Above the blackboard in my office I have a fading copy of the picture D’ou venons nous? Que sommes nous? Ou allons nous? by Paul Gauguin. At the European Laboratory for Particle Physics, CERN, where I work as a theoretical physicist, these are some of the questions that we are trying to answer using particle physics.
We describe all the visible matter in the Universe and the way it behaves in terms of particles and the forces acting between them. The simplest theoretical framework for this description is called the Standard Model. It divides matter particles into two categories: quarks, which make up protons and neutrons, and hence nuclei; and leptons, which include electrons and other charged particles, as well as neutrinos. There are four known interactions between these fundamental particles: the strong nuclear force, electromagnetism, the weak force responsible for much radioactivity, and gravity.
Over the past 10 years, the interplay of theoretical predictions and experimental observations has led us to believe that the Standard Model is roughly right. Indeed one of the most successful experiments in particle physics – the discovery of the so-called W and Z particles in 1983 at CERN – verified an important prediction of the Standard Model. In fact, so far, there are no confirmed results from particle physics experiments that actually conflict with the Standard Model.
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Nevertheless, there are a large number of unsatisfactory features of the model that raise more theoretical questions than they answer. And the Large Electron Positron collider (LEP) which was commissioned two years ago at CERN, has been designed to examine the Standard Model in more detail. The collider is a huge ring 25 kilometres in length. It accelerates electrons and their positively charged antiparticles, positrons, so that they smash into each other at an energy which is currently about 90 gigaelectronvolts. LEP is now testing the Standard Model at a higher order of magnitude of precision than was ever possible before. Also, LEP is beginning to investigate with some success theoretical ideas that go beyond the Standard Model. These extensions not only sweep away some of the inadequacies of the model but also help to explain how the Universe evolved in the way it did. Indeed, theorists are now combining particle physics and cosmology into a coherent framework for understanding nature. The high energies of LEP, for example, recreate the conditions that were prevalent in the Universe only 10-10 seconds after it exploded into existence in the big bang.
Some of the latest results from LEP indicate that there will be some interesting new physics at energies of around 1000 gigaelectronvolts – equivalent to examining the Universe at a much earlier period of 10-12 seconds. Such energies will be readily attainable with the proton-proton colliders such as the Large Hadron Collider to be built at CERN and the Superconducting Super Collider being built in the US. Both accelerators are due to be ready by the end of the decade. So the results from LEP give physicists some insight into the experiments to be carried out at the LHC and at the SSC. To see how this will work we need now to look at the Standard Model in a little more detail. Theorists employ a powerful and aesthetically pleasing approach to explaining the behaviour of particles which embodies the mathematical notion of symmetry. These symmetries are expressed in terms of the properties of the particles, or quantum numbers, describing electrical charge, spin and so on. For example, each particle has a corresponding oppositely charged antiparticle related by C symmetry, and particles with opposite spins, are related by parity (called P symmetry). The changes that particles can undergo when the direction of the arrow of time is reversed are related by T symmetry. The individual symmetries C, P and T are all approximate but their combination, called CPT, is believed to be exact. The next thing to note is that the matter particles – six flavours of quarks and six leptons – come in ‘generations’ with two quarks and two leptons in each generation. The first generation consists of the up and down quarks and the electron and its accompanying neutrino, the second contains the strange and charm quarks, the muon and its neutrino, and the third, the top and bottom quark, the tau particle and neutrino.
The forces of nature
The Standard Model uses what are called gauge theories to describe three of the four forces that particles feel – the strong, electromagnetic and weak interactions. These theories are also based on symmetry, describing the interactions in terms of the exchange of particles called gauge bosons. The electromagnetic force is carried by photons, the weak force by neutral Z bosons and charge, and the strong force by gluons. In recent years, theorists have been attempting to combine the forces into a unified gauge theory. In 1967 Sheldon Glashow, Steven Weinberg and Abdus Salam combined the electromagnetic theory called quantum electrodynamics with the gauge theory of weak interactions into an electroweak gauge theory. Indeed, the discovery of the W and Z particles was the culmination of predictions of the electroweak theory.
Although such predictions have agreed very well with experiment, the Standard Model is called a model rather than theory because no one regards it as the last word on elementary particles and their interactions. Many of their attributes are put in by hand, for instance the quantum numbers that describe properties such as charge and spin. The Standard Model contains at least 20 parameters which it does not pin down. They include the masses of the quarks and leptons, and the W and Z bosons, the strengths, or couplings, of the forces, two other parameters, which specify the lowest possible energy state (in other words, the energy of vacuum when all the particles and fields have been removed), and the four other parameters needed to describe the couplings of leptons to the charged W bosons. The Standard Model also doesn’t predict how many generations of particles there are.
