Some of the profound questions about elementary particles and forces and the universe will be described; questions that might be answered as the Large Hadron Collider at CERN turns on this year. For example: What gives mass to elementary particles? Do all the forces between particles arise from a single basic force? What is the dark matter that makes up one fourth of the universe and is critical to the formation of galaxies? One speculative theory that seeks to address some of these questions is called supersymmetry. It uses quantum variables to describe space and time and suggests that every known particle has a yet-undiscovered superpartner particle. These new particles may soon be discovered at the Large Hadron Collider.

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Well, it’s always a pleasure to be here, to address so many brilliant young students and distinguished and brilliant colleagues. I thought I would talk today on the exciting topic of what awaits us in the near future in particle physics. As you all know we await with increasing excitement the opening of the Large Hadron Collider at CERN. And I wanted to give you a bit of the reasons for the excitement, that the experimenters, the machine accelerators, physicists and the theorists, maybe especially the theorists are feeling in these last few months before new data will flow. We have, as you know, completed in the 20th century a marvellous theory of matter and of force, the Standard Model of Elementary Particles. Many of the laureates here participated in that wonderful adventure. We were a lucky generation or two to have been born at the right time. And the generation of students that I address today is also lucky because they are entering research and physics, especially those who are intending or working in particle physics, at the right time as well. A time where we will, with luck, get marvellous clues from nature itself as to its internal structure. The experimental discoveries in the 20th century lead us finally to complete the Standard Model of Elementary Particles, to identify the basic constituents of matter. All of the matter that we need to construct, all of the matter that we observe on earth. There is of course dark matter, I’ll come back to that. But we have identified these basic constituents of matter that lie, from which we build atoms, from which we build nuclei and quarks and leptons, the electron and the up and down quarks that make up ordinary atoms, their partners, the neutrino and 3 families of quarks and leptons. We’ve identified these basic constituents of matter, measured with increasing precision their masses and mixings, but don’t really understand them. We do understand with great clarity and elegance the basic forces of nature. And in the 20th century we completed the understanding of the atomic and nuclear forces. The electromagnetic force mediated by the photon was understood at the quantum level in the 20th century and confirmed with unbelievable precision, sometimes to one part in a billion or more. But the Standard Model required understanding also of the forces that act within the nuclei that are so hard to discern since they are both very localised within the very small nucleus and their very nature is hidden by their dynamics. And those of course are the strong nuclear force that acts within the nucleus on a hidden quality of the quarks called colour and the weak force that changes one quark to another, one flavour of quark to another or an electron to a neutrino is responsible thus for the transmutation of elements and radioactivity. These forces we learned are consequences of a beautiful symmetry property of nature. A symmetry under local transformations, rotations, but not rotations in space but rather in the space of labels of these particles, labels such as colour or flavour. This is a remarkable achievement, it took maybe since Democritus, 2,000 years to complete. And it seems, much to the disappointment of my experimental colleagues, to work extremely well. There really are no phenomena in the laboratory that are not explained with increased precision by the Standard Model. In fact it works perhaps to the edge of the universe, and we see no reason why it doesn’t work when extrapolated down to the Planck length, there is no paradoxical features of the theory until we get to the Planck length. So this is an extraordinary achievement of fundamental physics and of particle physics but it might be wrong, we haven’t tested it beyond a nano-nanometer. And we suspect that there might be missing elements that we haven’t yet discovered. And the theory raises so many new questions that we are convinced that it must be incomplete in some way. Surely at the Planck length but probably before. In fact I like to say that the most important product of knowledge, like the development of the Standard Model is ignorance. By which I mean not of course bad ignorance, the kind that causes wars and bigotry, but rather informed ignorance. Good questions that can be probed and answered by observation, by experiment and by theory. And we have such questions nowadays, so many that I don’t have time but to discuss perhaps 2 of them. But there’s so many and the questions that we ask today in particle physics, in cosmology, are in many ways much more fascinating and profound than the questions that we were asking when I was your age and just starting to do research in physics. And we’re now perhaps in a position to begin to get important clues as to how to approach the answer to some of these questions. And especially from the Large Hadron Collider which is turning on in CERN, this is a picture of the ring which is of course below ground, running through France and Switzerland, near Lake Geneva, this is the Geneva airport. And what kind of questions can we probe? Well, there are questions within the Standard Model that must be asked, and aspects of the Standard Model that must be confirmed. The nature of the forces is pretty well confirmed in great detail, the nature of matter is pretty well confirmed in great detail. But an important aspect of the Standard Model is the mechanism for the breaking of the symmetry, the