The Higgs, supersymmetry and all that

10 January 2020

John Ellis reflects on 50 years spent working at the forefront of theoretical high-energy physics and whether the field is ripe for a change of paradigm.

John Ellis

What would you say were the best and the worst of times in your half-century-long career as a theorist?

The two best times, in chronological order, were the 1979 discovery of the gluon in three-jet events at DESY, which Mary Gaillard, Graham Ross and I had proposed three years earlier, and the discovery of the Higgs boson at CERN in 2012, in particular because one of the most distinctive signatures for the Higgs, its decay to two photons, was something Gaillard, Dimitri Nanopoulos and I had calculated in 1975. There was a big build up to the Higgs and it was a really emotional moment. The first of the two worst times was in 2000 with the closure of LEP, because maybe there was a glimpse of the Higgs boson. In fact, in retrospect the decision was correct because the Higgs wasn’t there. The other time was in September 2008 when there was the electrical accident in the LHC soon after it started up. No theoretical missing factor-of-two could be so tragic.

Your 1975 work on the phenomenology of the Higgs boson was the starting point for the Higgs hunt. When did you realise that the particle was more likely than not to exist?

Our paper, published in 1976, helped people think about how to look for the Higgs boson, but it didn’t move to the top of the physics agenda until after the discovery of the W and Z bosons in 1983. When we wrote the paper, things like spontaneous symmetry breaking were regarded as speculative hypotheses by the distinguished grey-haired scientists of the day. Then, in the early 1990s, precision measurements at LEP enabled us to look at the radiative corrections induced by the Higgs and they painted a consistent picture that suggested the Higgs would be relatively light (less than about 300 GeV). I was sort of morally convinced beforehand that the Higgs had to exist, but by the early 1990s it was clear that, indirectly, we had seen it. Before that there were alternative models of electroweak symmetry breaking but LEP killed most of them off.

To what extent does the Higgs boson represent a “portal” to new physics?

The Higgs boson is often presented as completing the Standard Model (SM) and solving lots of problems. Actually, it opens up a whole bunch of new ones. We know now that there is at least one particle that looks like an effective elementary scalar field. It’s an entirely new type of object that we’ve never encountered before, and every single aspect of the Higgs is problematic from a theoretical point of view. Its mass: we know that in the SM it is subject to quadratic corrections that make the hierarchy of mass scales unstable.

Every single aspect of the Higgs is problematic from a theoretical point of view

Its couplings to fermions: those are what produce the mixing of quarks, which is a complete mystery. The quartic term of the Higgs potential in the SM goes negative if you extrapolate it to high energies, the theory becomes unstable and the universe is doomed. And, in principle, you can add a constant term to the Higgs potential, which is the infamous cosmological constant that we know exists in the universe today but that is much, much smaller than would seem natural from the point of view of Higgs theory. Presumably some new physics comes in to fix these problems, and that makes the Higgs sector of the SM Lagrangian look like the obvious portal to that new physics.

In what sense do you feel an emotional connection to theory?

The Higgs discovery is testament to the power of mathematics to describe nature. People often talk about beauty as being a guide to theory, but I am always a bit sceptical about that because it depends on how you define beauty. For me, a piece of engineering can be beautiful even if it looks ugly. The LHC is a beautiful machine from that point of view, and the SM is a beautiful theoretical machine that is driven by mathematics. At the end of the day, mathematics is nothing but logic taken as far as you can.

Do you recall the moment you first encountered supersymmetry (SUSY), and what convinced you of its potential?

I guess it must have been around 1980. Of course I knew that Julius Wess and Bruno Zumino had discovered SUSY as a theoretical framework, but their motivations didn’t convince me. Then people like Luciano Maiani, Ed Witten and others pointed out that SUSY could help stabilise the hierarchy of mass scales that we find in physics, such as the electroweak, Planck and grand unification scales. For me, the first phenomenological indication that indicated SUSY could be related to reality was our realisation in 1983 that SUSY offered a great candidate for dark matter in the form of the lightest supersymmetric particle. The second was a few years later when LEP provided very precise measurements of the electroweak mixing angle, which were in perfect agreement with supersymmetric (but not non-supersymmetric) grand unified theories. The third indication was around 1991 when we calculated the mass of the lightest supersymmetric Higgs boson and got a mass up to about 130 GeV, which was being indicated by LEP as a very plausible value, and agrees with the experimental value.

There was great excitement about SUSY ahead of the LHC start-up. In hindsight, does the non-discovery so far make the idea less likely?

Certainly it’s disappointing. And I have to face the possibility that even if SUSY is there, I might not live to meet her. But I don’t think it’s necessarily a problem for the underlying theory. There are certainly scenarios that can provide the dark matter even if the supersymmetric particles are rather heavier than we originally thought, and such models are still consistent with the mass of the Higgs boson. The information you get from unification of the couplings at high energies also doesn’t exclude SUSY particles weighing 10 TeV or so. Clearly, as the masses of the sparticles increase, you have to do more fine tuning to solve the electroweak hierarchy problem. On the other hand, the amount of fine tuning is still many, many orders of magnitude less than what you’d have to postulate without it! It’s a question of how much resistance to pain you have. That said, to my mind the LHC has actually provided three additional reasons for loving SUSY. One is the correct prediction for the Higgs mass. Another is that SUSY stabilises the electroweak vacuum (without it, SM calculations show that the vacuum is metastable). The third is that in a SUSY model, the Higgs couplings to other particles, while not exactly the same as in the SM, should be pretty close – and of course that’s consistent with what has been measured so far.

