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Particle physics 2000 – Particle physics tries to answer big questions. Why is there more matter than anti-matter in the Universe; where does mass come from; and what holds the Universe together? Recently British physicists proposed a strategy for research called Particle physics 2000 which was based on these three questions and their implications. The plan is to concentrate on studying the asymmetry associated with the weak force, hunting the Higgs particle which is supposed to give other particles mass, and finally, searching for dark matter which may make up most of the Universe. Over the next few weeks, ¿ìè¶ÌÊÓƵ will publish three articles to explain the theory and experiments behind these priorities for fundamental research

We live in an asymmetrical Universe, built mainly from atoms in which negatively charged electrons orbit tiny nuclei made of positively charged protons and neutral neutrons. Antimatter – the ‘mirror’ form of matter with positive ‘electrons’ circulating a negative nucleus – does not seem to exist naturally in any great quantity. Yet the equations describing how the basic subatomic particles behave are symmetrical between matter and antimatter. According to current cosmological ideas these equations governed the formation of subatomic particles in the early Universe, and should have produced equal amounts of matter and antimatter. So what happened to this initial symmetry between matter and its mirror form?

In 1967 the Soviet theorist Andrei Sakharov showed that for there to be more matter than antimatter, three conditions are needed. First, there should have been a period in the early Universe when the processes taking place were well out of equilibrium; secondly, the proton (and the antiproton) must be unstable because, otherwise they can only be created and annihilated in pairs and so would always remain in balance; and thirdly, matter and antimatter must be different in other ways besides having a different electric charge. Without this extra asymmetry protons and antiprotons would decay or recombine at the same rate and we would still be left with a symmetrical Universe.

Are there any subatomic particles that behave differently from their antiparticles? As it happens, kaons show this matter-antimatter asymmetry. Experiments can detect a subtle difference in the way neutral (uncharged) kaons and antikaons behave. This tiny effect may not be connected with the grander asymmetry between matter and antimatter in the Universe. However, trying to understand the results of the experiments may shed some light on the asymmetry at work in the early stages of the Universe. There is an additional bonus from studying the asymmetry in neutral kaons. It may explain why the Universe is blessed with more fundamental particles than seem necessary to make normal, stable matter.

Symmetry has an important role in creating elegant mathematical pictures of the world in terms of elementary particles and the forces between them. It can help to simplify calculations. But more fundamentally, symmetry describes the well known laws of conservation. For example, the symmetries in the equations describing collisions between particles in relation to space and time express the property that the total amounts of energy and momentum are the same after the collision as they were before. Similarly, the conservation of electric charge reflects symmetry in the equations of the theory of electromagnetism. So, symmetry in physics has more than a purely aesthetic appeal.

When we consider collisions between particles (and between antiparticles), three special symmetries are needed to complete the picture. They are called ‘parity’, ‘charge conjugation’ and ‘time reversal’, or P, C and T. They are important because any theory describing how the particles interact, such as the so-called Standard Model, must look the same after applying all three symmetries. Each of the symmetries P, C and T is like a mirror that physicists can apply to their mathematical descriptions of particles. In the language of quantum mechanics, a particle is described by a wave function, which when squared gives the probability of finding the particle in a given state at a particular moment. The ‘mirrors’ act on these wave functions.

The parity mirror, for example, reverses the signs of the coordinate system in which you define the wave function. As Figure 1 shows, this mathematical mirror produces a complete inversion in space, rather than the reflection you get in a real mirror. The charge-conjugation mirror exchanges particles for antiparticles and vice versa (see Figure 2a). And the operation of time-reversal exchanges ‘before’ and ‘after’ (see Figure 2b). These mathematical mirrors describe real physical processes. For example, to test the symmetry of the time-reversal mirror we could compare the probability that an electron interacted with a proton to produce a neutrino and a neutron with the probability of the reverse process.FIG-mg18164802.jpg

The worlds on each side of these mirrors could be equally viable. But nature is more devious. Although there are four fundamental forces between subatomic particles – the electromagnetic force, the strong and weak nuclear forces and gravity – only the first two respect each of these symmetries separately. The weak force – which underlies radioactivity in which beta particles (electrons) are emitted, and the chain of processes that fuels the Sun – has no respect for parity symmetry. It ‘violates’ parity.

