Imagine There’s No God Particle

It’s easy if you try (as John Lennon would say).

The LHC is back in business after a technical stop, getting ready to collide protons for the next couple months, perhaps reaching an integrated luminosity of about 5 inverse femtobarns. This is a factor of four higher than the luminosity used in most analyses that have been made public so far, and the latest projections are that this should allow an exclusion of a Higgs over the entire expected mass range at 95% confidence level, if such a particle really doesn’t exist.

My pre-LHC predictions (see here) of five years ago have held up well, and nothing yet has changed my view that a Higgs particle scenario and a no-Higgs scenario are equally likely. The best argument for a Higgs in the mass range of 114-145 GeV is that it’s the simplest way anyone has found of making the Standard Model work, and explains a range of precision electroweak measurements.

The best argument against the Higgs is that elementary linear scalar fields are problematic (since not asymptotically free) and esthetically displeasing (not geometrical and constrained by symmetries, so lead to lots of undetermined parameters, mainly for the Yukawas that determine the masses of all fermions). By analogy with the theory of superconductivity though, one can imagine that the Higgs makes a good low-energy effective theory (a la Landau-Ginzburg), even if there’s a more interesting fundamental theory, which may require going to a smaller distance scale (a la BCS theory). As the allowed Higgs mass range has narrowed though, I’m starting to think that there may be something to the argument that it’s implausible that the mass would end up being in the hardest mass range for colliders to examine. More likely it’s just not there, and the hardest range is the last one to fall to experiment.

By the way, I was interviewed about this on a Wired podcast (see here), not sure how it turned out. I don’t think I said anything surprising or controversial.

The imminent arrival of an experimental result deciding the issue of the SM Higgs has focused attention on what the implications will be, and here’s what I’ve been thinking:

If the SM Higgs is found, there will be rejoicing at first at CERN and within the physics community, and an appropriately proud announcement to the public. Debate will begin on who gets the Nobel: experimentalists? which of the 6000+ people at LHC/CMS/ATLAS? or theorists? Anderson/Higgs/Englert/Brout/Guralnik/Hagen/Kibble, or ? I gather Brout is no longer with us, maybe this will have to wait until the list gets down to three by attrition. Probably the best case would be for Weinberg/Salam, but they already were rewarded for the SM. Maybe the Swedes could make Weinberg’s a double. The LHC experimentalists would have an active research program for many years trying to measure the Higgs properties. Theorists though would face the gloomy prospect that these would just agree with the SM. We’d be stuck pretty much where we have been for thirty years: no clues as to how to do better than the SM.

What though if the SM Higgs gets ruled out? CERN may consider this an embarassment, but it’s actually a far more exciting result, one even more worthy of the Nobel than finding the long-sought particle. SUSY enthusiasts will claim this means it’s a SUSY Higgs, and model builders will get to work on constructing more complicated models designed to explain the result by making the Higgs even harder to see (Matt Strassler is starting to write about such models here). My guess would be though that no Higgs means the argument from esthetics was right, so adding in more scalar fields in some complex pattern isn’t a very plausible explanation of the null result.

A commenter here pointed out that this possibility was discussed during the debate over the SSC, when it was argued that, in the case of no Higgs, you would need a 40 TeV machine to look at W/Z scattering, to get information about what was really going on. The LHC should be capable of quite high luminosity, which may compensate for its lower energy in such searches, see a recent discussion here.

My own very vague favorite idea has always been that, non-perturbatively, there’s something important we’re missing in our understanding of gauge symmetry in chiral gauge theories and that this may hold the secret to the mystery of electroweak symmetry breaking. While this idea has been a motivation for research I’ve been pursuing in recent years, I can’t claim to have made any progress on it. My second real blog posting here was about this, back in 2004, leading to a torrent of abuse. Maybe if there’s no Higgs, SUSY and extra dimensions are gone, this could become a legitimate question in the eyes of mainstream theorists.

You-hoo-oo-oo-oo, you may say I’m a dreamer
But I’m not the only one…

Update: It seems that I’m definitely not the only one inspired by John Lennon recently, with CIP beating me to this a while ago.

