LHC Heavy Ion Collisions

In about a weeks time the Large Hadron Collider will stop proton-proton physics for this year and the physicists working on ATLAS, CMS and LHCb will work hard on their 50/pb of data to try to figure out if supersymmetry exists in nature. Meanwhile the LHC will continue running for another month colliding lead ions instead of protons. The main experiment designed to take advantage of these heavy-ion collisions is ALICE, but ATLAS and CMS will also take a look.

One of the exciting features of the Heavy-Ion collisions will be the total amount of energy in each collision. I don’t know how high they will actually get in this first series of runs but the target seems to be about 2.7 TeV per nucleon. Lead nuclei have 207 nucleons so the total centre of mass-energy could be as high as 1100 TeV. That is enough energy to create a million protons. The LHC is about to become the worlds first Petatron collider. (Edit: actually it will be half this energy for this year with full energy in 2013, see comments)

Sadly this does not mean they will be exploring the particle spectrum at such high energies. When heavy ions collide it is more like lots of small collisions between the quarks and gluons in the nuclei so the energy does not get concentrated into the production of any single heavy particles. Instead you can get lots of lighter particles that can form a very hot plasma ball. The interactions involved are dominated by QCD so this experiment is mostly a study of QCD phenomena.

If you want an idea of what such a collision will look like have a look at what has been seen at the RHIC collider. Here is a typical example with thousands of particles produced. The RHIC uses energies of 500 GeV per nucleon so we can expect something like 5 times as many particles at the LHC.

The aim of these experiments is to find out something about the phase diagram of QCD. According to various theories it probably looks like this

All the stuff to the bottom right is what happens in neutron stars at very high densities of matter. There is not much possibility of recreating such conditions in any experiment because they only way to produce the densities required are by using the enormous pressures due to gravity that occur inside neutron stars.We will have to rely on astronomical observations to probe those regions of the phase diagram. RHIC and the LHC are better suited to looking at the top left where the enourmous collision energies produce a plasma at very high temperature.

The hadronic matter phase is what we are used to at low temperature and at most nuclear density. Here the quarks are confined inside hadrons and mesons. At higher temperatures and densities theory predicts that the quarks will enter a deconfined phase where hadrons do not form. Instead the quarks and gluons just form a liquid-like plasma where they can flow around freely. You can cross from the hadronic phase to the quark gluon plasma over a first order phase transition (the thick red line) where the two phases mix just like gas and liquid in boiling water. However, at lower densities you can pass from one phase to another without going through the phase transition. A similar thing happens with water turning to steam at high pressure. The first order phase transition stops at a critical point and one objective of RHIC has been to try to find this point experimentally. This requires running with lower energy, not higher energy, so the LHC is not looking for the same thing.

Instead the LHC will be able to explore the crossover region where there is a smooth change from confined to deconfined matter, but there is something else in this region. Another phase transition is though to be crossed over, but it is a second order phase transition, not first order. This is the phase transition for chiral symmetry breaking.

The QCD Lagrangian has an approximate symmetry known as chrial symmetry that relates different flavours of quarks and left and right chiral states. The symmetry is broken by any quark mass but the up and down quark masses are small enough for this symmetry to be a good approximation. the symmetry is also broken by the electric charges, but this is also a relatively small effect. The spontaneous symmetry breaking leaves a residual symmetry which is isospin and it generates Goldstone bosons such as the pion. The pion would be massless if the symmetry was exact. At high temperatures the chiral symmetry is restored, so there must be a transition. lattice calculations suggest that it is around temperatures corresponding to 170 MeV.

With symmetry breaking phase transitions it is not possible to have a cross-over region if the symmetry is exact. A symmetry is either broken or not. You cant go smoothly from one phase to another. However, chiral symmetry is not exact in QCD so the phase transition will not be sharp. It is though to coincide with the deconfining phase transition up to the critical point and then continue across to the zero density axis as shown on my diagram. Actually it could separate before the critical point, we don’t know for sure.