To what extent is SUSY driving considerations for the next collider?

I still think it’s a relatively clear-cut and well-motivated scenario for physics at the multi-TeV scale. But obviously its importance is less than it was in the early 1990s when we were proposing the LHC. That said, if you want a specific benchmark scenario for new physics at a future collider, SUSY would still be my go-to model, because you can calculate accurate predictions. As for new physics beyond the Higgs and more generally the precision measurements that you can make in the electroweak sector, the next topic that comes to my mind is dark matter. If dark matter is made of weakly-interacting massive particles (WIMPs), a high-energy Future Circular Collider should be able to discover it. You can look at SUSY at various different levels. One is that you just add in these new particles and make sure they have the right couplings to fix the hierarchy problem. But at a more fundamental level you can write down a Lagrangian, postulate this boson-fermion symmetry and follow the mathematics through. Then there is a deeper picture, which is to talk about additional fermionic (or quantum) dimensions of space–time. If SUSY were to be discovered, that would be one of the most profound insights into the nature of reality that we could get.

If SUSY is not a symmetry of nature, what would be the implications for attempts to go beyond the SM, e.g. quantum gravity?

We are never going to know that SUSY is not there. String theorists could probably live with very heavy SUSY particles. When I first started thinking about SUSY in the 1980s there was this motivation related to fine tuning, but there weren’t many other reasons why SUSY should show up at low energies. More arguments came later, for example, dark matter, which are nice but a matter of taste. I and my grandchildren will have passed on, humans could still be exploring physics way below the Planck scale, and string theorists could still be cool with that.

How high do the masses of the super-partners need to go before SUSY ceases to offer a compelling solution for the hierarchy problem and dark matter?

Beyond about 10 TeV it is difficult to see how it can provide the dark matter unless you change the early expansion history of the universe – which of course is quite possible, because we have no idea what the universe was doing when the temperature was above an MeV. Indeed, many of my string colleagues have been arguing that the expansion history could be rather different from the conventional adiabatic smooth expansion that people tend to use as the default. In this case supersymmetric particles could weigh 10 or even 30 TeV and still provide the dark matter. As for the hierarchy problem, obviously things get tougher to bear.

What can we infer about SUSY as a theory of fundamental particles from its recent “avatars” in lasers and condensed-matter systems?

I don’t know. It’s not really clear to me that the word “SUSY” is being used in the same sense that I would use it. Supersymmetric quantum mechanics was taken as a motivation for the laser setup (CERN Courier March/April 2019 p10), but whether the deeper mathematics of SUSY has much to do with the way this setup works I’m not sure. The case of topological condensed-matter systems is potentially a more interesting place to explore what this particular face of SUSY actually looks like, as you can study more of its properties under controlled conditions. The danger is that, when people bandy around the idea of SUSY, often they just have in mind this fermion–boson partnership. The real essence of SUSY goes beyond that and includes the couplings of these particles, and it’s not clear to me that in these effective-SUSY systems one can talk in a meaningful way about what the couplings look like.

Has the LHC new-physics no-show so far impacted what theorists work on?

In general, I think that members of the theoretical community have diversified their interests and are thinking about alternative dark-matter scenarios, and about alternative ways to stabilise the hierarchy problem. People are certainly exploring new theoretical avenues, which is very healthy and, in a way, there is much more freedom for young theorists today than there might have been in the past. Personally, I would be rather reluctant at this time to propose to a PhD student a thesis that was based solely on SUSY – the people who are hiring are quite likely to want them to be not just working on SUSY and maybe even not working on SUSY at all. I would regard that as a bit unfair, but there are always fashions in theoretical physics.

Following a long and highly successful period of theory-led research, culminating in the completion of the SM, what signposts does theory offer experimentalists from here?

I would broaden your question. In particle physics, yes, we have the SM, which over the past 50 years has been the dominant paradigm. But there is also a paradigm in cosmology and gravitation – general relativity and the idea of a big bang – initiated a century ago by Einstein. The 2016 discovery of gravitational waves almost four years ago was the “Higgs moment” for gravity, and that community now finds itself in the same fix that we do, in that they have this theory-led paradigm that doesn’t indicate where to go next.

The discovery of gravitational waves almost four years ago was the “Higgs moment” for gravity

Gravitational waves are going to tell us a lot about astrophysics, but whether they will tell us about quantum gravity is not so obvious. The Higgs boson, meanwhile, tells us that we have a theory that works fantastically well but leaves many mysteries – such as dark matter, the origin of matter, neutrino masses, cosmological inflation, etc – still standing. These are a mixture of theoretical, phenomenological and experimental problems suggesting life beyond the SM. But we don’t have any clear signposts today. The theoretical cats are wandering off in all directions, and that’s good because maybe one of the cats will find something interesting. But there is still a dialogue going on between theory and experiment, and it’s a dialogue that is maybe less of a monologue than it was during the rise of the SM and general relativity. The problems we face in going beyond the current paradigms in fundamental physics are the hardest we’ve faced yet, and we are going to need all the dialogue we can muster between theorists, experimentalists, astrophysicists and cosmologists.

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