What's new in

p-Adic Physics

Note: Newest contributions are at the top!



Year 2016

Delicacies of the induced spinor structure and SUSY mystery

The discussion of induced spinor structure leads to a modification of an earlier idea (one of the many) about how SUSY could be realized in TGD in such a manner that experiments at LHC energies could not discover it and one should perform experiments at the other end of energy spectrum at energies which correspond to the thermal energy about .025 eV at room temperature. I have the feeling that this observation could be of crucial importance for understanding of SUSY.

The notion of induced spinor field deserves a more detailed discussion. Consider first induced spinor structures.

  1. Induced spinor field are spinors of M4× CP2 for which modes are characterized by chirality (quark or lepton like) and em charge and weak isospin.
  2. Induced spinor spinor structure involves the projection of gamma matrices defining induced gamma matrices. This gives rise to superconformal symmetry if the action contains only volume term.

    When Kähler action is present, superconformal symmetry requires that the modified gamma matrices are contractions of canonical momentum currents with imbedding space gamma matrices. Modified gammas appear in the modified Dirac equation and action, whose solution at string world sheets trivializes by super-conformal invariance to same procedure as in the case of string models.

  3. Induced spinor fields correspond to two chiralities carrying quark number and lepton number. Quark chirality does not carry color as spin-like quantum number but it corresponds to a color partial wave in CP2 degrees of freedom: color is analogous to angular momentum. This reduces to spinor harmonics of CP2 describing the ground states of the representations of super-symplectic algebra.

    The harmonics do not satisfy correct correlation between color and electroweak quantum numbers although the triality t=0 for leptonic waves and t=1 for quark waves. There are two manners to solve the problem.

    1. Super-symplectic generators applied to the ground state to get vanishing ground states weight instead of the tachyonic one carry color and would give for the physical states correct correlation: leptons/quarks correspond to the same triality zero(one partial wave irrespective of charge state. This option is assumed in p-adic mass calculations.
    2. Since in TGD elementary particles correspond to pairs of wormhole contacts with weak isospin vanishing for the entire pair, one must have pair of left and right-handed neutrinos at the second wormhole throat. It is possible that the anomalous color quantum numbers for the entire state vanish and one obtains the experimental correlation between color and weak quantum numbers. This option is less plausible since the cancellation of anomalous color is not local as assume in p-adic mass calculations.
The understanding of the details of the fermionic and actually also geometric dynamics has taken a long time. Super-conformal symmetry assigning to the geometric action of an object with given dimension an analog of Dirac action allows however to fix the dynamics uniquely and there is indeed dimensional hierarchy resembling brane hierarchy.
  1. The basic observation was following. The condition that the spinor modes have well-defined em charge implies that they are localized to 2-D string world sheets with vanishing W boson gauge fields which would mix different charge states. At string boundaries classical induced W boson gauge potentials guarantee this. Super-conformal symmetry requires that this 2-surface gives rise to 2-D action which is area term plus topological term defined by the flux of Kähler form.
  2. The most plausible assumption is that induced spinor fields have also interior component but that the contribution from these 2-surfaces gives additional delta function like contribution: this would be analogous to the situation for branes. Fermionic action would be accompanied by an area term by supersymmetry fixing modified Dirac action completely once the bosonic actions for geometric object is known. This is nothing but super-conformal symmetry.

    One would actually have the analog of brane-hierarchy consisting of surfaces with dimension D= 4,3,2,1 carrying induced spinor fields which can be regarded as independent dynamical variables and characterized by geometric action which is D-dimensional analog of the action for Kähler charged point particle. This fermionic hierarchy would accompany the hierarchy of geometric objects with these dimensions and the modified Dirac action would be uniquely determined by the corresponding geometric action principle (Kähler charged point like particle, string world sheet with area term plus Kähler flux, light-like 3-surface with Chern-Simons term, 4-D space-time surface with Kähler action).

  3. This hierarchy of dynamics is consistent with SH only if the dynamics for higher dimensional objects is induced from that for lower dimensional objects - string world sheets or maybe even their boundaries orbits of point like fermions. Number theoretic vision suggests that this induction relies algebraic continuation for preferred extremals. Note that quaternion analyticity means that quaternion analytic function is determined by its values at 1-D curves.
  4. Quantum-classical correspondences (QCI) requires that the classical Noether charges are equal to the eigenvalues of the fermionic charges for surfaces of dimension D=0,1,2,3 at the ends of the CDs. These charges would not be separately conserved. Charges could flow between objects of dimension D+1 and D - from interior to boundary and vice versa. Four-momenta and also other charges would be complex as in twistor approach: could complex values relate somehow to the finite life-time of the state?

    If quantum theory is square root of thermodynamics as ZEO suggests, the idea that particle state would carry information also about its life-time or the time scale of CD to which is associated could make sense. For complex values of αK there would be also flow of canonical and super-canonical momentum currents between Euclidian and Minkowskian regions crucial for understand gravitational interaction as momentum exchange at imbedding space level.

  5. What could be the physical interpretation of the bosonic and fermionic charges associated with objects of given dimension? Condensed matter physicists assign routinely physical states to objects of various dimensions: is this assignment much more than a practical approximation or could condensed matter physics already be probing many-sheeted physics?
SUSY and TGD

From this one ends up to the possibility of identifying the counterpart of SUSY in TGD framework. There are several options to consider.

  1. The analog of brane hierarchy is realized also in TGD. Geometric action has parts assignable to 4-surface, 3-D light like regions between Minkowskian and Euclidian regions, 2-D string world sheets, and their 1-D boundaries. They are fixed uniquely. Also their fermionic counterparts - analogs of Dirac action - are fixed by super-conformal symmetry. Elementary particles reduce so composites consisting of point-like fermions at boundaries of wormhole throats of a pair of wormhole contacts.

    This forces to consider 3 kinds of SUSYs! The SUSYs associated with string world sheets and space-time interiors would be broken since there is a mixing between M4 chiralities in the modified Dirac action. The mass scale of the broken SUSY would correspond to the length scale of these geometric objects and one might argue that decoupling between the degrees of freedom considered occurs at high energies and explains why no evidence for SUSY has been observed at LHC. Also the fact that the addition of massive fermions at these dimensions can be interpreted differently. 3-D light-like 3-surfaces would be however an exception.