When the LHC starts Ion-collisions at ramped energies it will be a leap ahead of where the RHIC has been looking. It has been said that it is one of the largest jumps in energy for a specific type of accelerator ever taken. The regions explored are thought to be similar to the conditions in the big bang a little after inflation stopped. It will be very interesting to see what happens.

35 Responses to LHC Heavy Ion Collisions

  1. Bill K says:

    Yes! The lead ion collisions have gotten much less publicity, but I think have much more potential for producing new physics in the short term. As you point out, ALICE represents a real leap ahead. I just hope they have allowed enough time in the schedule for it, when you consider how much time it has taken to tune the LHC for protons. Switching to lead is nontrivial, not just for the LHC but also for the PS and SPS.

    “..the target seems to be about 2.7 TeV per nucleon. Lead nuclei have 207 nucleons so the total centre of mass-energy could be as high as 1100 TeV.”

    That’s with full current in the magnets, which no longer applies. Figure half of that. (And it’s lead 208, not 207!)

    Plans change, but at one time the “early ion scheme” called for 62 bunches initially.

    • Philip Gibbs says:

      You could be right about it being half that, but I have seen contradictory statements from different sources.

      It has been said that the setup for protons will actually work for the lead ions so it should not take long to get started, we shall see. They may not be going for verry high luminosity, especially since ALICE has been working with lower luminosity than the other experiments. The cross section is higher of course.

  2. Luboš Motl says:

    The graphs indicate that we won’t see much. Well, there will still be 5D black holes created, won’t they?

    • Philip Gibbs says:

      They will still be producing some QGP so it might be interesting. Not sure what the effect of the 5D black holes will be.

  3. Lawrence B. Crowell says:

    Heavy ion collisions will be a many body system with large N. So we might get some AdS/CFT stuff if there are extra large dimensions that have scales compatible with these scales. So we might indeed get a 5-dim black hole. The QCD plasma has structure that is formally identical to a black hole. The explosion of the quark-gluon plasma is a form of Hawking radiation.

  4. Wait a moment! If General Relativity is the long length scale limit of something more fundamental – be its strings or something else about which I have a slightest idea;-)- and if G is a parameter analogous to a parameter characterizing condensed matter, why are we taking black holes and Planck length so deadly seriously?

    Could it be more realistic to forget black holes for a moment and start from elementary particles and think hardly what they might be in terms of space-time geometry?

  5. Bill K says:

    The phase diagram is hypothetical. And while it’s highly interesting, it doesn’t really depict what ATLAS and RHIC are about. And if you’re looking for effects of extra dimensions, I think you’ll be disappointed too. ATLAS is about standard model, many body QCD.

    All of this is unexplored territory, and quite important, even if it’s not what a purist might consider ‘fundamental.’ It’s like embarking on the exploration of nuclear physics for the first time. For example it’s still an open question whether RHIC succeeded in producing a quark gluon plasma or something else. People talk further about color glass condensates (a saturated gluon state), bubbles of broken parity, and so on.

    • Lawrence B. Crowell says:

      The LHC heavy ion experiments appear not to give anything qualitatively different from RHIC, if we take this phenomenology at face value, but the temperature scale that is probed is larger. The signals to noise ratio should be better as a result. The signal might contain data for color glass condensates and QCD with a broken chiral phase. There are some hints of AdS physics with RHIC, which we might get a better handle on. If there is a role of extral large dimensions, say a correspondence between AdS and QCD we might get some data on this, or conversely rule it out in this domain of observation.

  6. My bet is that LHC heavy ion experiments will give more data about
    quark gluon plasma confined inside color magnetic flux tubes. Something
    rather boring as compared to black holes and other romantic stuff until on remembers that M-theorist would call these flux tubes branes.

    I am not too enthusiastic about bringing in AdS and even less about black holes at LHC. I regard this soup of branes and strings and black holes and AdS and whatever as as outcome of the fact that string theory was never really able to describe particles and 4-D classical gravity so that the whole approach reduced to a confusing mixture of old and new ideas believed to be related to each other. Old wine in new bottles. The situation in thermodynamics before Boltzmann was similar to this. A thorough conceptual turnout is badly needed.