local symmetry that underlies the weak interactions. There is an Ansatz, there is a theory for how that symmetry is broken, called the Higgs mechanism which predicts, in the simplest version, a particle, a very distinctive particle which hasn’t yet been observed. The observation of the Higgs particle thus is an important confirmation of the Standard Model. Most of us theorists believe the experiments will confirm the Standard Model but this is crucial. More interesting from my point of view are the new discoveries that are likely at the LHC and I’m going to concentrate just on one possibility, which I think is the most likely and in some ways the most exciting, and that is the potential discovery of supersymmetry. Now, before I start with discussing these particular questions and how the LHC could answer them, let me tell you a bit about what you might think is a boring subject but underlies our knowledge and our ignorance about the fundamental structure of matter and force, namely the properties of the vacuum. It is the vacuum that theorists like myself study all the time, our job is to understand nothing. If we understand the vacuum, the rest is trivial. All the particles that we observe are little fluctuations on the background of the vacuum. So the hard job is to understand the vacuum. It is the properties of the quantum vacuum, in the Standard Model for example, that produce the symmetry breaking that produces the masses of the elementary quarks and leptons. It is the properties of the vacuum in quantum chromo dynamics that produces the antiscreening or asymptotic freedom that confines quarks permanently within nucleons. And it is the symmetry breaking possible in a quantum vacuum that allows us to contemplate new and marvellous symmetries like supersymmetry, it is that dynamics of the vacuum that hides those symmetries from us. But you might think the vacuum is a boring place, for most people this is their picture of the vacuum. This is a good picture of the classical vacuum, the ground state, the lowest energy state of the universe, totally boring. But in quantum mechanics nothing can be that boring. Heisenberg taught us that if you have a pendulum, it can’t be in its classical ground state with no energy, just inert like this, because when you observe it you set it in motion, there is also a zero point motion to any dynamical variable, to any dynamical entity. And in fact that is true of the vacuum. The vacuum is of course full of these quantum fields that mediate electromagnetism, the electromagnetic field and similar fields that mediate the weak and strong nuclear forces. And those fields can’t just be zero, inert, because when you observe them you change their state, you excite them, they are fluctuating like the pendulum, they undergo zero point motion. A field is nothing more than a whole bunch, an infinite number of harmonic oscillators. So this is the picture of the vacuum. We can make this movie of fluctuating fields in the vacuum because we have a good theory which is well tested. This range of nuclear, I mean this is the size of a proton, the dominant fluctuating fields are those of quantum chromodynamics and we can calculate their fluctuations using lattice gauge theory. And this is a movie that’s made of the fluctuating fields in QCD. So this is how you should think about the vacuum, in the real world of this nuclear scales. And it’s a complicated medium that can give rise to complicated phenomena, such as symmetry breaking. And it is the phenomena of symmetry breaking, which was one of the most important discoveries, theoretical discoveries in the 20th century. It allowed us to contemplate new symmetries which were not manifest in the universe as we see it, because those symmetries we understood could be broken. Symmetries of the laws of nature but not apparent or manifest in the state of nature. And you're all acquainted with this phenomena, after all you all know that the laws of physics are invariant under rotations, you rotate the laboratory, you get the same results for all of your experiments, the laws of physics are symmetric or invariant under spatial rotations. And yet this room of course is not, you’re out there and not there. But of course the room is full of people, you came, you sat down. Remove all the people, all the chairs, the air, everything in the room, you´re left with the vacuum. The vacuum is clearly symmetric if the laws are symmetric, not necessarily because remember, the vacuum is this complicated dynamical medium. And the dynamics might order things and break the symmetry as it does in this room. So it is the properties of this complicated dynamical medium that we’re trying to figure out. And in the case of the Standard Model, that is what gives rise to the Higgs mechanism. The famous Mexican hat potential that tells us that the state of a field, the Higgs field, likes to be asymmetric under rotations in the space of labels of this field. The same local symmetry that underlies the electroweak interaction. It is the fact that in this complicated medium, this is the ground state and it’s not symmetric under these rotations. That breaks the symmetry, it is the symmetry, which when unbroken prevents particles, elementary fermions, electrons and quarks from acquiring a mass. And so this mechanism within the electroweak theory can produce masses for the electrons and quarks. It’s the dynamics of this vacuum also that is responsible for the remarkable properties of quantum chromo dynamics. Such as the fact that when quarks are brought together the force between them gets weaker and weaker, that’s known as asymptotic freedom. Very useful because it helps us calculate the backgrounds for the LHC experiments, which are totally dominated by the strong nuclear force, by QCD phenomena, which by now are uninteresting because we understand them. And understanding them and with a weak force we can calculate these backgrounds, a necessary step to dig out the almost invisible signals of new physics at the LHC. It is also the properties of this vacuum that explains how the force between the quarks gets very strong at large distances, leading to quark confinement. In