By almost all measures, the Higgs Symposium at the University of Edinburgh, as part of the new Higgs Centre for Theoretical Physics, was a great success. The only negative was that Professor Peter Higgs himself had a bad cold this week, and had to cancel his talk, as well as missing the majority of the talks by others. Obviously all of us in attendance were very disappointed not to hear directly from him, and we wish him a speedy recovery.

Other than this big hole in the schedule, the talks given at the symposium seemed to me to form a coherent summary of where we are right now in our understanding of the Higgs field and particle. They were full of interesting material, and wonderfully complementary to one another. This motivates me to try to provide, for non-experts, some future articles on what the conference attendees had to say. But to write such articles well takes time. So for now, here’s the quick version summarizing the last few talks, along the lines of the summaries I wrote (here and here) of the earlier talks. The slides from all the talks are posted here.

Here we go:

First off on Thursday afternoon was Nima Arkani-Hamed, professor at the Institute for Advanced Study, and co-inventor of the modern versions of the ideas of Large Extra Dimensions, Split Supersymmetry, and the Little Higgs. Arkani-Hamed (whom you can see in action here) has for the past year been thinking about the challenges to the simplest versions of supersymmetry posed by a Higgs particle with a mass of 125 GeV/c², as the newly discovered particle at the Large Hadron Collider [LHC] appears to be. There are two classes of solutions that he covered.

- Add new particles and forces not expected in the simplest (“minimal”) variants of supersymmetry, such that effects of the new forces directly push up the mass of the Higgs particle.
- Relax the requirement that supersymmetry completely solve the hierarchy problem (which means the rest of that problem has to be solved some other way, perhaps by accident or by a selection effect). This would allow some of the superpartner particles predicted by supersymmetry to be heavier than often expected, which in turn moves the Higgs mass upward through subtle quantum effects, due to virtual particles.

The important thing, as Arkani-Hamed emphasized, is that whether or not you like these ideas, both case (1) and case (2) are probably falsifiable (i.e., can be ruled out by LHC data); for example, even in case (2), where fewer particles would be discovered at the LHC than in standard supersymmetry, their properties would be quite striking.

The next speaker was David Kosower, professor at Saclay, France, whom I’ve mentioned before as one of the members of the BlackHat collaboration. Kosower explained how a revolution in calculational techniques, drawing on various tricks obtained from quantum field theory, from supersymmetry and from string theory, has taken place recently. Among the most dramatic applications is making possible many calculations that are necessary for high-quality measurements at the LHC… calculations that were thought to be far out of reach just a few years ago. I can’t emphasize enough how important and how exciting these advances are to those of us who’d been watching the slow though steady progress of the previous twenty years. Another application is to understanding the most symmetric and often most instructive of quantum field theories, the so-called N=4 supersymmetric gauge theory, which has many forms of remarkable quantum behavior. Even though it is by no means the real world, it’s astonishing how much of relevance to the real world we’ve learned by studying it. Someday I’ll write about it on this website. One thing that Kosower mentioned was that the new techniques from this seemingly esoteric N=4 supersymmetric theory have been used to improve the understanding of the mathematical results of more general particle physics calculations, making it possible to simplify the formulas for production of the Higgs particle significantly. *(As with string theory, supersymmetry is a field of study that gets a lot of naive criticism from some quarters as being irrelevant to physics; but in fact, as this example shows, supersymmetry has been enormously important to particle physics and quantum field theory, often in surprising ways.)*

The last speaker of the day was Harvard professor Subir Sachdev, who is not a particle physicist at all: he is a condensed matter physicist (and in particular interested in things like metals, insulators, superconductors, superfluids, phase transitions, and the like.) There’s a long history of particle physicists and condensed matter physicists teaching each other important lessons about how quantum systems work — both the Higgs field and the confinement of quarks are related to superconductivity — and Sachdev has for some years been serving a cross-over role. I hope I describe him fairly as an expert (among other things) in quantum field theory’s applications in condensed matter. During the last decade he has been studying the advances that high-energy physicists like me have been making in supersymmetric field theory and in string theory, to see what he can learn for use in condensed matter. (A substantial number of string theorists have been participating in this effort as well.)

