proportional to at least second power of prime p perhaps assignable to Higgs like contribution or contribution of string like objects assignable to elementary particle.

  2. One can decompose Γn to M4 and CP2 parts corresponding to the contractions of the canonical momentum density with M4 and CP2 gamma matrices respectively:

    Γn = Tn(M4)+ Tn(CP2) .

    Tn(M4) involves M4 gamma matrices is determined by the energy momentum tensor TK of Kähler action determined by its imbedding space variation coming from the induced metric. Tn(CP2) involves CP2 gamma matrices and is sum coming from the imbedding space variations coming from a variation with respect to the induced metric and induced Kähler form. M4 and CP2 contributions are orthogonal to each other as imbedding space vectors.

  3. The square of the mass boundary condition gives

    (p+Tn(M4))k(p+Tn(M4))k +Tnk(CP2)Tnk(CP2)=0 .

    This condition can be simplified if one assumes that the direction of classical energy momentum density vector Tnk(M4) is same as four momentum pk. This assumption is motivated by quantum classical correspondence. This would give

    Tnk(M4)= α (x) pk .

    The coeffcient α can depend on the position along string.

  4. With these assumptions the condition reads

    (1+α)2 p2 +Tnk(CP2)Tnk(CP2)=0 .

    and gives

    Tnk(CP2)Tnk(CP2)/(1+α)2=- mn2 .

    where mn2 is the mass squared associated with the state as given by the vanishing of L0 action on the state.

    In coordinate changes the left hand changes in position dependent manner but the change of the factor α compensates the change of T2(CP2) term so that the condition is general coordinate invariant statement.

  5. Combiging this with the mass shell condition coming from the vanishing of the action of L0 gives

    Tnk(CP2)Tnk(CP2)= -(1+α)2m02(hgr+n) .

    One can solve α from this condition:

    α=+/- S/Mn -1 , S2k== - Tnk(CP2)Tnk(CP2) (≥ 0) .

  6. The interpretation of the effective metric defined by the Kähler-Dirac gamma matrices has been a longstanding problem. It seems that the geffnn of this metric appears naturally if one assumes that Super-Virasoro conditions for L0 is equivalent with that given by the boundary condition for Kähler-Dirac equation.
The conclusion is that the Higgs like term could provide classical space correlate for the basic stringy mass formulate. p-Adic mass calculations apply thermodynamics with mass squared replacing the energy in the usual thermodynamics. In Zero Energy Ontology p-adic thermodynamics is replaced with its square root and one would have quantum superposition of space-time surfaces with mass squared values mn2 with probabilities given by p-adic thermodynamics. The 3-momenta could be identical for these contributions but energies would differ. This does not break Lorenz invariance but would mean extremely small breaking of time translation invariance characterized by the inverse of p-adic prime. The breaking is of the order of of 10-38 for electron characterized by Mersenne prime M127. For the evolution of TGD view about the relationship of Higgs mechanism and p-adic mass calculations see the chapter "Higgs or something else".



Experimental evidence for sterile neutrino?

Many physicists are somewhat disappointed to the results from LHC: the expected discovery of Higgs has been seen as the main achievement of LHC hitherto. Much more was expected. To my opinion there is no reason for disappointment. The exclusion of the standard SUSY at expected energy scale is very far reaching negative result. Also the fact that Higgs mass is too small to be stable without fine tuning is of great theoretical importance. The negative results concerning heavy dark matter candidates are precious guidelines for theoreticians. The non-QCD like behavior in heavy ion collisions and proton-ion collisions is bypassed my mentioning something about AdS/CFT correspondence and non-perturbative QCD effects. I tend to see these effects as direct evidence for M89 hadron physics (see this).

In any case, something interesting has emerged quite recently. Resonaances tells that the recent analysis of X-ray spectrum of galactic clusters claims the presence of monochromatic 3.5 keV photon line. The proposed interpretation is as a decay product of sterile 7 keV neutrino transforming first to a left-handed neutrino and then decaying to photon and neutrino via a loop involving W boson and electron. This is of course only one of the many interpretations. Even the existence of line is highly questionable.

One of the poorly understood aspects of TGD is right-handed neutrino, which is obviously the TGD counterpart of the inert neutrino.