How do we know that the weak force ignores the parity mirror? The neutrino interacts with other matter only through the weak force (and gravity for which there is as yet no good quantum theory so we ignore it). Neutrinos are emitted whenever neutrons decay, and also bombard the Earth in vast numbers emitted from the nuclear reactions at the Sun’s core. Each neutrino always spins like a left-handed screw thread – anticlockwise about its direction of motion. The antineutrino, by contrast, always spins in a right-handed fashion. The parity mirror would turn a left-handed neutrino into a right-handed neutrino (see Figure 3a) – something that does not exist in nature. The neutrino is like a vampire: it has no reflection in the parity mirror.FIG-mg18164803.jpg

However, it is possible to restore the symmetry in the equations by using a different mirror – one that not only performs the parity operation, but also changes particles for antiparticles. This combined operation of charge conjugation and parity is called ‘CP’. To check that the CP operation does restore symmetry, look at what it does to the neutrino (see Figure 3b). The left-handed particle becomes a right-handed antiparticle, just as experiments show. CP therefore appears to give a symmetrical image even of the weak force. Once you cross into the looking-glass world of the CP mirror, there is no way of deciding which world you are in, even though one is predominantly matter and the other antimatter.FIG-mg18164803.jpg

EXPERIMENT WITH AN ALIEN

This means that if you were to communicate with aliens in a far-off galaxy, you would have no way of knowing whether they were built from matter or antimatter – which would be essential before making physical contact, because when matter and antimatter meet they annihilate into pure energy. Luckily there is an experiment you could ask the aliens to perform before inviting them to Earth, in which CP symmetry is violated.

In 1964, James Cronin, James Christenson, Rene Turlay and Val Fitch, working at the Brookhaven National Laboratory in New York, discovered that on rare occasions neutral kaons violate CP symmetry. The neutral kaon is a subatomic weirdo. One of its strangest features is that both the neutral kaon and its antiparticle decay in the same way – into two particles called pions. But if the neutral kaon and its antiparticle decay in the same way, then how do you tell the difference between them?

The answer is that you can’t. But that doesn’t matter because in quantum theory not knowing the outcome of an event is quite normal. Physicists describe quantum processes using statistical techniques; in other words they assess the probabilities of things happening. The usual technique is to add together all possible outcomes – or, to use technical language: ‘to form a superposition of all the appropriate wave functions’. This gives the most probable outcome – the resulting particle state. It turns out that when you try to detect neutral kaons what you actually see are not pure kaons and antikaons but two different ‘quantum mixtures’ of them.

The two mixtures decay in very different ways. One type lives for about 10-10 seconds before decaying almost always into two pions; this particle is called K-short. The other, which lives 600 times as long, is called K-long, and hardly ever decays into two pions, decaying instead into three pions, or into pions, neutrinos and electrons or muons.

What has this to do with symmetry and the CP mirror? It turns out that if symmetry in the CP mirror is exact, then the K-long should never decay to two pions in the way that the K-short almost always does. But, as Cronin and Fitch showed, on rare occasions the K-long does decay into two pions. CP symmetry is not inviolate, and there is an experiment that you can ask the aliens to perform before inviting them for dinner .

CP violation in neutral kaons is more than a curiosity, however. It is the only asymmetry between matter and antimatter that physicists can observe and study in detail, apart from that shown by the Universe as a whole. CP violation may, therefore, cast light on the grander mystery of why there is more matter than antimatter in the Universe.

THE GENERATION GAME

CP violation has another important role; it can be used to test the so-called Standard Model of particle physics. According to this model, all matter is built from two kinds of particles – the quarks and the leptons. The quarks make up many particles such as the everyday protons and neutrons of the atomic nucleus, and the more exotic short-lived pions and kaons. Quarks all feel the strong force which holds nuclei together. Leptons on the other hand, such as the electron and the neutrino, do not feel the strong force.

Studies of cosmic rays and of high-energy interactions at particle accelerators reveal that there are probably six types of quark (called up, down, strange, charm, bottom and top) and six leptons (the electron, muon, tau and their neutrino partners). The Standard Model classifies these fundamental particles into three ‘generations’ of increasing mass, each containing two quarks, one charged lepton and one neutrino. The first generation consists of the up and the down quarks, the electron and the electron-neutrino; in the second generation are the strange and the charm quarks, the muon and its neutrino; and the third generation includes the top and the bottom quarks, the tau and its neutrino partner.

Everyday matter is made from just the lightest generation. So why is there more than one generation? Are there any more still to be found? Recent results from LEP, the Large Electron-Positron Collider at the European particle physics laboratory, CERN, have answered the second question. They indicate that there can be no more than three types of neutrino, and this in turn implies that there can be no more than three generations of particles. But this still does not explain why there are three generations, and not two or only one. CP violation may help us to understand this puzzle.

