What is Strongly-Coupled Quantum Chromodynamics?

I don’t plan on filling my second post with a lot of mathematical symbols (although some of my posts may be more technical in the future). Instead, I want to scratch an itch.

The itch is an allergic reaction to statements I often hear about strongly-coupled quantum chromodynamics (usually called QCD). Basically these statements are that it’s all solved and anything remaining is a minor detail. I’ve tried to scratch this itch before (on Peter Woit’s blog, Not Even Wrong), but I never get satisfaction.

QCD is the theory of how quarks and gluons interact. In doing so, they produce all kinds of phenomena, in particular:

  1. the very existence of hadrons, the strongly-interacting particles (like the proton and neutron). Leaving out the details, these are bound states of quarks, held together by glue.
  2. how everything from electrons to nuclei behave in collisions, at high energies.

We understand the behavior of QCD at short distances (or high transverse momentum) very well. Experiments probing short distances are pretty convincing that the theory is right. This is because of the property called asymptotic freedom, which tells us that quarks and gluons interact very weakly at short distances. This is the weakly-coupled regimeOn the other hand very little is understood about why quarks are confined into hadrons or why the glue is massive (it is 99% of the hadrons’ mass!). This is the strongly-coupled regime.

Many physicists have tried to understand how confinement of quarks and the mass of glue (called the mass gap) follows from QCD. Even the Clay Mathematics Institute has gotten into the game, offering the weekly salary of someone who quits science to work on Wall Street.

My problem is with the claim that the strongly-coupled regime is understood, or nearly understood, a mere pimple on the beautiful wart of current theoretical ideas. Usually this claim is justified by arguing it is all just a string theory on a product of anti-DeSitter space and a five-sphere, with a few bells and whistles. But it’s a wrong claim.

The subject has a fascinating history, and I’m not going to summarize all of it here. Ken Wilson was the first person who saw how the strongly-coupled regime could be understood. It became clear that confinement and the mass gap could be true. Wilson also showed there was a strong-coupling expansion in which these phenomena were there. What is recovered is a kind of quark model, where hadrons form as color singlets. Unfortunately, extending this to genuine QCD is an open problem. The reason (as Wilson understood) is that this strong-coupling expansion has to be taken to many many orders to get the right strong-coupling description, where both asymptotic freedom and confinement are evident. And even that may not be good enough… Masses are multiples of an artificial scale, the lattice spacing. This scale has nothing to do with the QCD scale, emerging from dimensional transmutation.

The stringy models have the same trouble as Wilson’s. They are not guaranteed to describe real quarks or gluons. At best, they are phenomenological models. Just as with Wilson’s approach, the scale has nothing to do with the QCD scale.

Now there is a right strongly-coupled description of QCD, but we don’t know what it is. Wilson tells us how to find it. We start with QCD with a very large, nearly infinite ultraviolet cut-off. Then we integrate out all the short-wavelength degrees of freedom from the theory to get the strongly-coupled theory with a much smaller cut-off (say a few GeV). I wish I knew how to do this – it would solve the problem. This correct strongly-coupled description will be very complicated (with lots of features, called non-renormalizable operators). The probability of guessing it is zero.

Anyway, the message is this: We don’t yet understand strongly-coupled QCD.


8 thoughts on “What is Strongly-Coupled Quantum Chromodynamics?

  1. Dear Professor Orland,
    while I agree with the general tone of what you wrote in this post, I feel that perhaps is not making justice to the big body of work that lattice people have done [since many years ago]. It is my impression (I do not work on Lattice QFT, but have various colleagues doing so), that the problem of QCD is well advanced. They are able to simulate from unquenched dynamical flavors, different masses for the quarks, get correct values for the mass of the Pions, understand confinement and screening, etc. The way I see it (and here I may be tricked by my ignorance) is that QCD, thought as the theory that defined in the Lattice with the correct continuum limit gives results that match quite very well experiments. We all know that the problem of adding fermions is tricky, that it generated lots of interesting activities, but I believe that today experts coincide that they have a very accurate description of Chromodynamics (qualitative and quantitative).

    On the other hand, I disagree with your comment
    ”Usually this claim is justified by arguing it is all just a string theory on a product of anti-DeSitter space and a five-sphere, with a few bells and whistles. ”

    I think that ANY string theorist who have thought and worked on models in gauge-strings duality for theories of phenomenological interest, will never made the claim above. On the contrary, I believe they are all aware of the differences between the theories they work with and QCD, Yang-Mills or similar. I wanted to write this, because there are a lot of good, serious, not over-claimers string theorists, that work on those topics and are careful in writing their papers.
    As a final comment: may be, it is a bit ambitious to understand QCD using purely analytic methods. One should perhaps go for more tractable problems, pure Yang-Mills, Yang-Mills with adjoint quarks, etc. These toy models (with less interesting phenomenology) are a very good arena to test different ideas.