    • Bill K says:

      Everything is black holes and AdS/CFT these days.
      “When all you have is a hammer, everything looks like a nail.”

      • Ulla says:

        Maybe neither of these, but something more gentle 🙂 The pictures already here hints at a phase with parallell magnetic field (superconductive plasma phase?)

        My guess highly qualified 😀

      • Philip Gibbs says:

        Yes, the high density phases are thought to be color superconducting, but you can’t explore those regions with lattice theories and the structure shown here is just very speculative. The observation of neutron stars with more than twice solar mass suggests we know very little about that part of the diagram.

        The high temperature scale is a bit easier to understand and you can explore it on the lattice. In fact that is what I did for my doctorate 25 years ago.

      • Ulla says:

        A superconductive phase arranges itself in a two-directional plane along a matter-antimatter plane?

        A rather surrealistic picture is also that we dont really know the proton nor the electron, but we smash them and think we should know the result.

        Does anybody know the latest exact proton mass? Can it change (Rydbergs constant?)? The electron energy can be split in FQHE too. How? It is said when it meets the boundary. Is that fermions? One explanation is that it is the wavefunction of the electron (much bigger that the electron) that decides it.

        Wavefunctions in LHC?

  7. Lawrence B. Crowell says:

    The point is we might search for signatures of this sort of physics. It could always turn out that we have hammers when in fact we should have saws.

  8. One very interesting anomaly to search for are dark matter candidates. There is a highly interesting net of internal consistency building around CDF anomaly about which there was a lot of blog talk for two years ago. Blog talkers have however rather short memory span so that a short reminder is in order. A longer reminder with links and reference list can be found at my blog.

    a) For two years ago (rather precisely) CDF collabortion reported that there are indications for the existence of new particles with masses approximately 2, 4, 8 times of tau-lepton that 3.6,7.2, 14.4 GeV and decaying in a cascade like manner and ending mostly to muons at the last step. This also suggests a composite of two particles which are tau-lepton like in many respects but something non-lepton like must bind these leptonl ike particles together.

    b) Amazingly, in the latest New Scientist there is a story about evidence for galactic dark matter candidate form Fermi gamma ray telescope with mass in the range 7-9 GeV roughly and decaying to tau-pairs mostly and producing photons in this process. Could 7.2 GeV be there again!

    c) Already earlier gamma rays with energy about electron mass were reported as galactic dark matter candidate. Bound state of electron and positron like particles decaying to gamma pair? What binds them to a pair?

    d) According to the same source the dark matter candidate of DAMA is also in the mass range 7-11 GeV. Also CoGent reports something which my dark in this mass range. This is consistent with a particle with mass of about 7.2 GeV possibly created in the collision of cosmic rays with the nuclei in atmosphere.

    e) Pamela reported earlier evidence for positron excess above about 3.6 GeV. It ould result as a decay product of 7.2 GeV particle! The unpleasant news was that there was no proton excess predicted from the annihilation of the usual dark matter candidates.

    The common explanation would be a particle with mass 7.2 GeV decaying to lepton pairs but not to quark pairs. In TGD framework this candidate has been present for two decades now. The particle would be tau-pion, a bound state of color octet excitations of tau-leptons with mass equal to that of tau-lepton or octave of it (p-adic length scale hypothesis allows them).

    For electro-pion evidence accumulated already at seventies from heavy ion collisions but since weak boson decay widths excluded the existence of new particles at these energies it was forgotten. Electro-pions would explain also orthopositronium decay rate anomaly, and could be identified as the earlier galactic dark matter candidate producing via its decays the monochromatic gamma rays with energy about one electron mass. For muo-pion evidence was reported during 2007.

    Weak boson decay widths are not a problem if these particles are dark in the sense that they consist of colored excitations of leptons which do not couple directly to the ordinary gauge bosons. You can guess that I will next start to talk about hierarchy of Planck constants but I redeem you this time.;-).