The Standard Model shows that quarks can change from one type (or ‘flavour’) to another, through the weak force. For example, kaons contain a strange quark (or antiquark) but pions do not, so when a kaon decays into pions, the strange quark must change flavour into another kind of quark. In 1973, when physicists thought that three quarks were enough to build the Universe, Makoto Kobayashi and Toshihide Maskawa, at the University of Nagoya, considered all the possible flavour changes if there were six types of quark. Experiments have since revealed that there do seem to be six types of quark, but no more.

Now let’s look more closely at the neutral kaon’s wayward behaviour in the light of the six-quark idea of Kobayashi and Maskawa. Experiments and theory imply that the neutral kaon can change into its anti partner by its constituent quarks changing flavour. Comparing calculations for the process with experimental measurements reveals that at least the up quark and the charm quark flavours must be involved. And, if you include a smidgeon of top quark as well you may introduce just the right touch of CP violation to explain the experimental results. The contribution of Kobayashi and Maskawa was to point out that CP violation was possible in this way provided that there were at least three generations of quarks. So it looks as if three generations are necessary to explain asymmetry in nature.

DETECTING CP VIOLATION

If we go further, when the neutral kaon mixtures decay into two pions, the effects of all the generations of quarks introduce a small amount of CP violation into the decay. But the amount of CP violation depends on whether the decay results in two neutral pions or two charged pions. This gives you a number to measure – the difference in the amounts of CP violation for the two decays – which you can then compare with that predicted by theory.

Predicting the difference is tricky as there are many uncertainties in the calculations, not least that its ratio depends on the mass of the top quark. Although no one has seen the top quark yet, we have a good idea of what its mass should be from indirect measurements at LEP and elsewhere. Provided the mass is not too heavy (no more than about 200 times the mass of the proton), the latest theoretical ideas suggest that the amount of CP violation in the two decays should differ by between 0.3 and 1.2 per cent.

To verify this prediction it is necessary to measure a small effect within a small effect. CP violation happens in about 0.3 per cent of K-long decays, and since the expected difference between the rates of decays as shown by the CP violation ratio is less than about 1 per cent, such precision presents a formidable task. Researchers have to detect hundreds of thousands of neutral kaons, distinguish between the K-long and K-short mixtures, pick out the rare K-longs that decay to two pions, and then look for tiny differences in the amount of CP violation between the decays to charged and those to neutral pions.

Nevertheless two groups of researchers, at CERN and at Fermilab in the US, have proved equal to the challenge. Last summer, they presented their latest results at a conference in Geneva. Although their results are not in perfect agreement, each is consistent with the estimates given by the Standard Model. However, neither experiment is precise enough to exclude the possibility that there is no difference between the amount of CP violation in the two decays. So although the Standard Model is looking good, physicists are not yet satisified because the result is not clear-cut. What is needed is still greater precision, with still more data, and both groups propose to continue their efforts. In the meantime, the prediction may become sharper if future experiments can produce the top quark and measure its mass.

Although most physicists think that the CP violation observed in neutral kaons arises from flavour mixing described by the Standard Model, there are other plausible explanations. For example, a new ‘superweak’ force could explain CP violation but would give a ratio of zero. CP violation could also arise from another particle called the Higgs particle, which is supposed to give mass to particles in the Standard Model. Like the top quark it is a tantalising object because it has yet to be discovered. To produce CP violation more than one Higgs particle must exist, and they give rise to almost any value for the ratio.

You can narrow down the possibilities by looking instead for T violation, the violation of time-reversal symmetry (see Figure 2b). This involves studying the neutron. Although the neutron has no net electric charge, it contains quarks that are charged. If this charge is unequally spread out, the neutron will act like a small electric dipole (the electrical equivalent of a short bar magnet). If we apply T-symmetry (see Figure 4) to change the direction of spin of the neutron while leaving the distribution of electric charge unchanged, we see that the configuration is not the same. The small electric dipole combined with its spin is called the electric dipole moment of the neutron, and should be zero in a T-symmetrical world.FIG-mg18164804.jpg

The electric dipole moment of a neutron can be measured and compared with predictions from the Standard Model, the superweak model and the Higgs models. The first two models give a small electric dipole and the third model predicts a large one. A series of beautifully precise experiments at the Laue-Langevin Institute in Grenoble, by a team from the University of Sussex and the Rutherford Appleton Laboratory in the UK, exclude the simplest Higgs models. The experiments are extremely delicate, involving the observation of the decays of neutrons over long periods of time in the presence of oscillating electric fields. The effects are tiny, and so stray electric and magnetic fields have to be kept out.