  2. For 3-D light-like surfaces the modified Dirac action associated with the Chern-Simons term does not mix M4 chiralities (signature of massivation) at all since modified gamma matrices have only CP2 part in this case. All fermions can have well-defined chirality. Even more: the modified gamma matrices have no M4 part in this case so that these modes carry no four-momentum - only electroweak quantum numbers and spin. Obviously, the excitation of these fermionic modes would be an ideal manner to create spartners of ordinary particles consting of fermion at the fermion lines. SUSY would be present if the spin of these excitations couples - to various interactions and would be exact in absence of coupling to interior spinor fields.

    What would be these excitations? Chern-Simons action and its fermionic counterpart are non-vanishing only if the CP2 projection is 3-D so that one can use CP2 coordinates. This strongly suggests that the modified Dirac equation demands that the spinor modes are covariantly constant and correspond to covariantly constant right-handed neutrino providing only spin.

    If the spin of the right-handed neutrino adds to the spin of the particle and the net spin couples to dynamics, N=2 SUSY is in question. One would have just action with unbroken SUSY at QFT limit? But why also right-handed neutrino spin would couple to dynamics if only CP2 gamma matrices appear in Chern-Simons-Dirac action? It would seem that it is independent degree of freedom having no electroweak and color nor even gravitational couplings by its covariant constancy. I have ended up with just the same SUSY-or-no-SUSY that I have had earlier.

  3. Can the geometric action for light-like 3-surfaces contain Chern-Simons term?
    1. Since the volume term vanishes identically in this case, one could indeed argue that also the counterpart of Kähler action is excluded. Moreover, for so called massless extremals of Kähler action reduces to Chern-Simons terms in Minkowskian regions and this could happen quite generally: TGD with only Kähler action would be almost topological QFT as I have proposed. Volume term however changes the situation via the cosmological constant. Kähler-Dirac action in the interior does not reduce to its Chern-Simons analog at light-like 3-surface.
    2. The problem is that the Chern-Simons term at the two sides of the light-like 3-surface differs by factor (-1)1/2 coming from the ratio of (g4)1/2 factors which themselves approach to zero: one would have the analog of dipole layer. This strongly suggests that one should not include Chern-Simons term at all.

      Suppose however that Chern-Simons terms are present at the two sides and αK is real so that nothing goes through the horizon forming the analog of dipole layer. Both bosonic and fermionic degrees of freedom for Euclidian and Minkowskian regions would decouple completely but currents would flow to the analog of dipole layer. This is not physically attractive.

      The canonical momentum current and its super counterpart would give fermionic source term ΓnΨint,+/- in the modified Dirac equation defined by Chern-Simons term at given side +/-: +/- refers to Minkowskian/Euclidian part of the interior. The source term is proportional to ΓnΨint,+/- and Γn is in principle mixture of M4 and CP2 gamma matrices and therefore induces mixing of M4 chiralities and therefore also 3-D SUSY breaking. It must be however emphasized that Γn is singular and one must be consider the limit carefully also in the case that one has only continuity conditions. The limit is not completely understood.

    3. If αK is complex, there is coupling between the two regions and the simplest assumption has been that there is no Chern-Simons term as action and one has just continuity conditions for canonical momentum current and hits super counterpart.
    The cautious conclusion is that 3-D Chern-Simons term and its fermionic counterpart are absent.
  4. What about the addition of fermions at string world sheets and interior of space-time surface (D=2 and D=4). For instance, in the case of hadrons D=2 excitations could correspond to addition of quark in the interior of hadronic string implying additional states besides the states obtained assuming only quarks at string ends. Let us consider the interior (D=4). The smallness of cosmological constant implies that the contribution to the four-momentum from interior should be rather small so that an interpretation in terms of broken SUSY might make sense. There would be mass m∼ .03 eV per volume with size defined by the Compton scale hbar/m. Note however that cosmological constant has spectrum coming as inverse powers of prime so that also higher mass scales are possible.

    This interpretation might allow to understand the failure to find SUSY at LHC. Sparticles could be obtained by adding interior right-handed neutrinos and antineutrinos to the particle state. They could be also associated with the magnetic body of the particle. Since they do not have color and weak interactions, SUSY is not badly broken. If the mass difference between particle and sparticle is of order m=.03 eV characterizing ρvac, particle and sparticle could not be distinguished in higher energy physics at LHC since it probes much shorter scales and sees only the particle. I have already earlier proposed a variant of this mechanism but without SUSY breaking.

    To discover SUSY one should do very low energy physics in the energy range m∼ .03 eV having same order of magnitude as thermal energy kT= 2.6× 10-2 eV at room temperature 25 oC. One should be able to demonstrate experimentally the existence of sparticle with mass differing by about m∼ .03 eV from the mass of the particle (one cannot of course exclude higher mass values if Λ has spectrum). An interesting question is whether the sfermions associated with standard fermions could give rise to Bose-Einstein condensates whose existence in the length scale of large neutron is strongly suggested by TGD view about living matter.

See the chapter SUSY in TGD Universe.



Muon surplus in high energy cosmic ray showers as an indication for new hadron physics

According to the article "Viewpoint: Cosmic-Ray Showers Reveal Muon Mystery in APS Physics (see this) Pierre Auger Observatory reports that there is 30 per cent muon surplus in cosmic rays at ultrahigh energy around 1019 eV (see this). These events are at the knee of cosmic ray energy distribution: at higher energies the flux of cosmic rays should be reduced due to the loss of energy with cosmic microwave background. There are actually indications that this does not take place but this is not the point now. This article tells about how these showers are detected and also provides a simple model for the showers.

This energy is estimated in the rest system of Earth and corresponds to the energy of 130 TeV in cm mass system for a collision with nucleon. This is roughly 10 times the cm energy of 14 TeV at LHC. The shower produced by the cosmic ray is a cascade in which high energy cosmic ray gradually loses its energy via hadron production. The muons are relatively low energy muons resulting in hadronic decays, mostly pion decays, since most of the energy ends up to charged pions producing muons and electrons and neutral pions decaying rapidly to gamma pairs. The electron-positron pairs produced in the electromagnetic showers from neutral pions mask the electrons produced in neutral pion decay to electrons so that the possible surplus can be detected only for muons.