    Leptopion condensates are predicted to be created in high energy collisions of charged particles generating strong *non-orthogonal* electric and magnetic fields and the “instanton density” E.B defines the model for the production. This kind of fields are certainly created in heavy ion collisions at LHC and the anomaly which I explain in terms of electro-pion was indeed discovered in heavy ion collisions. As I already noticed, links and references can be found
    from the longer reminder my blog..

    • Ulla says:


      Two alphas? Two different worlds? One world outside SM? What IS this? By Cornell?
      How can there be two alphas, then there also must be two kinds of em-force? And a changing Planck constant, because alpha cannot change alone?

      Is this second em-force detectable at LHC?

    • Lawrence B. Crowell says:

      The masses reported were different from what you state. The PAMELA detector results were in line with neutralino masses of .1 to 1 TeV as I recall. The neutralino is a state defined by the superpartners of the photon, Z and neutral Higgs, where these all have the same quantum numbers. I think that the masses of DM particles are considerably larger than what you are quoting. A 10GeV particle is pretty easily detected, even if that detection is found in a missing momentum, similar to how neutrinos were inferred.

    • Bill K says:

      Lawrence, I don’t think they are considering neutralinos. Although PAMELA talked about greater masses, the new paper from FGST


      says, “We fi nd a particularly good fit for dark matter particles with masses in the range of 7.3-9.2 GeV annihilating to [tau lepton pairs]”

      and cites similarity with earlier results from CoGeNT and DAMA.

      • Lawrence B. Crowell says:

        Oh dang! The big question which comes to mind is why these would not have been seen in accelerator physics? Clearly if they decay into tau particles they have some interaction with luminous matter and I would expect there to be some CDF data on missing momentum for certain events that do not fit neutrino data.

        I suspect as Philip says that this is probably a misinterpretation of data. Something about this does not smell right.

    • Philip Gibbs says:

      The new dark matter claim is very controversial. It is near the limits of Fermi observation and might be explained by other events such as supernovae. Some of the approximations used have also been questioned.

      Such a light dark matter candidate does seem unlikely because you would think that it would have been seen. It would have to interact very weakly with normal matter not to have been created in accelerators and seen as missing mass, but that is not an impossibility.

  9. To Lawrence:

    It is quite possible that leptopions (e-. mu-, tau-) have been detected in accelerator physics but forgotten because they are not allowed by standard model. Look at reference list at my blog. CDF anomaly was just about the decay cascade leading to mostly muons analogous to a decay of 14.4 GeV taupion to two 7.2 to two 3.6 GeV taupion with mass just above two tau mass so that the decay to tau pairs was strongly inhibited by the lack of phase space and muons dominated in the final state.

    The production amplitude for leptopions is essentially the Fourier transform for the instanton term defined by the inner product of E and B and production characteristics are very different from those for usual particle production: electropions were produces almost at rest in cm system. One must know what one is searching for and even more so in LHC.

    By looking at graph of paper you find that positron excess begins around 3.6 GeV. The production of positron pairs is from decays of tau-pions rather than annihilations of dark particles. Decay rate involves one unknown parameter which characterizes the phase transition changing Planck constant and having interpretation as leakage between sectors of imbedding space with different values of hbar. It is analogous to non-dagonal element of mass matrix for Feynman graphs.

    I of course agree with Phil that new dark matter (it it is dark matter at all!) claims are controversial. What makes me take them seriously is that CDF, Fermi, DAMA, Cogent, and Pamela might have interpretation in terms of tau-pions with mass of 7.2 GeV and the fact that TGD predicted already two decades ago leptopions and evidence for all leptopions have been found. Add to this galactic gamma ray anomaly at .511 MeV detected already earlier and having interpretation in terms of electro-pion decays and you must admit that there is a clear pattern. Something similar should be found at muon mass. The usual dark matter candidates are purely phenomenological guesses: in TGD framework they are basic prediction of the theory.