Update: On the topic of this posting, see Slava Rychkov’s talk that just appeared on the arXiv. From the summary:

We have seen many impressive new physics limits set at this conference. But, have we ever truly believed in the models that are being pushed away? Z-prime, CMSSM, split SUSY, to name a few? I myself certainly never believed in these. Take Z-prime. In spite of what you may have heard, this is a completely unmotivated extension of the SM. It solves nothing of its problems and has nothing to do with Naturalness. Same for split SUSY, anathema to Naturalness. CMSSM is the only victim on the list for which I feel sorry, but we can’t give up on SUSY just because this straightjacketed version of it failed.

Another early casualty has been the Large Extra Dimensions scenario. But again, this was hardly a bona fide solution to the hierarchy problem. The mechanism which cuts off the Higgs mass quadratic divergence has not been concretely specified. It’s only because the idea was so original that we ever gave it the benefit of the doubt. Now with LHC limits on the (4+n)-dimensional Planck scale already a factor two above the Tevatron limits, it’s basically gone. The truth is, apart from SUSY, there are only two other motivated scenarios for TeV-scale physics: strong EWSB and Composite Higgs. I mentioned some of the signals expected in these models. Unlike CMSSM, they typically require much higher luminosity to be seen.

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89 Responses to Imagine There’s No God Particle

  1. Paolo Valtancoli says:

    I studied in my thesis the quantization of chiral symmetry in gauge theory in presence of anomalies. For what I remember the main problem is that the anomalies ruin unitarity. Now that I have more experience with noncommutative geometry, it is pretty natural that anomalies, being nonlocal, enter in conflict with unitarity. Maybe one should try to extend the notion of quantization, by allowing that pure states go into mixed states, i.e. introducing a microscopic arrow of time in quantum field theory.

  2. Amitabha says:

    While it is not polite to plug one’s own work here, I would simply like to mention that it is possible to get massive vector bosons even in the absence of a Higgs particle.

  3. chris says:

    Paolo,

    t’Hooft has been working on this for over a decade now.

  4. ru says:

    So I read Matt Strassler’s Higgs FAQ, and he says that whether or not there are Higgs particles, there is definitely a Higgs field, “essentially by definition”.

    Do you (plural) agree with this assertion?

  5. Thomas Larsson says:

    No Higgs: spontanous breaking of EW symmetry is wrong.
    Dynamic symmetry breaking: no expert, but know that technicolor models are already in trouble, and a Cooper pair of technifermions should effectively look like a Higgs, so probably wrong.
    Explicit symmetry breaking: ouch, too ugly!!!
    So if all other modes of EW symmetry breaking is wrong, how could the electro-weak symmetry be broken. Easy, by symmetry breaking 🙂

  6. Marton Trencseni says:

    Can someone point to a good paper that discusses/re-examines the state of EW symmetry breaking assuming no Higgs is found? Thank you.

  7. DB says:

    “The best argument for a Higgs in the mass range of 114-145 GeV is that it’s the simplest way anyone has found of making the Standard Model work, and explains a range of precision electroweak measurements. ”

    Let’s put on our sceptic’s hat for a moment.

    The second argument is iffy at best. The Review of Particle Physics (Higgs Bosons: theory and Searches, May 2010, p.12) quotes the best global fit to precision electroweak data giving the mass of the SM Higgs at 87(+35/-26)GeV. So the heaviest an SM Higgs could be, and remain consistent with precision EW is 122GeV.

    This tension has been around since LEPII ruled out Higgs below 114GeV leading to the waving of many hands in the interim, not least the “reworking” of the EW fits to “incorporate” the direct search result of LEPII.

    The other problem posed by Higgs is the implication of the scalar Higgs field for cosmology. Under reasonable assumptions, the vacuum energy contribution of the Higgs field results in a cosmological constant fifty times larger than the one actually measured, contributing to some of the anthropic fine-tuning nonsense, notably that peddled by a certain Steven Weinberg as far back as 1987.

    Another Nobel Laureate, Martinus Veltman, has been openly derided for expressing long-held scepticism towards the Higg mechanism. It will be some irony if he is vindicated, and a catastrophe for the HEP establishement which pitched the LHC to funding politicians on the basis that the Higgs was a slam dunk.

    Back 2000, Nobel Laurate Martinus Veltman was on record expressing scepticism on the existence of the Higgs Boson.