Since cosmic rays are mostly protons and nuclei the primary collisions should involve a primary collision of cosmic ray particle with a nucleon of atmosphere. The anomalously large muon yield suggests an anomalous yield of proton-antiproton pairs produced in the first few collisions. Protons and antiprotons would then collide with nuclei of atmosphere and lose their energy and give rise to anomalously large number of pions and eventually muons.

Unless the models for the production (constrained by LHC data) underestimate muon yield, new physics is required to explain the source of proton-antiproton pairs is needed.

In TGD framework one can consider two scaled up variants of hadron physics as candidates for the new physics.

  1. The first candidate corresponds to M89 hadron physics for which hadron masses would be obtained by a scaling with factor 512 from the masses of ordinary hadrons characterized by Mersenne prime M107= 2107-1. There are several bumps bumps identifiable as pseudo-scalar mesons with predicted masses also some bumps identifiable as some scaled up vector mesons (see this). Also the unexpected properties of what was expected to be quark gluon plasma suggest M89 hadron physics. In particular, the evidence for string like states suggests M89 mesons. If the situation is quantum critical, M89 have scaled up Compton length. The natural guess is that it corresponds to the size of ordinary hadrons.

    The proton of M89(=289-1) hadron physics would have mass of 512 GeV so that the production of M89 hadrons could take place at energies, which for ordinary hadrons would correspond to 260 GeV meaning that perturbative M89 QCD could be used. The quarks of this hadron physics would hadronize either directly to ordinary M107 or to M89 hadrons. In both cases a phase transition like process would lead from M89 hadrons or to M107 hadrons and produce a surplus of protons and antiprotons whose collisions with the nuclei of atmosphere would produce a surplus of pions.

  2. One can also consider M79 hadron physics, where MG,79 corresponds to Gaussian Mersenne (1+i)79-1. The mass scale would be 32 times higher than that for M89 hadron physics and correspond to 8 GeV for ordinary hadron collisions. Also now perturbative QCD would apply.
One can argue that M89 or MG,79 hadron physics comes in play for collisions with small enough impact parameter and gives an additive contribution to the total rate of protons and antiproton production. The additional contribution would be of the same order of magnitude as that from M107 hadron physics.

Could quantum criticality play some role now?

  1. What is the situation is quantum critical with heff/h>1? The first naive guess is that at the level of tree diagrams corresponding to classical theory the production rate has has no dependence on Planck constant so that nothing happens. A less naive guess is that something similar to that possibly taking place at LHC and RHIC happens. Quantum critical collisions in which protons just pass by each other could yield dark pseudo-scalar mesons.
  2. If quantum criticality corresponds to peripheral collisions, the rate for pseudo-scalar production would be large unlike for central collisions. The instanton action determined to a high degree by anomaly considerations would be determined the rate of production for pseudo-scalar mesons. Vector boson dominance would allow to estimate the rate for the production of vector bosons. Peripherality could make the observation of these collisions difficult: especially so if the peripheral collisions are rejected because they are not expected to involve strong interactions and be therefore uninteresting. This might explain the disappearance of 750 GeV bump.
  3. Suppose that quantum criticality for peripheral collisions at LHC and RHIC enters into game above the mass scale of M89 pion with mass about 65 mp≈ 65 GeV and leads to creation of M89 mesons. By a simple scaling argument the same would happen in the case of MG,79 hadron physics above 65 mp(89)= 3.3 × 104 TeV to be compared with the collision energy of ultrahigh energy cosmic rays about 13× 104 TeV.
See the article M89 Hadron Physics and Quantum Criticality or the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic Physics".



Critizing the view about elementary particles

The concrete model for elementary particles has developed gradually during years and is by no means final. In the recent model elementary particle corresponds to a pair of wormhole contacts and monopole flux runs between the throats of of the two contacts at the two space-time sheets and through the contacts between space-time sheets.

The first criticism relates to twistor lift of TGD. In the case of Kähler action the wormhole contacts correspond to deformations for pieces of CP2 type vacuum extremals for which the 1-D M4 projection is light-like random curve. Twistor lift adds to Kähler action a volume term proportional to cosmological constant and forces the vacuum extremal to be a minimal surface carrying non-vanishing light-like momentum (this is of course very natural): one could call this surface CP2 extremal. This implies that M4 projection is light-like geodesic: this is physically rather natural.

Twistor lift leads to a loss of the proposed space-time correlate of massivation used also to justify p-adic thermodynamics: the average velocity for a light-like random curve is smaller than maximal signal velocity - this would be a clear classical signal for massivation. One could however conjecture that the M4 projection for the light-like boundaries of string world sheets becomes light-like geodesic of M4× CP2 instead light-like geodesic of M4 and that this serves as the correlate for the massivation in 4-D sense.

Second criticism is that I have not considered in detail what the monopole flux hypothesis really means at the level of detail. Since the monopole flux is due to the CP2 topology, there must be a closed 2-surface which carries this flux. This implies that the flux tube cannot have boundaries at larger space-time surface but one has just the flux tube which closed cross section obtained as a deformation of a cosmic string like object X2× Y2, where X2 is minimal surface in M4 and Y2 a complex surface of CP2 characterized by genus. Deformation would have 4-D M4 projection instead of 2-D string world sheet.

Note: One can also consider objects for which the flux is not monopole flux: in this case one would have deformations of surfaces of type X2× S2, S2 homologically trivial geodesic sphere: these are non-vacuum extremals for the twistor lift of Kähler action (volume term). The net magnetic flux would vanish - as a matter fact, the induced Kähler form would vanish identically for the simplest situation. These objects might serve as correlates for gravitons since the induced metric is the only field degree of freedom. One could also have non-vanishing fluxes for flux tubes with disk-like cross section.

If this is the case, the elementary particles would be much simpler than I have though hitherto.