fact we can picture that also using lattice QCD, here’s a movie of what happens in quantum chromo dynamics if you take a quark and an anti quark and pull them apart, again using lattice gauge theory to solve the theory. And here’s the picture, you see that the flux is confined to a tube and simple freshman physics will tell you that if the flux, the colour flux, which is like the electric field in QCD, is confined to a tube, you’ll get a constant force and a linearly increasing energy. That’s why you can’t pull the quarks out of mesons. This is a picture of the proton, when you try to separate the 3 quarks contained in a proton from each other, you develop a kind of a flux tube as well, except it has a 3-fold structure. It is also these properties of the vacuum allow us to contemplate the unification of the forces of nature. The forces of the Standard Model, those 3 forces that act within the atom and the nucleus all appear similar, they’re all consequences of local symmetries. And asymptotic freedom allows us to imagine that the strong force might become equal to the weak force. And indeed, when the Standard Model was extrapolated to high energies, we got the first indication of unification and of unification at a very high energy scale. This scale is so high that gravity becomes important. Gravity is an extraordinarily weak force, down by 40 orders of magnitude in the atom from the atomic and nuclear forces. But gravity is proportional to mass, couples to mass, mass according to Einstein is energy, so if you go to very high energies, the force of gravity increases quadratically. These forces vary logarithmically and they meet at this famous Planck scale, the scale where gravity is a strong force at atomic distances. As strong a force between quarks as is the nuclear force that binds them together. This is a very strong hint from the extrapolation of our present theoretical framework which so far works, that all of the forces of nature might be unified at this immense scale which is almost impossible today for us to imagine probing directly. That of course has led to enormous speculation, some of it wonderful, which I think will survive and eventually might produce our understanding of the unified theory. Most exciting ideas go under the name of string theory and started out at least by imagining that the elementary particles are not pointlike but vibrations of an extended object. I don’t have time to talk about that, maybe later today if you ask questions. Instead I’ll tell you about what we might expect to show up at the LHC, which is almost as exciting, a new symmetry of nature, a quantum symmetry of space and time called supersymmetry, which we believe might very well show up at the LHC. So what is supersymmetry? Well, the easiest way to describe a symmetry is to describe the space on which the symmetry transformations act. So, rotational symmetry of course, which leads to conservation of angular momentum, is describable as rotations of ordinary space. Einstein’s relativity are rotations in spacetime or boosts. So to describe supersymmetry I should describe superspace, so what is superspace? Well, you all know what spacetime is, we use space and time to label events in nature, fields or wave functions or functions of points in space and time, and symmetries are transformations of spacetime or spacetimesymmetries. So,superspace is simply a spacetime where we have more dimensions. You’ve heard of more dimensions, these dimensions I denote by Theta because they are measured in strange units, strange numbers. So the way they are different from X and Y, these new directions in space, is that the numbers used to measure along this axis are non commuting numbers. Numbers so that if you multiple 2 of them in different orders, you get results that differ by a sign, they don’t commute under multiplication. Well,mathematicians invent all sorts of numbers, these numbers are called Grassmannian variables or numbers, they’re not any stranger than the square root of -1, which you’re accustomed to working with, in fact they’re simpler. And you can imagine mathematically a space which has these extra dimensions, fermionic because they don’t commute. And you can imagine rotations between ordinary dimensions and these new dimensions, or among the new dimensions. It turns out, and this was discovered almost 40 years ago or 35 years ago, first in string theory and then extended to ordinary field theories, that there’s a beautiful mathematical structure in which Einstein’s theory of relativity, special and general, fits naturally, which extends space to superspace. Very beautiful, very elegant. One problem: For every particle here, for every boson in a theory involving space and time normally, if you make it supersymmetric and have these extra rotations, you will rotate those bosons into new particles and they will be fermions. You can see this by taking a field which depends on X, the usual spatial coordinates, and these new ones Theta, and make a Taylor series expansion. It’s easy because since Theta times Theta is minus Theta times Theta, it must be 0. So the Taylor series expension only has 2 terms. Grassmannian variables are very neat. And the first term is just an ordinary field, say a boson, the term proportion to Theta must be a fermionic field. Because this variable anti commutes, so must this be an anti commuting field or a fermion field. So it turns out that in supersymmetric theories, for every particle there must be another particle, spin differing by one half unit and different statistics. The quark must be accompanied by what we call a squark, the electron by a selectron, the photon by a photino, everyparticle we’ve ever seen, there’s another particle which we haven’t. Some people say, well, half the particles predicted by supersymmetric theories have been seen. But of course, they’re only the particles we had before. So the theory is ruled out? No way, because of symmetry breaking we can imagine symmetries of the laws of nature that are broken by the vacuum. By this complicated state of the vacuum. And if the scale of supersymmetry breaking is high, say a TeV, those particles, the new particles