  8. Yatima says:

    a catastrophe for the HEP establishement which pitched the LHC to funding politicians on the basis that the Higgs was a slam dunk

    Really, why? It’s not as if people holding the purse strings were promised lucite blocks with an embedded Higgs that they could show off at home. Or antigravity devices to revive the (flagging, money-printing, laden-by-social-promises-that-can’t-and-won’t-be-kept, arbitrarily warfaring) national economies.

    There was a decision by the respective national funding agencies to go ahead and contribute to a project for which the outcome was open-ended, maybe get some redistribution effects for industry, parking space for PhDs, work for university departments as well as the occasion to do international collaboration and speeches in front of worthy audiences.

    LHC did a lot more than the international space station, and no-one is embarrassed about the 150 billion USD or so that went into it.

  9. Bernhard says:

    “Debate will begin on who gets the Nobel: experimentalists? which of the 6000+ people at LHC/CMS/ATLAS? or theorists? Anderson/Higgs/Englert/Brout/Guralnik/Hagen/Kibble, or ?”

    From the experimental side, LHC collaborations as a whole should start getting Nobel prizes with CERN director going to Stockholm to get it, representing them, not simply give to the spokesperson of an experiment. The prize should go to the whole collaboration and although I agree 10M SEK is not really much and can’t pay the collaboration electricity bill, it’s the correc thing to do.

    From theorists, tough call…

  10. Bernhard says:

    But to be clear, I believe it should be a shared prize between theory and experiment, I’m just not sure which theorist should get.

  11. Chris Oakley says:

    At first I detested the term “God particle”, feeling that it was merely an invention of those too ignorant to understand that a particle with zero rest mass could still exist. However, given the possibilities for humour and/or relating to popular culture I am slowly coming round to it.

  12. Igor Khavkine says:

    @Amitabha, about your [arXiv:1107.1501]. It’s likely that your construction is equivalent to the Stückelberg mechanism, where gauge bosons are derivatively coupled to auxiliary scalar fields instead of 2-forms (2-forms in 4d are in fact equivalent to scalar fields [Weinberg, v.I, 8.8]). However, an analysis by Dütsch & Scharf [arXiv:hep-th/9612091] shows that a Higgs field is then still required if both renormalizability and freedom from gauge anomalies are required. They are probably not the first to get this result, but their analysis is quite careful. This makes me skeptical about the viability of your construction. 🙁

  13. DB says:

    @Yatima
    Perhaps catastrophe is putting it too strongly, but the HEP establishment will lose a great deal of credibility with funding politicians if the Higgs doesn’t turn up, or, at least, a discovery of comparable importance is not forthcoming within a reasonable timeframe. It was seen as a pretty safe bet and sold as one. CERN, don’t forget, has been outmanoevered by the US on more than one occasion, and the prestige to Europe that would accrue from discovering the Higgs is what these politicians are really paying out for, and the other benefits that you mention are viewed by them as mere cream on the strawberries.

  14. Igor Khavkine says:

    A follow up on my last comment. It seems to me that the case for a Higgs-like mechanism is solidly backed up by the requirement of simultaneous renormalizability and freedom from gauge anomalies. According to Dütsch & Scharf, allowing the theory to be gauge anomalous eliminates the need for a Higgs field and results in a model that’s apparently due to Curci & Ferrari.

    Naturally, I wonder: is known whether a Higgs field is still needed if one drops the renormalizability requirement instead? After all, to quote Weinberg: “Non-renormalizable theories are just as renormalizable(*) as renormalizable ones.” Of course, he uses the term “renormalizable” in two somewhat different technical senses. I believe that the (*) sense is the more important one.

  15. Thomas Larsson says:

    Btw, Brout will not receive a Nobel for Higgs. It is not awarded posthumously.

  16. bonk says:

    DB: “The Review of Particle Physics (Higgs Bosons: theory and Searches, May 2010, p.12) quotes the best global fit to precision electroweak data giving the mass of the SM Higgs at 87(+35/-26)GeV. So the heaviest an SM Higgs could be, and remain consistent with precision EW is 122GeV.”

    That’s exactly why I think that ruling out heavier higgs mass at the LHC is evidence for the standard model, rather than a warning that something might be wrong. But somehow many people including Peter don’t share this opinion.

  17. anonomous says:

    “The LHC is back in business after a technical stop, getting ready to collide protons for the next couple months”

    This is what I fear the most – not proving or disproving the existence of the Higgs but not getting enough data by the end of the year because of a major technical outage like the one in 2008. My experience is that Murphy’s law is much like the uncertainty principle – the less you pay attention to it the larger it’s momentum gets!