  1. Elementary particles would be simply closed flux tubes which look like very long flattened squares. Short sides with length of order CP2 radius would be identifiable as pieces of deformed CP2 type extremals having Euclidian signature of the induced metric. Long sides would be deformed cosmic strings with Minkowskian signature with apparent ends, which are light-like 3-surfaces at which the induced 4-metric is degenerate. Both Minkowskian and Euclidian regions of closed flux tubes would be accompanied by fermionic strings. These objects would topologically condense at larger space-time sheets with wormhole contacts that do not carry monopole flux: touching the larger space-time surface but not sticking to it.
  2. One could understand why the genus for all wormhole throats must be the same for the simplest states as the TGD explanation of family replication phenomenon demands. Of course, the change of the topology along string like object cannot be excluded but very probably corresponds to an unstable higher mass excitation.
  3. The basic particle reactions would include re-connections of closed string like objects and their reversals. The replication of 3-surfaces would remain a new element brought by TGD. The basic processes at fermionic level would be reconnections of closed fermionic strings. The new element would be the presence of Euclidian regions allowing to talk about effective boundaries of strings as boundaries between the Minkowskian or Euclidian regions. This would simplify enormously the description of particle reactions by bringing in description topologically highly analogous to that provided by closed strings.
  4. The original picture need not of course be wrong: it is only slightly more complex than the above proposal. One would have two space-time sheets connected by a pair of wormhole contacts between, which most of the magnetic flux would flow like in flux tube. The flux from the throat could emerges more or less spherically but eventually end up to the second wormhole throat. The sheets would be connected along their boundaries so that 3-space would be connected. The absence of boundary terms in the action implies this. The monopole fluxes would sum up to a vanishing flux at the boundary, where gluing of the sheets of the covering takes place.
There is a further question to be answered. Are the fermionic strings closed or not? Fermionic strings have certainly the Minkowskian portions ending at the light-like partonic orbits at Minkowskian-Euclidian boundaries. But do the fermionic strings have also Euclidian portions so that the signature of particle would be 2+2 kinks of a closed fermionic string? If strong for of holography is true in both Euclidian and Minkowskian regions, this is highly suggestive option.

If only Minkowskian portions are present, particles could be seen as pairs of open fermionic strings and the counterparts of open string vertices would be possible besides reconnection of closed strings. For this option one can also consider single fermionic open strings connecting wormhole contacts: now possible flux tube would not carry monopole flux.

For background see Massless states and particle massivation .



Toponium at 30.4 GeV?

Prof. Matt Strassler tells about a gem found from old data files of ALEPH experiment by Arno Heisner. The 3-sigma bump appears at 30.40 GeV and could be a statistical fluctuation and probably is so. It has been found to decay to muon pairs and b-quark pairs. The particle that Strassler christens V (V for vector) would have spin 1.

Years ago I commented a candidate for scaled down top quark reported by Aleph: this had mass around 55 GeV and the proposal was that it corresponds to p-adically scaled up b quark with estimated mass of 52.3 GeV.

Could TGD allow to identify V as a scaled up variant of some spin 1 meson?

  1. p-adic length scale hypothesis states that particle mass scales correspond to certain primes p≈ 2k, k>0 integer. Prime values of k are of special interest. Ordinary hadronic space-time sheets would correspond to hadronic space-time sheets labelled by Mersenne prime p=M107=2107-1 and quarks would be labelled by corresponding integers k.
  2. For low mass mesons the contribution from color magnetic flux tubes to mass dominates whereas for higher mass mesons consisting of heavy quarks heavy quark contribution is dominant. This suggests that the large mass of V must result by an upwards scaling of some light quark mass or downwards scaling of top quark mass by a power of square root of 2.
  3. The mass of b quark is around 4.2-4.6 GeV and Upsilon meson has mass about 9.5 GeV so that at most about 1.4 GeV from total mass would correspond to the non-perturbative color contribution partially from the magnetic body. Top quark mass is about 172.4 GeV and p-adic mass calculations suggest k=94 (M89) for top. If the masses for heavy quark mesons are additive as the example of Upsilon suggests, the non-existing top pair vector meson - toponium - would have mass about m= 2× 172.4 GeV =344.8 GeV.
  4. Could the observed bump correspond to p-adically scaled down version of toponium with k= 94+7=101, which is prime? The mass of toponium would be 30.47 GeV, which is consistent with the mass of the bump. If this picture is correct, V would be premature toponium able to exist for prime k=101. Its decays to b quark pair are consistent with this.
  5. Tommaso Dorigo argues that the signal is spurious since the produced muons tend to be parallel to b quarks in cm system of Z0. Matt Strassler identifies the production mechanism as a direct decay of Z0 and in this case Tommaso would be right: the direct 3-particle decay of Z0→ b+bbar+V would produce different angular distribution for V. One cannot of course exclude the possibility that the interpretation of Tommaso is that muon pairs are from decays of V in its own rest frame in which case they certainly cannot be parallel to b quarks. So elementary mistake from a professional particle physicist looks rather implausible. The challenge of the experiments was indeed to distinguish the muon pairs from muons resulting from b quarks decaying semileptonically and being highly parallel to b quarks.

    A further objection of Tommaso is that the gluons should have roughly opposite momenta and fusion seems highly implausible classically since the gluons tend to be emitted in opposite directions. Quantally the argument does not look so lethal if one thinks in terms of plane waves rather than wave packets. Also fermion exchange is involved so that the fusion is not local process.

  6. How the bump appearing in Z0→ b+bbar+V would be produced if toponium is in question? The mechanism would be essentially the same as in the production of Ψ/J meson by a c+cbar pair. The lowest order diagram would correspond to gluon fusion. Both b and bbar emit gluon and these could annihilate to a top pair and these would form the bound state. Do virtual t and tbar have ordinary masses 172 GeV or scaled down masses of about 15 GeV? The checking which option is correct would require numerical calculation and a model for the fusion of the pair to toponium.

    That the momenta of muons are parallel to those of b and bbar could be indeed understood. One can approximate gluons with energy about 15 GeV as a brehmstrahlung almost parallel/antiparallel to the direction of b/bbar both having energy about 45 GeV in the cm system of Z0. In cm they would combine to V with helicity in direction of axis nearly parallel to the direction defined by the opposite momenta of b and bbar. The V with spin 1 would decay to a muon pair with helicities in the direction of this axis, and since relativistic muons are in question, the momenta would by helicity conservation tend to be in the direction of this axis as observed.