We can gather all the theoretical problems arising from the Standard Model into three categories: the problems of flavour, mass and unification. Take the problem of flavour first. We would like to explain why there are the number of quarks and leptons there are; how the ratios of the different masses arise and why quarks and leptons decay into each other at the rates they do. Our present situation resembles that of the Russian chemist Dmitri Mendeleev in 1869, who classified about two-thirds of the chemical elements known into the periodic table which incorporated some of their empirical properties, but he did not have a theory to explain how the periodic table arose. It took quantum mechanics and Niels Bohr’s theory of atomic structure to explain it.
Next there is the problem of mass. Why do matter particles and some gauge bosons have mass while photons and gluons are mass-less? Within the Standard Model theorists have to postulate a mythical particle called the Higgs boson which gives the other particles mass. So far no one has seen any experimental evidence for the Higgs. A consistent theory of the Higgs boson is likely to involve a symmetry beyond those already mentioned. One important idea is called supersymmetry. It encompasses the particles called fermions with a spinof one half and the force particles,the bosons, which have integral spin. This leads to whole new family of particles not yet discovered because every fermion has a supersym-metric boson partner and every boson has a fermion partner.
Finally, there is the problem of unification. Theorists would like to unify all the known particle interactions into one gauge theory – a grand unified theory, or GUT, of which there are several candidates. This would mean unifying the electroweak theory with the theory of strong interactions called quantum chromodynamics.
The ultimate goal is to include the force of gravity by formulating a satisfactory quantum theory of gravity. Such a theory of everything, or TOE, would explain the origins of space and time themselves as well as the quantum numbers of all the particles. The only candidate for such a theory is string theory, in which the known particles are not infinitesimal, point-like objects as they now appear, but different modes of vibration of extended loops of string. In fact, I am working on ways of making the grand unified theory and supersymmetry fit with string theory, and also solving the problem of flavour in a novel way.
How is LEP probing the Standard Model and its possible extensions? The particle collisions at LEP produce large amounts of Z particles, up to 40 000 a day, which decay into pairs of quarks, pairs of leptons and pairs of neutrinos. By measuring the mass of the Z and studying the rates at which the different decays happen, experimentalists can glean information about the model. The LEP accelerator will be upgraded in a few years the addition of further accelerating elements to enable us to increase the collision energy to that which can produce pairs of W particles.
So far neither LEP nor any other accelerator has detected the top quark which is absolutely necessary for the Standard Model to remain intact. Unfortunately, the model does not predict the mass of the top quark, and it is probably too heavy to be found at LEP. Nevertheless, experiments at LEP have given useful indirect constraints on its mass. When experimenters looked at the mass of the Z particle and the ways it decayed, they could measure the relative strengths of the weak and electromagnetic forces. The value of the top quark’s mass affects the ratio slightly even though it cannot actually be produced. This is because the top quark can participate in the decays as a ‘virtual’ particle by virtue of the uncertainty principle of quantum mechanics. By comparing the ratio measured at LEP with that measured in experiments in other fields, such as atomic physics, we can work back and calculate what must be the limits on the mass of the top quark. We find that the top quark mass has to be about 125 gigaelectronvolts, with a probable error of about 20 per cent. Comparing this prediction and the mass of the top quark when it is discovered will be a crucial test of the Standard Model.
Experiments at LEP have not found any direct evidence yet for the Higgs boson either, despite having reached a wider range of masses than people had thought possible at this stage of the game. These direct searches for the Higgs are continuing and may yet find it. Some information correlated with that about the top quark mass is indeed now emerging, but it will not be very useful for constraining the Higgs boson until the top quark mass is measured directly.
Nevertheless, measurements provided by LEP are already ruling out some ideas about the nature of the Higgs boson. Some theorists have suggested that the Higgs boson might not be elementary but made of other particles, perhaps a bound state of a top quark or antiquark, or of new particles nicknamed ‘techniquarks’ which are bound to each other by very strong new forces called ‘technicolour’ interactions. These models seem to be ruled out by the indirect LEP measurements of the top quark and the Higgs boson masses respectively.
So far we have been considering LEP measurements of the Z boson mass and visible decays into quarks and leptons. LEP has also been able to measure the rate at which the Z boson decays into neutrinos. In 1989, soon after LEP was commissioned, the total number of neutrinos was three. The Standard Model tells us that this also determines the total number of quark and lepton families. LEP’s fantastic profusion of Zs enables us to measure this sort of decay very easily. We now know that any new neutral particles are produced at less than one-tenth the rate of any neutrino. This is a powerful constraint on possible extensions to the Standard Model.