    Why it would be important to take this proposal seriously is that I am not talking some ad hoc particle whose properties are fitted to reproduce some experimental anomaly. I am talking about copies of entire hadron physics like physics and about new view about color since both leptons and quarks would have higher color excitations. The new view about color makes also possible separate conservation of lepton and quark numbers. GUTs predict proton decay and we have not observed it! GUTs lead to symmetry breaking scenarios where the ratio of mass scales for heaviest and lightest fermions of multiplet is about 10^12 (top/neutrino mass ratio): I would call this un-natural! In TGD p-adic mass scale becomes a new notion and family replication has topological explanations so that standard model gauge group is enough. Maybe it is time to return to the roots and challenge the ad hoc assumption made at seventies which transformed to postulates when superstring model emerged and theoreticians forgot the fundamentals and took particle physics as mere low energy limit of string theory.

    • Bill K says:

      Matti, does TGD have anything to say about neutrino oscillations?

      Yesterday’s press release from MiniBooNE gives added credence to the LSND findings — they see an excess of oscillations in the antineutrino beam. (Which as reported earlier, was not seen in the neutrino beam.)

  10. I have discussed Miniboone anomaly at my blog. Neutrinos and antineutrinos can appear in several p-adic mass scales as can also other fermions. Neutrinos and antineutrinos could appear in different p-adic mass in neutrino mixing experiments. If this happens it leads to apparent breaking of CPT and forces the introduction of sterile neutrino in standard physics approach.

  11. Ervin Goldfain says:

    CPT theorem is valid for field theories that are local and Lorentz invariant. In my opinion, the MiniBoone anomaly (if confirmed) raises a foundational issue: can Nature be described by non-local theories that preserve Lorentz invariance? If the answer is yes, then CPT symmetry can be violated in principle without breaking Lorentz invariance. This sounds paradoxical if we believe our current understanding. There may be however some deep dynamical reasons for the purported asymmetry of neutrinos and antineutrinos. Sterile neutrinos may turn out to be wishful thinking after all.

  12. Lawrence B. Crowell says:

    Ervin and Matti,

    I think the issue has little to do with fiddling around with standard quantum field theory of particles. As Ervin says the CPT discrete symmetry assumptions involves locality and Lorentz symmetry. The problem probably involves locality, or the manner by which field amplitudes are described on space. Yet this sort of construction clearly can’t apply in general. If the field amplitude is for gravitation itself, then this amplitude has a propagator which is described on the same field amplitudes. Some sort of relaxation of physical principles is required. The loss of locality appears to be the likely candidate. By relaxing locality we can prevent this sort of viscious feedback we might otherwise have.

    Of course these MiniBoone and LSND data involves weak interaction physics, not gravity. Yet is may be that gravitation is an emergent field on a boundary which has a dual structure to conformal QFT. Of course we have yet to know for certain, but I think that from 10^{-17}cm to 10^{-33} cm there is a renormalization group flow of quantum fields, so gravity may play a type of role at the unification energy where the Higgs condensate produces particles. This renormalization flow may take a low energy field to the Planck scale at high energy with a continuous flow to quantum gravity, where nonlocality of field amplitudes likely holds. So there may be a loss of locality at the 10^{-17}cm scale which perturbs physics in a way which is unexpected.

  13. ervin goldfain says:


    You are right to say that “Some sort of relaxation of physical principles is required. The loss of locality appears to be the likely candidate. By relaxing locality we can prevent this sort of vicious feedback we might otherwise have”.

    But before jumping into emergent gravity arguments, let’s recall that many anomalies and broken symmetries are related in a way or another to phenomena on high energy scales: mass generation in EW sector, parity non-conservation and chiral symmetry breaking, anomalous magnetic moments of charged leptons, non-unitarity of lepton mixing matrix due to neutrino oscillations, the alleged violation of CPT in MiniBoone experiments, formation of quark-gluon plasma and GLASMA in collisions of heavy particles, the CDF anomaly, the PAMELA excess of positrons and so on. In my view, all these facts are beginning to hint that time-asymmetric and non-local field theories are among the most likely candidates for physics beyond SM.