  18. Pingback: If we can actually find out something, maybe cosmology will become a science again … | Uncommon Descent

  19. frank says:

    Peter,

    did you reread that 2006 comment of Lubos in your blog where he answers “B” saying that the LHC “must” find something, and that it was “againt logic” that it found nothing? He wrote that the LHC “had to” find something at 1 TeV (we are already beyond that). Lets wait till Christmas, and then he should get depressed while eating his own words.

    By the way, Lubos is now claiming in his blog that the possibility that nothing happens at 1 TeV scale “is in the literature since the 1980s” – a statement which is completely false. I claim to have read every review on the standard model since that date and have not found a single mention of this option. In contrast, the general, unanimous opinion is that standard model has to break down at 1 or 2 TeV. Now that the LHC is telling us otherwise, everybody who has ever written a review with a title such as “beyond the standard model” should get a red face.

    What would be even more interesting is to have a discussion on the arguments that led people claiming that the standard model is “incomplete” or even “wrong” at 1 or 2 TeV. There are a number of such arguments, and obviously they are all wrong. The whole issue shows that nobody from the quantum field theory “experts” who abused you so much in 2006, from Distler to Lubos to Srednicki, said anything correct about the limitations of the standard model from the time they are in charge of teaching about it. (Remember how they questioned your qualifications, as if truth in physics depended on the qualification of the messenger?) I wonder how these people are doing now.

  20. Amitabha says:

    Igor, this discussion is not strictly on-topic, so Peter is unlikely to encourage its continuation, but I would like to mention that the recent paper is only a part of the story — you may want to look at Phys. Rev. D63 (2001) 105002 regarding renormalizability, and bring the discussion to email if you wish.

    And this is not the Stuckelberg mechanism — the two-form is not dual to a scalar. Weinberg’s statement about equivalence is not very useful when the fields have cubic or higher couplings — even though there is only one degree of freedom (per gauge index), which you can think of as a scalar, it is not possible to write the theory as a local field theory in terms of that single degree of freedom. But you probably knew that already.

    If a theorem claims that a Higgs field or similar is `required’, it usually assumes that all degrees of freedom appear as local fields in the action. Even though the two-form action is local, the actual degree of freedom does not appear in the action in a local combination. IIRC that is why these theorems are not applicable to this case.

  21. OhDear says:

    frank, your comment is way premature. The LHC has not shown there is nothing going on at the TeV scale. We are not “beyond” 1 TeV (only cMSSM and other constrained variants are ruled out). The time may well come for red faces among BSM physicists, but that time is not now.

  22. mark says:

    +1 to OhDear

    All thats been ruled out are the simplest SUSY models surely? We are hardly at the point where you have to concoct absurdly contrived models to explain its absence (yet).

  23. Paolo Valtancoli says:

    I think that physicist should learn from the failure of LHC a simple pratical principle, i.e. that Nature is essential, nothing that you see is superfluous. That’s why I am convinced that all the models proposing a river of extra particles to be detected have
    a lot of chances to be wrong.

  24. Bernhard says:

    Peter,

    I wonder if the Higgs is not discovered (and this seems more and more plausible) if people will shift the holy grail of physics research to electroweak symmetry breaking, as you have been discussing for years now. Personally I think it’s also a fascinating but more tangible question, perhaps one we really need to answer properly before worrying too much with gravity. In any case, would be ironic to see the very same people who fought against you some years ago to engage in the activity you pointed out as the most important one… 😀

  25. Charles says:

    I think the big question is what if it is determined there is no “boson” (it could be a composite particle) but there is a mechanism? I am not sure that is being clearly stated or addressed here. Or I am not getting it (quite possible).

    What does LHC do?
    What does the Nobel Academy do? (PH gets a lot of credit for this “sentence” on the boson)
    What happens to the SM?

    Thanks.

  26. DB says:

    A curious PR release from the Tevatron to Reuters claims that it will be in a position “to rule out the existence of a Higgs boson with a mass within the most likely range” before is shuts down for good on September 30th. Is this a last attempt at an end-run around the LHC:? “we discovered the non-existence of the Higgs before you did”!

    http://www.reuters.com/article/2011/09/05/us-science-higgs-idUSTRE78445C20110905

    Of course, the phrase “with a mass within the most likely range” can be interpreted many ways.