    Thanks for the post.


  2. Hi Carlos,

    I did not say anything about simulations in my post. I completely agree that lattice simulations have been very successful and are here to stay (full disclosure. One of my interests is simulation with cold atomic lattices. I hope this may complement Monte-Carlo, but I don’t expect it to replace Monte-Carlo). Nor am I saying that the string approaches have no merit.

    Maybe not ANY string theorist says we understand strong coupling QCD, but I have heard it with my own ears on several occasions. There are comment threads in Not Even Wrong where precisely this has been asserted by one or more participants. This last circumstance is the reason for the post.

    We may never have an analytic understanding of QCD at strong coupling, or even of pure Yang-Mills, as you suggest. In my opinion, such an understanding is worth working towards, even I don’t live to see it.


  3. Perhaps a closely related naive question from a non-physicist would be OK here: How can people be so confident about understanding QCD when the apparent empirical anomalies relating to protons are so big? For example, in the CERN briefing book it says that attempts to derive the spin of the proton from the spin of its corresponding quarks are far from successful–off by a large multiple. Similarly, the collision of tranversely polarized proton beams gives scattering results that are off from predictions not by tiny, at-the-limit-of-observation amounts but by factors of two or so and the anomaly increases with energy. What am I missing that makes these big apparent misses of the theory so innocuous?

    If there is no way to explain this kind of thing to non-physicists, feel free to ignore me. But I have some interest in the history and philosophy of science, and so claims that “the Standard Model is so great at explaining all the experiments that it’s hard to make theoretical progress” baffle me given these apparent ready-to-hand anomalies.


  4. srp,

    … claims that “the Standard Model is so great at explaining all the experiments that it’s hard to make theoretical progress” baffle me given these apparent ready-to-hand anomalies.

    I did not make such a claim. I said (nearly) the opposite. While it is clear that straightforward predictions of the Standard Model stand up well to experiments, I accept that not everything in the SM is understood. In the post, I tried to discuss an aspect we don’t understand.

    The spin of the proton is very tough, even for the best lattice simulations (maybe someone else can comment on this. I am not an expert on it). Baryons are messy complicated things, and it is not easy to predict the outcome of spin physics experiments.


    • Peter:

      Yes, I noticed that you were not falling in line with this questionable claim about the Standard Model that bothers me, which is why I thought you might be a good person to ask about these specific issues since you mentioned your long-time “itch.” But if you haven’t thought about this or just think that these are mostly difficulties in correctly deriving predictions from theory rather than imperfections in the theory itself, that’s fine.

      I’ve gotten the impression that these proton spin issues are generally taken to be merely messy technical “mop-up” problems, relegated to a community of numerical simulators, rather than serious theoretical flaws. The question of which issues become burning ones and which do not (in various fields) is interesting to me.


    • BTW, for future reference of what we both mean by excessive claims for the Standard Model, perhaps we can use this quotation from Peter Woit in his recent essay as a standard:

      “The huge success of the Standard Model has put particle theory in a dicult
      position, with little in the way of experimental hints of the right direction to look
      for a better theory.”

      Found in http://www.math.columbia.edu/~woit/mathphys.pdf


      • srp

        I think Peter Woit is right, provided he’s referring to electroweak physics, and some aspects of the strong interaction. His statement is a bit generally worded, but I think that is what he means. He’s not discussing lacunae in Standard Model predictions, but whether it has evident flaws.

        My own statement would be, “what we can CONFIDENTLY COMPUTE with the Standard Model works exceeding well. For that reason, we have no hints of new physics beyond the Standard Model.”

        Anyway, the post is about what we would like to compute in QCD, and not about superseding QCD with another theory.

        Nearly every scientific theory has some gaps, but we don’t simply assume gaps are fundamental flaws.


      • Thanks. That’s a clear statement. So the supposition is that the apparent anomalies are really just incorrect calculations/estimations of what the theory says, rather than correct calculations that don’t fit observations. Gaps rather than flaws, as you put it.

        I suppose that a “lacuna” or “gap” is a relative thing, i.e. there must be some warrant for the involved physicists’ statements that the observations are surprising or puzzling given the theory. If one couldn’t calculate at all what should happen than the observations wouldn’t be a surprise or a puzzle. So presumably they have some preliminary, rough way of calculating that generates expectations, but when those expectations are not met empirically the diagnosis is that better calculations are needed.


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