    • Lawrence B. Crowell says:

      It might sound overly wide to consider black holes and the like. However, high energy physics is likely ending with the LHC. Beyond the year 2030 or maybe at best 2040 I suspect that will be it. The LHC may be upgraded in the 2020 time frame to push the energy up or to improve the detectors, but the end of the game is clearly coming, even though the great adventure is now upon us. So unless the universe is some sort of deception, I suspect that physics at the 10^{-17}cm scale has a continuous scaling principle up to the string length ~ 10^{-32} to 10^{-31}cm. This is I think some conformal renormalization group flow. Without some sort of physics of that nature we are blind to the foundations.

      I will add to this my suspicion that our species may well perform an “Orkin Man Job” on itself this century, if you get my drift. So if we are to figure out the foundations of the universe up to the limits of what is observable, it might behoove us to do it in the next 15-25 years. Time is short.

      So with that in mind I might attempt to propose something of this nature, where as a toy model consider a five dimensional “spacetime plus R” space. This fifth dimension is a space with a gauge connection or potential A = φ which defines a force F = -dφ/dx_5, for x_5 a parameter on this fifth dimension. To make this even simpler the potential might just be φ = -gx_5, similar to simple gravity near Earth and the force. For the fifth dimension a simple interval [0, L] the black hole case is x = L and the quasi-black hole or QCD plasma is at x = 0. So the black hole at the top for particle masses m ~ 0 has this continual flow to heavy masses at the bottom. This might connect with Zamolodchickov’s s = -1/2 massive conformal theory. So maybe there is some duality on these boundaries, which connects up with what they guys are saying. So the duality between spacetime isometries on these boundaries and conformal symmetries, such as the massive conformal symmetry which might exist on x = 0.

      One possible approach to this is with the gauge condition on a string interacting with a black hole. The transverse modes of a string are computed with a gauge condition X^+ = 0 on the stretched horizon of a black hole. This is seen by the stationary observer fixed relative to the event horizon, or the FIDO frame. The freely falling observer (FREFO) observes something completely different, where the Weyl curvature induces another gauge condition X^- = 0. So the two observers then measure different physics, with different gauge conditions established by their choice of frames. This is a manifestation of Wheeler’s observation that an observer has two radically different choices of a frame — outside or inside the black hole.

      The two gauge conditions are then locally determined by some additional field. This additional field is a manifestation of additional dimensions with a parameter that sets the X^\pm gauge at two different parameter values. As a toy model consider a five dimensional “spacetime plus R” space. This fifth dimension is a space with a gauge connection or potential A = φ which defines a force F = -dφ/dx_5, for x_5 a parameter on this fifth dimension. The gauge condition on X^\pm is a function G(φ) which sets at φ = 0, π: X^- = τ, X^+ = τ at the two limits. The exterior and interior states of the string are then local gauge conditions as a superposition of amplitudes

      χ(φ) = sin(φ/2)X^+ + cos(φ/2)X^-.

      An obvious simple case would be where φ = πx_5 as a model similar to a constant gravity on Earth. This means the gauge conditions for spacetime on the FIDO and FREFO frames are set by a gauge condition on an internal symmetry. Local gauge transformations of this internal gauge field then determine the FIDO and FREFO gauge conditions as coordinate choices: on coordinate fixed at a constant proper distance from the black hole horizon and the other freely falling into the black hole.

      So this is where I think the loss of nonlocality may originate from in the 10^{-17} cm domain. This loss of nonlocality is not explicitly a gravitational interaction as such, but is a “shadow,” to use that term, of a deeper quantum gravitational physics. The string on the horizon has a correspondence with the string on the AdS boundary, and is the QFT we observe. The string on the interior of the black hole is the field theoretic information on the interior of the AdS, which is holographically projected to the boundary. That boundary is the world we live on.

  14. To Lawrence and Erwin:

    Fiddling with field theory is certainly not enough. I am convinced that the notion of (p-adic) length scale is one of them and at more general level related to algebraic universality involving the fusion reals and p-adic number fields to a larger structure. p-Adic length scale hypothesis is also closely related to non-locality since the p-adic length scale characterizes the size of particle as a geometric object with size of order Compton length. The breaking of CPT could however be only apparent.