This has important consequences for cosmology. Astrophysicists find observational evidence that the bulk of the matter in the Universe is invisible, on scales ranging from galactic halos to clusters of galaxies. Moreover, accepted methods of calculating how elements were formed in the early Universe only work if the total amount of ordinary matter in the Universe is less than one-tenth of the critical density needed to halt its expansion. Current theories, however, require the density of matter in the Universe to be the same as this critical density. Some of the dark matter is undoubtedly conventional, but most physicists believe that most of it consists of some neutral unknown particle.
Theorists have suggested many candidates. These include massive neutrinos, the lightest supersymmetric particles – possibly photinos, Zinos or Higgsinos (the supersymmetric partners of the photon, Z and Higgs bosons) and another boson predicted in theories going beyond the Standard Model called the axion which was invented to keep the strong interactions symmetrical with respect to the direction of the arrow of time.
LEP cannot exclude the possibility that one of the three known neutrinos has a small mass, but it does exclude the existence of any extra neutrino with mass up to 40 gigaelectronvolts or more. Cosmologists believe that there could not be enough of such massive neutrinos left in the Universe to provide the critical density. This would apply to ‘sneutrinos’, the supersymmetric partners of neutrinos. However, LEP does leave open the possibility that the lightest supersymmetric particle could provide the critical density, although experiments infer that such a ‘neutralino’ must weigh as least 10 or 20 gigaelectronvolts.
What evidence is there for supersymmetric particles? If we measure the ratio of the strengths of the weak and electromagnetic forces from the way the Z decays, we can also measure the strength of the strong force from the Z decay (and elsewhere). If a grand unified theory was perfectly symmetrical, all three forces would have equal strengths. It is a fundamental tenet of a grand unified theory that at high enough energies – the situation 10-35 seconds of the start of the big bang – the interactions would be symmetrical. We find that the ratio of the weak and electromagnetic coupling is about 10 per cent below that required to become equal to the strong forces, if only the particles in the Standard Model are included. That’s close, but not close enough.
It turns out that supersymmetry remedies this discrepancy. Adding supersymmetric particles to the Standard Model changes the rate at which the strengths of the forces approach each other as energy is increased. If you add to each of the known particles its expected supersymmetric partner, theory and experiment agree to within 1 per cent. This agreement can be used to argue that the supersymmetric particles cannot weigh more than about 10 000 gigaelectronvolts.
Grand unified theories based on supersymmetry also predict three generations of matter particles. Just as the couplings converge to a certain value at a high enough energy, so do the masses of some quarks and leptons. Again, this allows you to calculate the ratios of the masses as they diverge. For example, starting from the mass of the tau lepton in the third generation of particles you can successfully predict the mass of the bottom quark. But this prediction only works if there are no more than three generations. In fact this is why I and some other theorists predicted the existence of only three generations years before theories of cosmological nucleosynthesis and LEP experiments converged on this number.
These empirical tests of a grand unified theory using data from LEP also bring us tantalisingly close to a theory of everything because the mass-energy scale at which the strengths of the strong, weak and electromagnetic interactions appear to become equal is close to that predicted by string theory.
Is there another way in which string theory can be tested by data from LEP? One possibility is that the relative strengths of the weak and electromagnetic interactions might differ slightly from those predicted by grand unified theories. Another intriguing feature of string theory is that it suggests that the top quark should be heavy, weighing around 100to 190 gigaelectronvolts, consistent with the range already indicated indirectly from precision data from LEP. From the point of view of string theory the deeper puzzle is not why the top quark is so heavy, but rather why the other quarks and leptons are so light.
Is there a need for a further accelerator after LEP? The answer is yes. The outstanding problem with the Standard Model that seems most likely to be solved is that of mass: there are firm arguments that the Higgs boson (and very likely its supersymmetrical acolytes) should have masses less than about 1000 gigaelectronvolts.
The technology does not yet seem available to cover this energy range with an electron-positron collider such as LEP, but it can be covered with a high energy proton-proton collider. The projects to build the LHC at CERN and the SSC in the US are now in their preliminary stages. The SSC is designed to have a higher energy, but the LHC would have a higher collision rate. They would probably each have only two major detectors, specialising in different ways of looking at the Higgs boson or supersymmetric particles.
In view of the relatively complicated nature of the high energy proton-proton collisions and the wealth of new phenomena to be sought, not to mention the well-proven scientific necessity of having rival teams check each other’s results, building both the SSC and the LHC will provide a welcome overlap in their complementary explorations of rich and virgin territory.
John Ellis is head of the Theory Division at CERN in Geneva