Are there other indications for scaled variants of quarks?
  1. Tony Smith has talked about indications for several mass peaks for top quark. I have discussed this here in terms of p-adic length scale hypothesis. There is evidence for a sharp peak in the mass distribution of the top quark in 140-150 GeV range). There is also a peak slightly below 120 GeV, which could correspond to a p-adically scaled down variant t quark with k=93 having mass 121.6 GeV for (Ye=0, Yt=1). There is also a small peak also around 265 GeV which could relate to m(t(95))=243.2 GeV. Therefore top could appear at least at p-adic scales k=93, 94, 95. This argument does not explain the peak in 140-150 GeV range rather near to top quark mass.
  2. What about Aleph anomaly? The value of k(b) somewhat uncertain. k(b)=103 is one possible value. I have considered the explanation of Aleph anomaly in terms of k=96 variant of b quark. The mass scaling would be by factor of 27/2, which would assign to mass mb=4.6 GeV mass of about 52 GeV to be compared with 55 GeV.
To sum up, the objections of Tommasso Dorigo might well kill the toponium proposal and the bump is probably a statistical fluctuation. It is however amazing that its mass comes out correctly from p-adic length scale hypothesis which does not allow fitting.

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



Still about induced spinor fields and TGD counterpart for Higgs

The understanding of the modified Dirac equation and of the possible classical counterpart of Higgs field in TGD framework is not completely satisfactory. The emergence of twistor lift of Kähler action inspired a fresh approach to the problem and it turned out that a very nice understanding of the situation emerges.

More precise formulation of the Dirac equation for the induced spinor fields is the first challenge. The well-definedness of em charge has turned out to be very powerful guideline in the understanding of the details of fermionic dynamics. Although induced spinor fields have also a part assignable space-time interior, the spinor modes at string world sheets determine the fermionic dynamics in accordance with strong form of holography (SH).

The well-definedness of em charged is guaranteed if induced spinors are associated with 2-D string world sheets with vanishing classical W boson fields. It turned out that an alternative manner to satisfy the condition is to assume that induced spinors at the boundaries of string world sheets are neutrino-like and that these string world sheets carry only classical W fields. Dirac action contains 4-D interior term and 2-D term assignable to string world sheets. Strong form of holography (SH) allows to interpret 4-D spinor modes as continuations of those assignable to string world sheets so that spinors at 2-D string world sheets determine quantum dynamics.

Twistor lift combined with this picture allows to formulate the Dirac action in more detail. Well-definedness of em charge implies that charged particles are associated with string world sheets assignable to the magnetic flux tubes assignable to homologically non-trivial geodesic sphere and neutrinos with those associated with homologically trivial geodesic sphere. This explains why neutrinos are so light and why dark energy density corresponds to neutrino mass scale, and provides also a new insight about color confinement.

A further important result is that the formalism works only for imbedding space dimension D=8. This is due the fact that the number of vector components is the same as the number of spinor components of fixed chirality for D=8 and corresponds directly to the octonionic triality.

p-Adic thermodynamics predicts elementary particle masses in excellent accuracy without Higgs vacuum expectation: the problem is to understand fermionic Higgs couplings. The observation that CP2 part of the modified gamma matrices gives rise to a term mixing M4 chiralities contain derivative allows to understand the mass-proportionality of the Higgs-fermion couplings at QFT limit.

See the chapter Higgs or something else?.



Misbehaving b-quarks and the magnetic body of proton

Science News tells about misbehaving bottom quarks (see also the ICHEP talk). Or perhaps one should talk about misbehaving b-hadrons - hadrons containing b- quarks. The mis-behavior appears in proton-proton collisions at LHC. This is not the only anomaly associated with proton. The spin of proton is still poorly understood and proton charge radius if quite not what it should be. Now we learn that there are more b-containing hadrons (b-hadrons) in the directions deviating considerably from the direction of proton beam: discrepancy factor is of order two.

How this could reflect the structure of proton? Color magnetic flux tubes are the new TGD based element in the model or proton: could they help? I assign to proton color magnetic flux tubes with size scale much larger than proton size - something like electron Compton length: most of the mass of proton is color magnetic energy associated with these tubes and they define the non-perturbative aspect of hadron physics in TGD framework. For instance, constituent quarks would be valence quarks plus their color flux tubes. Current quarks just the quarks whose masses give rather small contribution to proton mass.

What happens when two protons collide? In cm system the dipolar flux tubes get contracted in the direction of motion by Lorentz contraction. Suppose b-hadrons tend to leave proton along the color magnetic flux tubes (also ordinary em flux tubes could be in question). Lorentz contraction of flux tubes means that they tend to leave in directions orthogonal to the collision axis. Could this explain the misbehavior of b-hadrons?

But why only b-hadrons or some fraction of them should behave in this manner? Why not also lighter hadrons containing c and s? Could this relate to the much smaller size of b-quark defined by its Compton length λ= hbar/m(b) , m(b) = 4.2 GeV, which is much shorter than the Compton length of u-quark (the mass of constituent u quark is something like 300 MeV and the mass of current u quark is few MeVs. Could it be that lighter hadrons do not leave proton along flux tubes? Why? Are these hadrons or corresponding quarks too large to fit (topologically condense) inside protonic flux tube? b-quark is much more massive and has considerably smaller size than say c-quark with mass m(c) = 1.5 GeV and could be able to topologically condense inside the protonic flux tube. c quark should be too large, which suggests that the radius of flux tubes is larger than proton Compton length. This picture conforms with the view of perturbative QCD in which the primary processes take place at parton level. The hadronization would occur in longer time scale and generate the magnetic bodies of outgoing hadrons. The alternative idea that also the color magnetic body of hadron should fit inside the protonic color flux tube is not consistent with this view.

For details see the the chapter New Physics predicted by TGD: part II .



Is the new physics really so elementary as believed?

I think that that many colleagues have been thinking about the situation in particle physics. Is it really true that the "nightmare scenario" is realized: no deviations from the standard model? The basic disappointment of course comes from the fate 750 GeV Cernette, which does not exist anymore officially. I am also personally puzzled. Various bumps about which Lubos have kept count fit nicely to the spectrum of mesons of M89 hadron physics (almost)-predicted by TGD (see this, this, this, and this) . They have precisely the predicted masses differing by a factor 512 from those of M107 hadron physics, the good old hadron physics. Is it really possible that Universe has made a conspiracy to create so many statistical fluctuations just to the correct places? Could it be that something is wrong in the basic philosophy of experimental particle physics, which leads to the loss of information?