    Giving up locality means in my own framework in QFT picture replacement of point like particle with 3-surface- or by taking holography into account- partonic 2-surface and its 4-D tangent space data. M-theorists have of course varying views about non-locality but the original stringy view is that it becomes important only in Planck scale: in TGD macroscopic objects have also particle like quantal character giving them their identity since they correspond to space-time sheets having interpretation as regions of classical and quantum coherence.

    The twistor Grassmannian approach as developed by Nima Arkani-Hamed and others and leading to a conjecture of Yangian variant of conformal invariance is to my opinion best that has happened in theoretical physics for decades. It provides a very promising view about the character of non-locality present already at level of N=4 SYMs. Yangian algebra is Hopf algebra and its generators are multi-local. Even better, the notion of Yangian is also universal and therefore generalizable. In particular, one can replace the conformal transformations of M^4 with corresponding Kac-Moody type algebra resulting when point like particle is replaced with a partonic 2-surface. The Yangians of super-conformal algebras define excellent candidate for the ultimate symmetries in my own approach.

    One of the remarkable properties of Yangian is that one has a hierarchy of multi-local conserved currents each of which would represent basic observables such as four-momentum. The reason is that co-product maps the generator of symmetry to that acting in the tensor product in non-trivial manner (something more than just the sum of the generators as for non-interacting systems with trivial co-product). The four-momenta of bound states or at least the interaction parts of them could correspond to multilocal currents with a universal form dictated by the Yangian character of the algebra. The co-product would map the Poincare charges at given level of multilocality to higher level of multilocality. What comes in mind first is non-perturbative QCD and multilocal description of hadrons in terms of Yangians.

    Yangian symmetry of N=4 SYM is broken by IR divergences. Therefore the suggestion is very clear. The improved theory must be free of IR divergences and possess exact Yangian symmetry. My own approach suggests how this might be realized. All physical particle are massive bound states of the massless basic building bricks: even photon, gluons, and graviton have small mass characterizing the IR cutoff determined by experimental situation. Wormhole throats (partonic 2-surfaces) would represent these massless fundamental objects. One particular amazing outcome is that spin one particles identified as wormhole contacts carrying fermion antifermion pairs are necessarily massive since the spin projections of fermion and antifermion must sum up to one so that three-momenta must be opposite and mass is unavoidably generated. Higgs vacuum expectation is not needed and even photon and other massless particles must have a small mass. Higgs (and its colored invariant) exist only to serve the metabolic needs of gauge bosons including photon and gluons. For details see my blog.

  15. Bill K says:

    Matti and Lawrence, Thanks for very interesting comments on CPT violation and nonlocality! I don’t believe anything quite this radical is implied by the MiniBooNE/LSND results, however. Just CP violation, maybe in the form of a CKM-style matrix for neutrinos.

  16. Lawrence B. Crowell says:

    Bill and Matti,

    Bill, you are right of course if this turns out to be CP violations, unless of course there turns out to be some sort of axion physics involved. Though I think that is maybe less than likely. CP violations and PMNS or CKM matrix physics is fairly well understood. The discrepancy between υ and υ-bar is interesting though, which suggests this may not be standard CP physics. If there is some sort of CPT violation and a loss of QFT locality, then things do get interesting. This might then involve some generalization of the Coleman-Mandula theoretm, where there might be some additional “5th dimension at work. Who knows, maybe there is a more general discrete symmetry CPTU, where U pertains to an additional time direction with AdS. It is interesting to ponder, though I have no explicit hypothesis along those lines.

    Matti, String theory loosens some ideas of locality in the standard point QFT theory. Susskind’s strings on black holes also remove some standard ideas we generally have about the locality of events in spacetime. Some of what you write has connections of the physics of extended quantum systems, such as strings. The issue of wormholes is a bit strange to me. Largely I think these are vacuum states objects that have no classical analogue. The black hole is predominant, and for AdS_4 with a black hole in it then near the black hole horizon AdS_4 – -> AdS_2xS^2 which has an SL(2,R) conformal group of quantum mechanics.