In his talk, Sachdev described a couple of recently uncovered examples of condensed matter systems that can be studied experimentally and theoretically, one of which exhibits something like a Higgs field with a low-mass Higgs particle, and one of which (admittedly in two spatial dimensions) exhibits something like a high-mass, short-lifetime Higgs particle. These are interesting to see, though I admit I did not detect any lessons for particle physicists… perhaps I did not fully appreciate them, so take a look for yourself it you’re an expert. He concluded his talk with an application to a condensed matter-like problem of the “AdS/CFT” correspondence — specifically, the use of string theory or gravity to solve problems in quantum field theory. (Sachdev has reviewed this application of string theory in the recent past; click here.) To make a long story short, some remarkable insights about otherwise uncalculable aspects of the problem have emerged using these AdS/CFT methods. Perhaps, if luck holds, these insights will be useful in real-life condensed matter systems, but that’s too early to say.

Friday morning (which was supposed to include the talk by Higgs) only had two talks, one by me and one by Professor John Ellis, of King’s College London and CERN. Mine was entitled “Looking Beyond the Standard Model”, and I started by reminding the audience that the Standard Model (the equations describing all the known elementary forces and particles, including the newly discovered particle, assuming it is the simplest type of Higgs particle) is a self-contained and consistent theory, but is deeply incomplete, as leaves all sorts of basic questions unanswered. (For instance, why the electron has two heavy cousins, the muon and the tau, is not explained, nor is the specific pattern of the matter particles’ masses and decay rates.) We’re therefore going to have to look beyond the Standard Model *someday*; we just don’t know if this will happen soon and rather suddenly (through a discovery of something unexpected at the LHC or elsewhere) or later and gradually (through a thorough, systematic study, lasting at least til 2020, that tells us that — to the available precision — the Standard Model’s equations predict everything observed at the LHC.)

I then focused on the question of what we ought to do during 2013-2014, while the LHC is shut down for repairs and upgrades, to maximize the chances of making a discovery hidden in the data collected in 2011-2012. What are the most promising measurements to make? My answer was that we should focus most on Higgs-related phenomena that are not expected in the Standard Model, asking the following questions:

- Is the Higgs-like particle ever produced in a fashion not expected in the Standard Model?
- Does the Higgs-like particle ever decay in a fashion not expected in the Standard Model?
- Are there any other types of Higgs-like particles hiding in the data?

Then I talked about what it would mean if the Standard Model, even though it can’t be the final word for particle physics, is the complete story for physics ** at the LHC**. The challenge in this case is that it isn’t entirely obvious which experiments to do next, or even what type of experiments are likely to yield clues, and it is very important to have an open mind and not to take anything for granted. Perhaps there are relatively inexpensive experiments that might be surprisingly relevant to the question — but someone has to be clever enough to realize this. More on this another time.

The last speaker, John Ellis, focused first on the question of how confident we should be that the new particle is a Higgs particle of some type. (I wrote about this for you here, back in July, in the early days after the discovery.) His answer was that there is quite a bit of evidence already, and there will be much more learned in the next few months of data analysis. Something that was new to me and seems rather remarkable is that the process in which a W particle and the new particle are produced together (see here for the standard production processes for Higgs particles) is very sensitive to the spin of the new particle; assuming the particle is produced in this mode with a rate not too far below that expected for a Standard Model Higgs, it would appear that it may be a very powerful way of excluding the hypothesis that the new particle has spin 2. *(All particles can intrinsically and incessantly rotate, a weird effect of quantum mechanics called “spin”; a general boson particle can potentially have spin 0, 1, 2, 3, etc., but the Higgs particle specifically must have spin 0 — i.e., it doesn’t rotate at all.) *

Next, Ellis — one of the world’s most prominent experts on supersymmetry as a solution to the hierarchy problem — considered what we have and haven’t learned about supersymmetry so far at the LHC. He concurred with others, including me, who disagreed with the LHCb experimentalist, quoted by the BBC reporter back in November, who said that a recent LHCb measurement “put supersymmetry in the hospital.” Aside from the point that this remark doesn’t make any scientific sense, it was factually inaccurate, as Ellis showed (and I explained to you back then.) The really powerful constraints on supersymmetry as a complete solution to the hierarchy problem — which is how most people mean it when talking about finding it at the LHC — don’t come from here. They come from the mass of the observed Higgs particle (which is almost impossible in the simplest variants of supersymmetry, as also discussed by Arkani-Hamed — see above) and from the lack of any evidence in LHC data of anything amiss with the Standard Model. In particular, standard searches for superpartner particles have come up empty (though I’ve warned you about drawing overly strong conclusions until a wider variety of studies are complete). Ellis took the point of view that the doors are still open, and it is still too early to draw any conclusions about supersymmetry being part of nature at the mass scales accessible to the LHC.