First of all, it is clear that new physics is badly needed to solve various theoretical problems such as fine tuning problem for Higgs mass to say nothing about the problem of understanding particle mass scales. New physics is necessary but it is not found. What goes wrong? Could it be that we are trying to discover wrong type of new physics?

Particle physics is thought to be about elementary objects. There would be no complications like those appearing in condensed matter physics: criticality or even quantum criticality, exotic quasiparticles, ... This simplifies the situation enormously but still one is dealing with a gigantic complexity. The calculation of scattering rates is technically extremely demanding but basically application of well-defined algorithms; Monte Carlo modelling of the actual scattering experiments such as high energy proton-proton collisions is also needed. One must also extract the signal from a gigantic background. These are extremely difficult challenges and LHC is a marvellous achievement of collaboration and coherence: like string quartet but with 10,000 players.

What one does is however not to just look what is there. There is no label in the particle telling "I am the exotic particle X that you are searching for". What one can do is to check whether the small effects - signatures - caused by a given particle candidate can be distinguished from the background noise. Finding a needle in haystack is child's play when compared with what one must achieve. If some totally new physics not fitting into the basic paradigms behind search algorithms is there, it is probably lost.

Returning to the puzzle under consideration: the alarming fact is that the colliding protons at LHC form a many-particle system! Could it happen that the situation is even more complex than believed and that phenomena like emergence and criticality encountered in condensed matter physics could be present and make life even more difficult?

As a matter of fact, already the phase transition from confined phase to perturbative QCD involving thermodynamical criticality would be example of this complexity. The surprise from RHIC and later LHC was that something indeed happened but was different than expected. The transition did not seem to take place to perturbative QCD predicting thermal "forgetfulness" and isotropic particle distributions from QCD plasma as black body radiation. For peripheral collisions - colliding particles just touching - indications for string like objects emerged. The notion of color glass was introduced and even AdS/CFT was tried (strings in 10-D space-time!) but without considerable success. As if a new kind of hadron physics with long range correlation in proton scale but with energy scale of hundreds of proton masses would have been present. This is mysterious since Compton lengths for this kind of objects should be of order weak boson Compton length.

In TGD Universe this new phase would be M89 hadron physics with large value heff =n×h, with n =512 to scale up M89 hadron Compton length to proton size scale to give long range correlations and fluctuation in proton scale characterizig quantum criticality. Instanton density I ∝ E• B for colliding protons would appear as a state variable analogous to say pressure in condensed matter and would be large just for the peripheral collisions. The production amplitude for pseucoscalar mesons of new hadron physics would by anomaly arguments be obtained as Fourier transform of I. The value of I would be essentially zero for head-on collisions and large only for peripheral collisions - particles just touching - in regions where E and B tend to be parallel. This would mean criticality. There could be similar criticality with respect to energy. If experimenter poses kinematical cutoffs - say pays attention only to collisions not too peripheral - the signal would be lost.

This would not be new. Already at seventies anomalous production of electron-positron pairs perhaps resulting from pseudoscalar state created near collision energy allowing to overcome Coulomb wall where reported: criticality again. The TGD model was in terms of leptopions (electro-pions) (see this) and later evidence for their muonic and tau counterparts have been reported. The model had of course a bad problem: the mass of leptopion is essentially twice that of lepton and one expects that colored lepton is also light. Weak boson decay widths do not allow this. If the leptopions are dark in TGD sense, the problem disappears. These exotic bumps where later forgotten: a good reason for this is that they are not allowed by the basic paradigms of particle physics and if they appear only at criticality they are bound to experience the fate of being labelled as statistical fluctuations.

This has served as an introduction to a heretic question: Could it be that LHC did not detect 750 GeV bosons because the kinematical cuts of the analysis eliminate the peripheral collisions for which protons just touch each other? Could these candidates for pseudo-scalars of M89 hadron physics be created by the instanton anomaly mechanism and only in periphery? And more generally, should particle physicists consider the possibility that they are not anymore studying collisions of simple elementary systems?

To find M89 pseudoscalars one should study peripheral collisions in which protons do not collide quite head-on and in which M89 pseudoscalars could be generated by em instanton mechanism. In peripheral situation it is easy to measure the energy emitted as particles since strong interactions are effectively absent - only the E•B interaction plus standard em interaction if TGD view is right (note that for neutral vector mesons the generalization of vector meson dominance based on effective action coupling neutral vector boson linearly to em gauge potential is highly suggestive). Unfortunately, peripheral collisions are undesired since beams are deflected from head-on course! These events are however detected but data end up to trash bin usually as also deflected protons!! Luckily, Risto Orava's team (see this and this) is studying just those p-p collisions, which are peripheral! It would be wonderful if they would find Cernettes and maybe also other M89 pseudo-scalars from the trashbin!

Large statistical fluctuation certainly occurred. The interpretation for the large statistical fluctuation giving rise to Cernette boom could be as the occurrence of un-usually large portion of peripheral events allowing the production of M89 mesons, in particular Cernettes.

To sum up, the deep irony is that particle physicists are trying desperately to find new physics although it has been found long ago but put under the rug since it did not conform with QCD and standard model. The reductionistic dogma dictates that the acceptable new physics must be consistent with the standard model: no wonder that everything indeed continues to be miraculously consistent with standard model and no new physics is found! Same is true in gravitational sector: reductionism demands that string model leads to GRT and the various anomalies challenging GRT are simply forgotten.

For details see the earlier blog post, the chapter New Physics predicted by TGD: part I or the article M89 hadron physics and quantum criticality.



Nothing new at LHC?

Lubos Motl has a commentary about articles released after ICHEP 2016 conference held in Chicago. Experimentalists tell "Nothing going beyond standard model". Depressing! Especially so because theorists have "known" that the New Physics must be there!

What looks strange from TGD point of view that alarge number of mesons of M89 =289-1 hadron physics predicted by TGD - scaled up variants of mesons of ordinary hadron physics (to which I assign Mersenne prime M107 =2107-1) appeared in the older data at lower energies as bumps with the predicted masses (see this.

Is there a nasty cosmic conspiracy to ridicule me;-) . Or are the produced mesons - at least the light ones indeed M89 mesons with large heff=n× h - as assumed in the model for the string like objects observed already at RHIC and later at LHC - and produced only at quantum criticality, which would be lost at higher energies. Of course not a single, experimentalist or theorist would take this seriously! Could this explanation apply to 750 GeV bump as I thought so first? No! This bump was announced in December 2015 on basis of the first analysis of data gathered since May 15 2015 (see this). Thus the diphoton bump that I identified as M89 eta meson is lost if one takes the results of analysics as final word.