  17. To Lawrence and Bill,

    this has been a very interesting discussion. To my best understanding different masses for neutrino and antineutrino imply CPT breaking and this requires breaking of Lorentz invariance. The geometry of causal diamond breaks Lorentz invariance to its subgroup spontaneously but one has a union of Poincare transforms of CDs so that at this level there is no breaking of Lorentz invariance. One might of course imagine CPT breaking by localization to single CD but I find p-adic length scale hypothesis much more attractive solution since it leads also to quantitative predictions.

    Lawrence wondered what I mean with wormholes. Wormholes in TGD framework are not those of GRT. They are the basic implication of many-sheeted space-time concept. One has space-time sheets with Minkowskian signature of the metric and when two sheets (distance in CP_2 direction of order 10^4 Planck lengths) touch a wormhole contact is formed. It took quite a long time to realize that these contacts can be interpreted as elementary particles. With holographic background this is the only reasonable interpretation.

    The wormhole contact interior in TGD has *Euclidian* signature of induced metric: this is completely in accordance with Poincare invariance since Poincare acts in imbedding space rather than at space-time. For a given contact there necessarily exist two light-like 3-surfaces at which the induced 4-metric is degenerate (determinant of g_ij vanishes). These light-like 3-surfaces define what I call wormhole throats. One could of course consider the possibility of Euclidian variants of Einstein-Rosen bridges also in GRT.

    Wormhole throats are identified as carriers of elementary particle quantum numbers and the pair defines the mathematical analogs of two black hole horizons associated with Einstein-Rosen bridge. The difference is that the signature of the induced metric changes at the throat whereas in GRT the roles of time and radial coordinate are permuted but signature stays Minkowskian. One obtains also black hole horizons for the vacuum extremal imbeddings of R-N metric in TGD but I am convinced that wormholes contacts take the role of black ole horizons in TGD framework. For instance, the formula for black-hole entropy generalizes in p-adic context and applies to elementary particles.
    The increase of total are for wormhole throats reflects directly the increase of particle number due to second law.

    Elementary particles correspond to wormhole contacts or pairs of these throats -as you wish. This is the left hand side of holographic correspondence: the interiors of the space-time sheets with Minkowskian metric defined the right hand side of holography and define the representation of particle physics in terms of induced gauge fields and metric at the sheets identified as coherence regions. Wormhole throat pairs are the lines of generalized Feynman diagrams and their vertices are 2-D partonic surfaces at which these lines meet. Note that these diagrams are not generalizations of stringy diagrams: also these exist but have nothing to do with particle decays but serve as space-time correlates for the propagation of a particle along two different routes simultaneously.

    A good model for the interior of wormhole contact is as a small deformation of a piece of what I call CP_2 type vacuum extremal. Isometric imbedding of CP_2 to M^4xCP_2 for which M^4 projection is light-like random curve. These CP_2 type vacuum extremals define TGD based model for the essence of being elementary particle since they are pointlike as far as CP_2 projection is considered. For instance, the light-likeness conditions reduce to Virasoro conditions: this led to the realization that conformal invariance of string models generalizes in TGD framework to that for light-like 3-surfaces. Deformed pieces of CP_2 type vacuum extremals or more precisely the pairs of wormhole throats can be seen as building blocks of generalized Feynman diagrams.

    At point like limit each line of generalized Feynman diagram reduces to a pair of points at distance of about 10^4 Planck lengths. This brings strongly in mind Connes non-commutative geometry picture and description of Higgs in terms of bundle with fiber having two points. Massivation indeed comes out twistorially: the points represent light-like momenta whose three-momenta for spin 1 are necessarily opposite so that mass is non-vanishing. There are excellent hopes for exact Yangian symmetry since the basic dynamical objects are massless and bound state formation brings in IR cutoff purely dynamically and resolves IR divergences.

  18. Lawrence B. Crowell says:


    I still often find myself scratching my head when reading your descriptions of TGD. All of this looks like some sort of condensate physics, similar to branes or maybe the Higgs field.

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