  1. The old idea is that covariantly constant right handed neutrino could generate N=2 super-symmetry in TGD Universe. In fact, all modes of induced spinor field would generate superconformal symmetries but electroweak interactions would break these symmetries for the modes carrying non-vanishing electroweak quantum numbers: they vanish for νR. This picture is now well-established at the level of WCW geometry (see this): super-conformal generators are labelled angular momentum and color representations plus two conformal weights: the conformal weight assignable to the light-like radial coordinate of light-cone boundary and the conformal weight assignable to string coordinate. It seems that these conformal weights are independent. The third integer labelling the states would label genuinely Yangian generators: it would tell the poly-locality of the generator with locus defined by partonic 2-surface: generators acting on single partonic 2-surface, 2 partonic 2-surfaces, ...
  2. It would seem that even the SUSY generated by νR must be badly broken unless one is able to invent dramatically different interpretation of SUSY. The scale of SUSY breaking and thus the value of the mass of right-handed neutrino remains open also in TGD. In lack of better one could of course argue that the mass scale must be CP2 mass scale because right-handed neutrino mixes considerably with the left-handed neutrino (and thus becomes massive) only in this scale. But why this argument does not apply also to left handed neutrino which must also mix with the right-handed one!
  3. One can of course criticize the proposed notion of SUSY: wonder whether fermion + extremely weakly interacting νR at same wormhole throat (or interior of 3-surface) can behave as single coherent entity as far spin is considered (see this)?
  4. The condition that the modes of induced spinor field have a well-defined electromagnetic charge eigenvalue (see this) requires that they are localized at 2-D string world sheets or partonic 2-surfaces: without this condition classical W boson fields would mix the em charged and neutral modes with each other. Right-handed neutrino is an exception since it has no electroweak couplings. Unless right-handed neutrino is covariantly constant, the modified gamma matrices can however mix the right-handed neutrino with the left handed one and this can induce transformation to charged mode. This does not happen if each modified gamma matrix can be written as a linear combination of either M4 or CP2 gamma matrices and modified Dirac equation is satisfied separately by M4 and CP2 parts of the modified Dirac equation.
  5. Is the localization of the modes other than covariantly constant neutrino to string world sheets a consequence of dynamics or should one assume this as a separate condition? If one wants similar localization in space-time regions of Euclidian signature - for which CP2 type vacuum extremal is a good representative - one must assume it as a separate condition. In number theoretic formulation string world sheets/partonic 2-surfaces would be commutative/co-commutative sub-manifolds of space-time surfaces which in turn would be associative or co-associative sub-manifolds of imbedding space possessing (hyper-)octonionic tangent space structure. For this option also right-handed neutrino would be localized to string world sheets. Right-handed neutrino would be covariantly constant only in 2-D sense.

    One can consider the possibility that νR is de-localized to the entire 4-D space-time sheet. This would certainly modify the interpretation of SUSY since the number of degrees of freedom would be reduced for νR.

  6. Non-covariantly constant right-handed neutrinos could mix with left-handed neutrinos but not with charged leptons if the localization to string world sheets is assumed for modes carrying non-vanishing electroweak quantum numbers. This would make possible the decay of right-handed to neutrino plus photon, and one cannot exclude the possibility that νR has mass 7 keV.

    Could this imply that particles and their spartners differ by this mass only? Could it be possible that practically unbroken SUSY could be there and we would not have observed it? Could one imagine that sfermions have annihilated leaving only states consisting of fundamental fermions? But shouldn't the total rate for the annihilation of photons to hadrons be two times the observed one? This option does not sound plausible.

    What if one assumes that given sparticle is charactrized by the same p-adic prime as corresponding particle but is dark in the sense that it corresponds to non-standard value of Planck constant. In this case sfermions would not appear in the same vertex with fermions and one could escape the most obvious contradictions with experimental facts. This leads to the notion of shadron: shadrons would be (see this) obtained by replacing quarks with dark squarks with nearly identical masses. I have asked whether so called X and Y bosons having no natural place in standard model of hadron could be this kind of creatures.

The interpretation of 3.5 keV photons as decay products of right-handed neutrinos is of course totally ad hoc. Another TGD inspired interpretation would be as photons resulting from the decays of excited nuclei to their ground state.
  1. Nuclear string model (see this) predicts that nuclei are string like objects formed from nucleons connected by color magnetic flux tubes having quark and antiquark at their ends. These flux tubes are long and define the "magnetic body" of nucleus. Quark and antiquark have opposite em charges for ordinary nuclei. When they have different charges one obtains exotic state: this predicts entire spectrum of exotic nuclei for which statistic is different from what proton and neutron numbers deduced from em charge and atomic weight would suggest. Exotic nuclei and large values of Planck constant could make also possible cold fusion (see this).
  2. What the mass difference between these states is, is not of course obvious. There is however an experimental finding (see Analysis of Gamma Radiation from a Radon Source: Indications of a Solar Influence) that nuclear decay rates oscillate with a period of year and the rates correlate with the distance from Sun. A possible explanation is that the gamma rays from Sun in few keV range excite the exotic nuclear states with different decay rate so that the average decay rate oscillates (see this). Note that nuclear excitation energies in keV range would also make possible interaction of nuclei with atoms and molecules.
  3. This allows to consider the possibility that the decays of exotic nuclei in galactic clusters generates 3.5 keV photons. The obvious question is why the spectrum would be concentrated at 3.5 keV in this case (second question is whether the energy is really concentrated at 3.5 keV: a lot of theory is involved with the analysis of the experiments). Do the energies of excited states depend on the color bond only so that they would be essentially same for all nuclei? Or does single excitation dominate in the spectrum? Or is this due to the fact that the thermal radiation leaking from the core of stars excites predominantly single state? Could E=3.5 keV correspond to the maximum intensity for thermal radiation in stellar core? If so, the temperature of the exciting radiation would be about T≈ E/3≈ 1.2× 107 K. This in the temperature around which formation of Helium by nuclear fusion has begun: the temperature at solar core is around 1.57× 107 K.

For background see the chapter SUSY in TGD Universe.



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