One should of course give up so easily. If the production mechanism is same as for electro-pion (see this), the production amplitude is by anomaly considerations proportional to the Fourier transform of the classical "instanton density" I= E• B. In head-on collisions one tends to have I=0 because E (nearly radial in cylindrical coordinates) and B (field lines rotating around z-axis) for given proton are orthogonal and differ only apart from sign factors when the protons are in same position. For peripheral collisions in which also strange looking production of string like configurations parallel to beams was observed in both heavy ion and proton-proton collisions, E1• B2 can be vanishing as one can understand by figuring out what the electric and magnetic fields lookl ike in the cm coordinates. There is clearly a kind of quantum criticality involved also in this sense. Could these events be lost by posing reasonable looking constraints on the production mechanism or kinematical cutoff? But why the first analysis would have shown the presence of these events? Have some criteria changed?

To find M89 pseudoscalars one should study peripheral collisions in which protons do not collide quite head-on and in which M89 pseudoscalars could be generated by em instanton mechanism. In peripheral situation it is easy to measure the energy emitted as particles since strong interactions are effectively absent - only the E•B interaction plus standard em interaction if TGD view is right. Unfortunately peripheral collisions are undesired since beams are deflected from head-on course! These events are however detected but data end up to trash bin usually as also deflected protons!! Luckily, Risto Orava's team (see this and this) is studying just those p-p collisions, which are peripheral! It would be wonderful if they would find Cernettes and maybe also other M89 pseudo-scalars from the trashbin!

For details see the chapter New Physics predicted by TGD: part I or the article M89 hadron physics and quantum criticality.



CKM mixing and CP breaking in leptonic sector?

Cabibbo-Kobayashi-Maskawa (CKM) matrix is 3× 3 unitary matrix describing the mixing of D type quarks in the couplings of W bosons to a pair of U and D type quarks. For 3 quarks it can involve phase factors implying CP breaking. The origin of the CKM matrix is a mystery in standard model.

In TGD framework CKM mixing is induced by the mixing of the topologies of 2-D partonic surfaces characterized by genus g=0,1,2 (the number handles added to sphere to obtain topology of partonic 2-surface) assignable to quarks and also leptons (see this and this). The first three genera are special since they allow a global conformal symmetry always whereas higher genera allow it only for special values of conformal moduli. This suggests that handles behave like free particles in many particle state that for higher genera and for three lowest genera the analog of bound state is in question.

The mixing is in general different for different charge states of quark or lepton so that for quarks the unitary mixing matrices for U and type quarks - call them simply U and D - are different. Same applies in leptonic sector. CKM mixing matrix is determined by the topological mixing being of form CKM=UD for quarks and of similar form for charged leptons and neutrinos.

The usual time-dependent neutrino mixing would correspond to the topological mixing. The time constancy assumed for CKM matrix for quarks must be consistent with the time dependence of U and D. Therefore one should have U= U1X(t) and D= D1X(t), where U1 and D1 are time independent unitary matrices.

In the adelic approach to TGD (see this and this) fusing real and various p-adic physics (correlates for cognition) would have elements in some algebraic extension of rationals inducing extensions of various p-adic number fields. The number theoretical universality of U1 and D1 matrices is very powerful constraint. U1 and D1 would be expressible in terms of roots of unity and e (ep is ordinary p-adic number so that p-adic extension is finite-dimensional) and would not allow exponential representation. These matrices would be constant for given algebraic extension of rationals.

It must be emphasized that the model for quark mixing developed for about 2 decades ago treats quarks as constituent quarks with rather larger masses determining hadron mass (constituent quark is identified as current valence quark plus its color magnetic body carrying most of the mass). The number theoretic assumptions about the mixing matrices are not consistent with the recent view: instead of roots of unity trigonometric functions reducing to rational numbers (Pythagorean triangles) were taken as the number theoretic ideal.

X(t) would be a matrix with real number/p-adic valued coefficients and in p-adic context it would be an imaginary exponential exp(itH) of a Hermitian generator H with the p-adic norm t < 1 to guarantee the existence of the p-adic exponential. CKM would be time independent for XU=XD. TGD view about what happens in state function reduction (see this, this, and this) implies that the time parameter t in time evolution operator is discretized and this would allow also X(tn) to belong to the algebraic extension.

For quarks XU= XD=Id is consistent with what is known experimentally: of course, the time dependent topological mixing of U or D type quarks would be seen in the behavior of proton. One also expects that the time dependent mixing is very small for charged leptons whereas the non-triviality of Xν(t) is suggested by neutrino mixing. Therefore the assumption XL=Xν is not consistent with the experimental facts and XL(t)=Id seems to be true a good approximation so that only Xν(t) would be non-trivial? Could the vanishing em charge of neutrinos and/or the vanishing weak couplings of right-handed neutrinos have something to do with this? If the μ-e anomaly in the decays of Higgs persists ( this), it could be seen as a direct evidence for CKM mixing in leptonic sector.

CP breaking is also possible. As a matter fact, one day after mentioning the CP breaking in leptonic sector I learned about indications for leptonic CP breaking emerging from T2K experiment performed in Japan: the rate for the muon-to-electron neutrino conversions is found to be higher than that for antineutrinos. Also the NOvA experiment in USA reports similar results. The statistical significance of the findings is rather low and the findings might suffer the usual fate. The topological breaking of CP symmetry would in turn induce the CP breaking the CKM matrix in both leptonic and quark sectors. Amusingly, it has never occurred to me whether topological mixing could provide the first principle explanation for CP breaking!

For background see the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic physics" and the article Some comments about  τ-μ anomaly of Higgs decays and anomalies of B meson decays.



CMS provides evidence for two new spin 2 mesons of M89 hadron physics

I summarized few days ago the recent evidence for M89 hadron physics (see this. Today Lubos told about very interesting new bumps reported by CMS in ZZ channel. There is 3-4 sigma evidence in favor of a 650 GeV boson. Lubos suggests an interpretation as bulk graviton of Randall-Sundrum model. Lubos mentions also evidence for a boson of gamma-gamma resonance with mass 975 GeV.