will weigh about a TeV of mass. And we haven’t yet been able to prove them. But why would you think that this symmetry has anything to do with nature and why should the scale be a TeV. There are 3 very important clues which are deep puzzles, observational and theoretical, based on observation, that convince some of us, like me, that this is a very good bet and I have a lot of 50/50 bets on supersymmetry riding on the LHC. First it helps unify the forces, the extrapolation of the Standard Model to high energies doesn’t, at this point with the incredibly beautiful high precision experiments of LEP, show unification. These 3 curves, or now inverse couplings on a logarithmic scale, don’t meet at a point. But if you add supersymmetry they do beautifully. that that’s the scale of the breaking, so that’s good. Supersymmetry also helps explain the mass hierarchy. The weak scale, the scale of the symmetry breaking of the weak interactions that sets the W mass scale over the Planck mass scale, this fundamental scale in physics is very small, why? We don’t understand that, but we have very beautiful potential explanations if you assume supersymmetric theories with a symmetry breaking at the scale of the W, at about a TeV. And finally dark matter, supersymmetry, supersymmetric extensions of the Standard Model almost automatically produce a candidate for dark matter, which you heard beautifully in George’s talk, permeates the universe. You see in the dark halo around our galaxy or in colliding galaxies. And if the mass scale of supersymmetry breaking again is in the TeV range, you can calculate the abundance of dark matter and it comes out to be 90%. Or viceversa, we see 90% of the matter as dark matter, therefore the scale is. So that is what we hope, some of us, to find at the LHC, confirmation of the Higgs and new things, maybe as exciting as supersymmetry. This is an incredible machine. The energy stored in this machine is so immense that you can compare it to the energy of an aircraft carrier moving at 30 knots. Building such a machine is an incredible achievement of human kind, beyond imagination. Not just the machine but the detectors. This is the compact, hardly compact, hardly small CMS detector, and this is the ATLAS detector, they have these incredible magnets you see here and the detector there, as it was being assembled. These detectors are mind-boggling, it is hard for me to imagine how the experimenters do this. They have something like 100 million electronic channels, a collision rate of 40 million events a second that within nanoseconds have to be reduced to 200 hertz. And even that will accumulate petabytes of data a year, incredible signals, mostly background from which one will have to find a Higgs and supersymmetry, that requires many people and indeed on these detectors 1,000’s of physicists have been working and will work. The Higgs particle may be very light but it turns out to be very difficult to detect since it has large, large backgrounds. Theory tells us in fact that the preferred value has already been excluded, but- this is Chi2- you know, we can easily imagine and expect that it might therefore be an indication that the Higgs particle is right around the corner of the energy that we can now achieve, and maybe the Tevatron is already producing many Higgs and might be a LHC. How will the Higgs particle be discovered? Well, this is a simulation of events, and experimenters and theorists have been trying to analyse the signals for now 15 years or more in a machine like the LHC. It will depend a lot on its mass, theory points to this region, in which the signal unfortunately is very small compared to the background, and these events might take years, I expect the Higgs will be discovered, predict. SUSY is easier and harder. Supersymmetric theories predict many new particles, for every particle we’ve ever seen, there’ll be another super symmetric partner and new particles beyond that probably. Their couplings are all known, the theory is very predictive, it has a symmetry, so we know how they couple. We know the force laws. What we don’t know is the pattern of symmetry breaking the masses and that means we can’t make exact predictions at all. But the rates are bound to be high because supersymmetry, if you supersymmetrise the world, you also super symmetrise the nuclear force and in these proton-proton collisions you mostly have nuclear QCD processes and there’ll be super symmetric versions of that. But the signals are very complicated and it will take a long time to prove that what you claim as supersymmetry really is. The signals are very complicated, you have these protons or bags of quarks hitting and at the microscopic level they produce supersymmetric gluons which decay to other super symmetric particles, and ordinary particles which come out as jets, and leptons come out, and at the end, the lightest supersymmetric partner is likely to be stable and therefore will just zoom through the detector and you’ll never see it. So you get jets and leptons and missing energy because you can’t detect all of the final states. In fact, the missing energy, these lightest supersymmetric particles are the candidates for dark matter. And their observation in these complicated events will be the detection of dark matter. This is a typical event, simulated, you can almost see that something is missing. All of these jets are carrying off a lot of energy in this direction, momentum has to be conserved, there must be some missing energy going out this way, maybe that’s dark matter. So I’m almost done, the discovery of supersymmetry, I would like to remind you, when you read it in the newspapers, just remember that that is the discovery of quantum dimensions of spacetime. We will be observing, as we always do, using both our eyes and our minds, new quantum dimensions of space and time. So that’s a big discovery. So we have a wonderful theory of elementary particles but the best is yet to come. Thank you.

# David Gross (2008)

## The Large Hadron Collider and the Super World

# David Gross (2008)

## The Large Hadron Collider and the Super World

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