At present, neutral kaons provide the only evidence we have for CP violation. However, the Standard Model does offer the possibility that it also happens in the decays of similar but heavier neutral particless called B-mesons.

B-mesons are in a sense the kaons of the third generation, in that they contain a bottom quark, whereas the kaons contain a strange quark. However, a B-meson is more than 10 times as heavy as a kaon, and this leads to subtle differences between the two particles. In particular, there are many more ways in which the B-meson can decay. This means that its lifetime is much shorter, of the order of picoseconds (millionths of millionths of a second) rather than nanoseconds (thousandths of millionths of a second).

Although the mixing of the B-meson and its antiparticle can be described exactly as in the kaon system, the two mixed states have nearly the same lifetime because there are so many possible decays – there is no easy way to divide the states into ‘B-short’ and ‘B-long’ on the basis of their lifetimes. So we need to look for new ways to search for CP violation.

Fortunately the kaons provide some guidance, because you can show CP violation in neutral kaons in a different way. The technique is to identify whether the kaon is the normal particle or its anti-partner, by looking at the other particles created in the same interaction producing the kaon. If CP symmetry holds, then the way the number of particles diminishes with time, as they decay, should be same for both kaons and antikaons.

THE FINAL PROOF

This method delivers conclusive, direct proof of the asymmetry between matter and antimatter, but it requires large numbers of decays to rival the precision of the other experiments: even with kaons hundreds of millions of decays must be observed. CPLEAR, an experiment studying kaons, has been running at CERN’s Low Energy Antiproton Ring, LEAR, which can produce millions of kaons a day. The CPLEAR team, from several European institutions including the University of Liverpool, has recently shown that the decay plots for the neutral kaon and the antikaon do show the expected small difference (see Figure 5).FIG-mg18164805.jpg

A similar experiment could also work with B-mesons, although there are some differences. In some cases the asymmetry could be quite large, as much as 10 per cent, compared with 0.3 per cent in kaons. This sounds like good news, but unfortunately the specific decays producing these large asymmetries are very rare. A very large number of B-meson decays will need to be studied before we can hope to see the effect – more than a hundred million, compared with the fewer than a million already studied in experiments across the world.

One possibility for observing such large numbers of B-mesons is to build a ‘B-factory’ – a particle machine – tuned to the appropriate energy for creating high intensities of bottom quarks. This could be built within about five years, and there are several proposals for such machines, in Germany, Japan, Russia, Switzerland and the US, but so far none has received full funding. Another attractive possibility would be to use the Large Hadron Collider (LHC), the next machine proposed for CERN. This will produce hundreds of millions of bottom quarks each year. However, unlike the B-factories, which are designed to produce bottom quarks over and above anything else, the bottom quarks at the LHC will be mixed in with all the other quarks. This means that physicists hoping to study bottom quarks at the LHC will have to develop clever techniques to separate the signal from the background.

We have known of CP violation in the weak force for more than 25 years, but we have still no real understanding of its origin. What we have discovered is that we live in a Universe designed to reveal a tantalisingly small amount of CP violation. Whether this is connected with the greater mystery of why there is more matter than antimatter in the Universe is still unclear. However, experiments that are being planned for the next century should bring us nearer to solving both these puzzles.

Ken Peach is a member of the physics department at the University of Edinburgh. He also works at CERN on CP violation.

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THE QUESTION TO ASK AN ALIEN

Can you tell, before you make physical contact, whether an alien in a distant galaxy lives in a world of matter or antimatter? If the symmetry between matter and antimatter were perfect, there would be no way to distinguish the two worlds – there would be no experiment you could ask the alien to perform which would tell you whether the lightweight particles orbiting the atoms of its world were electrons, as they are in matter, or positrons, as they are in antimatter.

However, CP violation in the decays of the neutral kaons provides the essential asymmetry that allows us to frame a question for the alien to answer. The longer lived neutral kaon, the K-long (K_L), can sometimes decay to produce an electron (e^–) or a positron (e⁺), together with a pion () and a neutrino (). The two decays look like:

_L⁺ +e^– + and K_L^– + e⁺ +

CP violation causes a slight difference between the rates at which these two decays occur, and if you measure the numbers of electrons and positrons produced, you find a slight excess of positrons.

So, you ask the alien to do the same experiment, and then ask about the larger number of particles produced. There is no absolute definition of positive and negative charge, but the alien can compare the charge with that of the ‘electrons’ in its atoms. If the alien says that it measures an excess of particles with the same sign as the particles orbiting its atoms, then you know that these are what we call positrons and the alien’s world is made of antimatter – and you politely decline its invitation to visit.