  27. AcademicLurker says:

    CERN, don’t forget, has been outmanoevered by the US on more than one occasion, and the prestige to Europe that would accrue from discovering the Higgs is what these politicians are really paying out for

    Hasn’t Europe in a sense already won on the prestige issue? With the U.S. powering down its colliders, CERN is now the only game in town*, in terms of experimental HEP.

    *to use a phrase that’s much disliked around here…

  28. Peter Woit says:

    DB,

    I think the caveat here is that, while a fully complete, combined D0+
    CDF analysis with all the Tevatron data (up to shutdown at end of Sept) might be able to rule out a Higgs in the interesting region above 114 GeV, my understanding is that the schedule for availability of this is the summer 2012 conferences. The LHC experiments have huge numbers of people to throw into these analyses, not so at all at the Tevatron these days. So, even if this works, it may come out after the LHC has already put out results about this. A good thing to have such very independent results though…

  29. Igor Khavkine says:

    Amitabha, I see now that you are right about the 2-form field not being equivalent to a scalar via a local field redefinition. I’m still skeptical about both renormalizability and non-anomalous gaug invariance being satisfied, but I’ll look into it. In any case, not being an expert in this area, I’m now happy to know another method (other than Stückelberg’s) of representing a system with second class constraints (Proca’s massive vector bosons) as one with only first class constraints. At the very least, your paper points to some interesting literature.

  30. Bernhard says:

    AcademicLurker,

    true, but only if the experimental activity “here” in Europe lead to a discovery, otherwise we are all going down.

  31. Peter Woit says:

    frank,

    Despite what one might think from the various hype fed the public, my impression of the situation has always been that virtually no one ever believed extra dimensions would show up at the LHC. As for SUSY, while it’s the most popular of “BSM” ideas, I still suspect that the median particle theorist would always have assigned it a probability of showing up at the LHC of somewhat less than 50%. So, the median theorist is probably not too surprised at no extra dims and no SUSY, but may have expected something unexpected to show up by 1 TeV, if not SUSY.

    Most theorists are aware of the argument that, if no Higgs, something else must show up to make WW scattering unitary, and that’s part of what people typically are thinking of when they say: if no Higgs, must be something around 1 TeV. This argument is going to get vastly more attention if the SM Higgs gets ruled out, which will be a very good thing. The basic problem for years is that theorists like to work on relatively easy problems in well-understood frameworks (like SUSY), not spend time banging their heads on a problem for which no one has a promising idea.

  32. Peter Woit says:

    OhDear,

    Besides SUSY, as I mentioned, limits on RS KK gravitons are already getting towards 2 TeV, and there’s lots of other exotic physics searches also ruling things out to that energy scale. From trying to follow the arguments about the state of SUSY searches, my impression of the situation is that they are already filling in holes in parameter space pointed out by model builders, and describing the situation as “no strongly interacting superpartners below 1 TeV” is a reasonable description of the generic situation, although of course special classes of models can always be found for which the bound is lower. Something else I don’t understand though is why anyone would believe there’s a large probability that the gluino will show up precisely above 500 GeV but below 1 TeV, making it worth their time to argue much about this.

  33. Mark says:

    “Something else I don’t understand though is why anyone would believe there’s a large probability that the gluino will show up precisely above 500 GeV but below 1 TeV, making it worth their time to argue much about this.”

    My best guess as to why Kane would make such a claim comes from this paper:
    http://arxiv.org/abs/1105.3765

    In particular, in eq. 2, where the first two terms on the right hand side almost cancel out, the next term denoted by R(t) contains a product A0*M3 (see the expression above eq. 3) where A0~O(10-50) TeV and M3 is directly related to the gluino mass. So, I suspect that for such models with very heavy scalars and trilinears Radiative Electroweak Symmetry Breaking , where the Higgs vev is of O(100) GeV, becomes much harder to achieve when M3 goes above 1 TeV because of the A0*M3 contribution. Again, this is just my guess.

  34. VP says:

    Looks like CERN might be preparing for the possibility of “No God Particle”. In the agenda of last June’s Scientific Policy Committee meeting there is a talk with the title:
    “Interim report on: The scientific significance of the possible exclusion of the SM Higgs boson in the mass range 114-600 GeV and how it should be best communicated.”