The symposium concluded with a panel discussion that included a number of the speakers and also scientific luminaries Lance Dixon (also part of BlackHat) and Guido Altarelli (a major figure in the field since the 1970s, who among many other things co-obtained the equations that are used in all modern calculations of proton-proton collisions, such as those at the LHC.) Much of the discussion focused on the question of whether a new particle collider to study the Higgs-like particle (a so-called “Higgs factory”) using electron-positron collisions should be proposed soon, and if so, of what type it should be. The options for such a machine would be a collider in a circular tunnel (like the LEP collider, which used to be located in what is now the LHC’s tunnel, but with 25% more energy per collision than the highest collision energy available at LEP) or one in a linear tunnel (technically more difficult and less certain financially, but able to be extended to higher energies eventually.) Another option is to push for the LHC — already itself a factory for Higgs particles, having produced 400,000 per experiment this year — to be upgraded beyond 2020. The reason such a machine would be desirable has to do with the “decoupling limit” described by Howie Haber in his talk earlier in the week. However, some serious thought has to go into whether any sort of proposal along these lines is premature. I don’t have a clear opinion on this yet; my current focus is on getting all the information we can out of the 2013-2014 data, since a single unexpected discovery would completely change the debate.

So ended the Higgs Symposium. My thanks and congratulations to the organizers; I am sure most attendees enjoyed it as much as I did!

A naive comment then: Is susy’s mathematical “triumph” still as huge as you describe it even if we consider that its *primary* role was never supposed to be an assistant of mathematics? Not to mention that theorists would go nuts some years ago if the biggest compliment they received was that their *mathematical* theories are nice…

Do not confuse mathematics and physics. Mathematics is something mathematicians are interested in. Calculations that physicists need to know the answers to are physics, not mathematics, even though they involve using math. Also, you’re putting words in my mouth by calling it a “triumph”, or “huge”; do you see those words in my text? I represented it as simply one of many, many interesting applications.

When I studied supersymmetry as a student 25 years ago, I was taught: (a) supersymmetry may or may not be part of the real world; (b) supersymmetry is a very useful tool for studying the real world; (c) supersymmetry is an idea with many applications to general issues in both physics and mathematics. And I have found this to be true, throughout my career. What do you mean by a “primary role”? I was never taught that supersymmetry had a “primary role”; I was taught to treat it as a tool in the tool box, like two-dimensional field theory and conformal field theory and string theory and effective field theory… and to apply this tool wherever it was useful. If you think this is somehow revising history, you don’t know the history. I can try to dig out my grant proposal from 2000 where I went to the Department of Energy with exactly this kind of story…

Can we make a Higgs factory by sticking a linac on the Tevatron? After all, it is really flat out there.

The Tevatron (the predecessor to the Large Hadron Collider, located at the Fermilab center outside Chicago) is not relevant… its circular tunnel is too small for a circular electron-positron collider of the required energy, and a linear tunnel would have to be built from scratch. The equipment needed to accelerate electrons is quite different from the equipment used at the Tevatron for the acceleration of protons and anti=protons, the creation of the anti-protons, etc.

Now, a linear collider could be built on the Fermilab site, yes. There’s enough room (and flatness matters less than geology, because this thing has to go underground a bit.) This has been widely discussed among US physicists for well over a decade.

However, the current congress, especially the House, is not only unlikely to support such an idea, it is quite likely to cut Fermilab deeply. I personally expect major damaging cuts to particle physics programs in the United States this year. It is even possible that the commitment of the US to the Large Hadron Collider will suffer major cuts — in grim reward for the US particle physics community’s major scientific contribution to the discovery of the Higgs particle.

Dear Prof. Strassler,

thanks for the nice summary of the latest talks.

What you write about the prospects of particle physics in the US is shoking, seems the governement wants to completely pull the country out of the game :-/

Are there possibilities to obtain the funding needed to reasonably do particle physics from other sources than the governement? I mean from financially powerfull people or from well doing companies in the economic system who appreciate the value of fundamental research and who are not that short sighted as the politicians?

In your country the idea of funding fundamental research by the governement seems to be completely broken now …