M89 hadron physics explains the masses for a variety of bumps observed hitherto. The first guess therefore that mesons of M89 hadron physics are in question. By performing the now boringly familiar scaling down of masses by factor 1/512 for the masses one obtains the masses of corresponding mesons of ordinary hadron physics: one obtains 1270 MeV and 1904 MeV corresponding to 650 GeV and 975 GeV. Do ordinary mesons with these masses exist?

To see that this is the case, one can go to the table of exotic mesons . There indeed is exotic graviton like meson f2++(1270). Complete success! There is also exotic meson f2++(1910): the mass differs from the predicted 1904 MeV by .15 per cent. Graviton like states understandable as tetraquark states not allowed by the original quark model would be in question. The interested reader can scale up the masses of other exotic mesons identifiable as candidates for tetraquarks to produce predictions for new bumps to be detected at LHC.

Both states have spin 2 as also Randall-Sundrum bulk gravitons. What distinguishes the explanations that TGD predicts the masses of these states with an excellent accuracy and predicts a lot of more: just take the table of mesons and multiply by 512 and you can tell your grand children that you predicted entire spectroscopy correctly!

In TGD framework these states are indeed possible. All elementary particles and also meson like states correspond to pairs of wormhole contacts. There is closed monopole flux tube with the shape of highly flattened square with long sides of the order of Compton length in question and short sides of the order of CP2 size. The wormhole throats of both wormhole contact carry quark and antiquark and and one can see the structure either as a pair of gauge boson like states associated with the contacts or as a pair of mesonlike states at the two space-time sheets involved.

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



Evidence for M89 ρ or ω

Evidence for M89 hadron physics is accumulating rapidly. I am grateful for Lubos for keeping book about the bumps: this helps enormously. In the latest posting I told about evidence for Z' a la TGD and indications for M89 J/Psi, which is vector meson. Now Lubos tells about excess, which could have interpretation as the lightest M89 vector meson - ρ89 or ω89. Mass is the predicted correctly with 5 per cent accuracy by the familiar p-adic scaling argument: multiply the mass of ordinary meson with 512.

Physics is sometimes simple but this does not mean that is numerology - as simple minded colleague, who prefers ultraheavy numerics instead of imaginative thinking, might argue: deep principles distilled through a work of 38 years are behind this simple rule.

This 375 GeV excess might indeed represent the lightest vector meson of M89 hadron physics. ρ and ω of standard hadron physics have mass 775 MeV and the scaled up mass is about 397 GeV, which is about 5 per cent heavier than the mass of Zgamma excess.

The decay ρ→ Z+γ describable at quark level via quark exchange diagram involving emission of Z and γ. The effective action would be proportional to Tr(ρ*γ*Z), where the product and trace are for antisymmetric field tensors. This kind effective action should describe also the decay to gamma pair. By angular momentum conservation the photons of gamma pairs should be in relative L=1 state. Since Z is relativistic, L=1 is expected to be favored also for Z+γ final state. Professional could immediately tell whether this is correct view. Similar argument applies to the decay of ω which is isospin singlet. For charged ρ also decays to Wγ and WZ are possible. Note that the next lightest vector meson would be K* with mass 892 MeV. K89 should have mass 457 GeV.

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



Direct evidence for Z' a la TGD and M89 J/Psi

The bumps indicating the presence of new physics predicted by TGD have begun to accumulate rapidly and personally I dare to regard the situation as settled: individual bumps do not matter but when an entire zoo of bumps with predicted masses emerges, the situation changes (see this, this and this). Colleagues (especially the finnish ones) will encounter quite a demanding challenge in explaining how it is possible that I am still forced visit in bread quee in order to cope with the basic metabolic needs;-).

Lubos told that there is direct evidence for Z' boson now: earlier the evidence was only indirect: breaking of universality and anomaly in angle distribution in B meson decays. Z' bump has mass around 3 TeV. TGD predicts 2.94 TeV mass for second generation Z breaking universality. The decay width by direct scaling would be .08 TeV and is is larger than deviation .06 TeV from 3 TeV. Lubos reported half year ago about excess at 2.9 GeV which is also consistent with TGD prediction.

Lubos tells also about 3 sigma bump at 1.650 TeV assigned to Kaluza-Klein graviton in the search for Higgs pairs hh decaying to bbbar+ bbbar. Kaluza-Klein gravitons are rather exotic creatures and in absence of any other support for superstring model they are not the first candidate coming into my mind. I do not know how strong the evidence for spin 2 is but I dare to consider the possibility of spin 1 and ask whether M89 hadronic physics could allow an identification for this bump.

  1. Very naively scaled up J/Psi of M107 hadron physics having spin J=1 and mass equal to 3.1 GeV would have mass 1.585 TeV: error is about 4 per cent. The effective action would be based on gradient coupling similar in form to Zhh coupling. The decays via hh → bbbar+bbbar could take place also now.
  2. This scaling might be too naive: the quarks of M89 might be same as those of ordinary hadron physics and only the color magnetic energy would be scaled up by factor 512. c quark mass is equal 1.29 GeV so that the magnetic energy of ordinary J/Psi would be equal to .52 GeV. If so, M89 version of J/Psi would have mass of only 269 GeV. Lubos tells also about evidence for a 2 sigma bump at 280 GeV identified as CP odd Higgs - this identification of course reflects the dream of Lubos about standard SUSY at LHC energies. However, the scaling of eta meson mass 547.8 MeV by 512 gives 280.4 GeV so that the interpretation as eta meson proposed already earlier is convincing. The naive scaling might be the correct thing to do also for mesons containing heavier quarks.
In any case, even if one forgets J/Psi, there is now direct evidence for as many as 3 new branches of physics predicted by TGD! Two scaled variants of hadron physics (M89 and MG,79) and second generation weak physics (MG,79)!

Colleagues have realized that history is in making. I read from popular article that theoreticians left their ongoing projects and have started to study 750 GeV bump and certainly also other bumps. Ellis talked already about entire new physics. TGD message has gone through! But no one mentions TGD although all is published in Huping Hu's journals and in Research Gate! No need for this in the recent science community based on ethics of brutal opportunism: steal, lie, betray as hippies expressed it.

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



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