  35. Peter Woit says:

    Mark,

    I see that that’s a carefully constructed example of a model with this feature, I still don’t understand why anyone would believe it….

  36. Charles says:

    “CERN, don’t forget, has been outmanoevered by the US on more than one occasion, and the prestige to Europe that would accrue from discovering the Higgs is what these politicians are really paying out for”

    This outcome is one of the sub-plots of the story. It is not just CERN vs. FermiLab but making the “Higgs” a true European story from theory to discovery. Folks are working together to make this happen at CERN and ultimately in Stockholm. Guralnik made this point in a historical survey from a theorist perspective (quoted on this blog months back). I’m also told t’Hooft also feels strongly the “Higgs” is an opportunity to make good on previous Stockholm snubs for European Nobels in favor for US scientists. The Veltman/t’Hooft Nobel paper listed all the 1964 theorists and referred to it as the “Higgs-Kibble mechanism”. Since being buttressed by the Nobel, it is the BEH Mechanism whenever he speaks or writes on the topic.

    Time will show if this broader European strategy is successful. Recent results from LHC certainly make it more interesting.

  37. Peter Woit says:

    Charles,

    Thanks. I haven’t followed the twists and turns of the names used over the years, but I did do my own historical research last year on the early literature, results were in this posting:

    http://www.math.columbia.edu/~woit/wordpress/?p=3282

  38. Rick Ryals says:

    Nobody has an answer for “ru”… ?

  39. Peter Woit says:

    Rick Ryals,

    I left that comment there in case it attracted an interesting response, but I’m not surprised it hasn’t. It’s not really well-defined (what exactly do you mean by “Higgs field” and what exactly do you mean by “by definition). Even choosing ways to make the question well-defined, it’s a complicated issue. And, all in all, I think trying to start discussions here of material on someone else’s blog is a bad idea. Better to discuss it over there, where the text explaining what the author means is in place, and he can clarify it as needed.

  40. Mark says:

    “I see that that’s a carefully constructed example of a model with this feature, I still don’t understand why anyone would believe it….”

    To be fair, Kane has been heavily advertising such a model during the past 4 or 5 years, while most SUSY folks, especially gauge mediators, were expecting light squarks and sleptons to show up, and I’m not surprised that as the CMSSM gets ruled out these ideas will draw more attention. Models with a split spectrum have been around for a while but the amount of splitting and the scale of SUSY breaking in bottom up approaches was always kind of arbitrary. On the other hand, Kane’s example is actually rooted in a top-down approach (see his work with Acharya et al), where the gaugino-scalar splitting is highly constrained. I personally don’t know how general such a spectrum really is but I do know that gaugino mass suppression relative to the gravitino mass is rather generic in many string compactifications, while scalar mass suppression is much “less generic”.

  41. Rick Ryals says:

    “I left that comment there in case it attracted an interesting response…”

    Okay, Peter, that’s what I was hoping for too, since I’ve already been to that blog and had some conversation with the author. Anyway, thanks for the reply.

  42. SpearMarktheSecond says:

    Thanks for finding the Govoni talk, Peter. Looks to me like page 23 indicates the LHC is not very promising for like-sign W’s. But maybe page 17 indicates W/Z scattering is hopeful in distinction from background… the raw number of events is awfully low, however.

    If the Higgs really is discovered between 115 GeV and 145 GeV, that will be amazing and should make heroes out of everyone involved. It is too easy to let the hype detract.

    Sure, there is always hype. Without hype there would have been no machine. The only guaranteed route to a totally predictable outcome is to do nothing… then for sure nothing gets discovered. If scientific funding had been easier for the last 20 years, the hype could have been dialed down. So I’m definitely in favor of copious forgiveness for the hype, particularly if the Higgs is 115-145 GeV.

    If no light Higgs, and the SSC was the right machine, darn, darn, darn.

  43. Thomas Larsson says:

    Looking back at my previous comment, I realize that it makes little sense. Fear of Peter’s censorship made me mutilate my comment into incomprensibility. So let me write a comment which is both on topic and does not explicitly mention my own work. A reference for the statements below is chapter 4 of Pressley-Segal: Loop groups.

    If the LHC does not see a Higgs, spontanous symmetry breaking is wrong (modulo more epicycles), and EW must be broken in some other way. The mechanism which has not been beaten to death by generations of physicists is anomalous symmetry breaking.

    To be precise, by a gauge anomaly I mean an extension of the group of gauge transformations, as in “the conformal anomaly is the central charge in the Virasoro algebra”. The group of gauge transformations in Yang-Mills theory has two types of extensions: the Mickelsson-Faddeev group, which is responsible for the anomalies found in QFT, and the central extension. The former has no unitary reps of quantum type (Pickrell 1989) and can hence not be used in physics. Anomalies of MF type must cancel, as they do in the SM.

    In contrast, the central extension does have unitary reps – in fact, the unitary irreps are classified in PS – and hence it may provide a mechanism for anomalous symmetry breaking. However, this extension does not arise in QFT, so if it is responsible for EW symmetry breaking, one must go beyond QFT. Unfortunately, I did not manage to turn this observation into useful physics, but my shortcomings do not change the mathematical facts above.

  44. Giotis says:

    Peter,

    Do you doubt that there is a field with a non zero VEV that breaks EW ?(*regardless* of its nature, properties and particle manifestation)

  45. Bernhard says:

    “Take Z-prime. In spite of what you may have heard, this is a completely unmotivated extension of the SM. It solves nothing of its problems and has nothing to do with Naturalness.”

    I strongly disagree with such a claim. Z´are neutral bosons that appear in many extensions of the SM, also in the most conservative, strongly motivated and only relying in model building rules for renormalizable gauge theories, such as the 331 models. It´s not correct to say these models don´t solve SM problems. I quote the generation problem, the solution of the strong CP problem and the explanation of the heavy top quark mass as a few. Not to say I am because of that a strongly believer, but the statement is incorrect.

  46. Bernhard says:

    sorry, *strong believer*

  47. DB says:

    @Peter
    “while a fully complete, combined D0+ CDF analysis with all the Tevatron data (up to shutdown at end of Sept) might be able to rule out a Higgs in the interesting region above 114 GeV, my understanding is that the schedule for availability of this is the summer 2012 conferences.”

    Dmitri Denisov of DZERO is on record in July as saying “We should be able to exclude the Higgs particle or see first hints of its existence in early 2012”.

    A key factor is that the Tevatron can detect the dominant mode of Higgs decay into quark anti-quark pairs, whereas due to its high QCD background the LHC is forced to look for the much rarer Higgs decay to pairs of W bosons decaying to two photons and therefore is at a disadvantage in the lower end of the remaining 114-145GeV range.

    The LHC has more bodies yet the Tevatron has more experience. Reminds me of the tortoise and the hare.

    That the Tevatron intends to race the LHC to the finish line is definitely the sense I get from reading the Fermilab PR release. Time will tell if it’s just bravado but I hope they make a real race out of it.

  48. Peter Woit says:

    Giotis,

    If there is no Higgs field, I think we really just don’t understand what is going on. One possibility is that there’s some other field (elementary or composite), with some other dynamics, that does what the Higgs field does. But there may be something else going on. How gauge degrees of freedom get handled in chiral non-abelian gauge theory is very tricky, maybe there’s some subtlety there we’re missing.

  49. null says:

    DB “A key factor is that the Tevatron can detect the dominant mode of Higgs decay into quark anti-quark pairs, whereas due to its high QCD background the LHC is forced to look for the much rarer Higgs decay to pairs of W bosons decaying to two photons and therefore is at a disadvantage in the lower end of the remaining 114-145GeV range.

    The LHC has more bodies yet the Tevatron has more experience. Reminds me of the tortoise and the hare.”

    Since Tevatron intends to shut down at the end of Sept, 2011, will it be able to present results in the interesting region of 115-145Gev? How long after Sept 2011 will Tevatron announce its results?

  50. SpearMarktheSecond says:

    Or maybe it is simply that the Higgs field is there, but the width of the Higgs is a whole lot larger than we expected, due to couplings to (as yet) unknown particles. I’m not aware of limits on the width of the Higgs from the precision electroweak, although maybe someone has looked into that. If only SM couplings, then we’d know the width up to QCD. But perhaps the width should be viewed as a parameter to be measured, in which case, maybe the Higgs can be so broad as to be everywhere, smeared out.

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