What is mass? On an everyday scale, it seems easy enough to understand. The more matter there is in something, the heavier it is. But at smaller scales, at the level of the fundamental particles of matter, mass is not really understood at all. Fortunately, there is some prospect for improving our understanding. High-energy experiments are close to testing the most plausible explanation we have for particle masses. Whether these ideas prove to be right or wrong, the results are guaranteed to guide us towards a clearer appreciation of what is meant by mass.
As Albert Einstein realised early this century, mass is a form of energy – the two are interchangeable. So the masses of atoms and nuclei depend not only on the total mass of their constituents but also on the energy that binds the constituents together. This much has been well understood for the past 70 years, and allows us, for example, to calculate precisely the amount of energy released in radioactive processes. It is when we come to consider the masses of the elementary particles within atoms and nuclei that the problems begin.
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Over the past three decades or so, research in particle physics has led to what is called the Standard Model. The basic components of the Standard Model are the particles of matter and the forces that act upon them. The ‘matter’ particles are the quarks (which make up protons, neutrons and other compound particles) and the leptons (which include the electron). They feel the electromagnetic, weak and strong forces, all of which appear to act through ‘messenger’ particles, called gauge bosons. The quarks and the leptons are also subject to gravity, but its influence is very small in comparison with the other forces, and it has yet to be described in a theory of all the forces.
Recent results from the Large Electron Positron (LEP) collider at the European research centre CERN, have shown that there are no more than six varieties of lepton and, by implication, six varieties of quark. Yet these quarks and leptons encompass a huge variation in mass. The neutral leptons, the neutrinos, are extremely light, and may well be massless, while the masses of the charged leptons vary from the electron to the tau, which is 3600 times as heavy as the electron. Similarly, the quarks vary in mass from those that are fractions of the proton’s mass to the quark known as ‘top’, which is apparently so heavy – more than 100 times the mass of the proton – that it has yet to be observed in experiments (see Figure 1).FIG-mg18174701.GIF
Nor does the wide range in masses end with the ‘matter’ particles. A similar disparity exists among the ‘messenger’ particles, the gauge bosons. The most familiar gauge boson is the photon, the electrically neutral, massless particle that mediates the electromagnetic force. As experiments have proved, the electromagnetic force is intimately related to the weak force, which underlies certain nuclear processes including forms of radioactivity. Yet the carriers of the weak force – the charged W+ and W- particles and the neutral Z 0 particle – are not massless like the photon; they are nearly 100 times as massive as the proton.
Naively, we could imagine that the heavy particles are simply larger or denser than the lighter particles, but that would not bring us any nearer to answering the basic questions. Why do these particles show such a wide range of masses? What indeed gives them their masses?
At present, the Standard Model cannot predict the masses of the quarks and the leptons. But it does contain a mechanism for endowing particles with mass. This is what we call the Higgs mechanism, named after one of the people who devised it, Peter Higgs of the University of Edinburgh.
The Higgs mechanism was invented in the early 1960s to introduce masses into Yang-Mills theories, which were developed initially to describe the strong force in terms of fields akin to the electromagnetic field. These theories showed the same kind of ‘symmetry’ as the well-understood and highly successful theory of electromagnetism. The importance of the Higgs mechanism was that it allowed particles associated with the Yang-Mills fields to have masses – a feature that in the absence of the Higgs mechanism destroyed the underlying symmetry of the theories.
How does the Higgs mechanism give particles mass? The basic idea is of a physical field permeating all of space – even the vacuum of perfectly empty space. This field is similar to an electromagnetic field or to a gravitational field, but not quite the same. Electromagnetic and gravitational fields are both directional – you are held on the Earth’s surface by the gravitational attraction towards the Earth. The Higgs field, on the other hand, has no direction, only a magnitude for all points in space. (In technical terms, the Higgs field is a scalar field, in contrast to the force fields, which are vector fields. This in turn implies that the carrier particle associated with the Higgs field must have zero intrinsic angular momentum, or spin, which is in contrast to the carriers of the force fields, which have spins of one unit.)
The Higgs field also has another relatively unusual property: its energy is minimum, not when the value of the field is zero, but when it has some other value. This is rather like the subatomic behaviour of a magnet. At low energies, below a certain temperature called the Curie temperature, the internal atomic magnets of a magnetic material are all aligned, and the magnetic field has a specific value. But above the Curie temperature, when the energy of the system is sufficiently high, the atomic magnets become randomly aligned and the net value of the magnetic field goes to zero.
You can imagine the potential energy of the Higgs field as being like the potential energy of a ball bearing in the bottom of a wine bottle. When the ball bearing is balanced on top of the bulge in the bottom of the bottle, this corresponds to a Higgs field of zero. There is then a symmetry about the ball bearing’s position because it can roll down in any direction; however, its potential energy is not the minimum possible. The potential energy is minimised when the ball falls to the bottom. This corresponds to the Higgs field having some non-zero value, with the symmetry apparently broken (see Figure 2).FIG-mg18174702.GIF
Suppose now that you can write down the equation that describes the energy of massless carrier particles of a symmetrical field. You find that if you introduce an additional field with the properties described above, then new terms appear in the equation. Some of these new terms refer to the interaction of the two fields, while the others are characteristic of massive particles. In other words, introducing the new field has turned the original theory of massless carrier particles into a theory in which the carrier particles can have masses – including the particle associated with the new field, the Higgs field. This particle is known as the Higgs boson, and it must interact with everything. Indeed, it is these extra interactions introduced by the Higgs mechanism that allow the theory to retain its symmetry. And they provide the key to discovering if nature really does work this way.
Higgs helps theorists
Soon after the invention of the Higgs mechanism, the theorists Steven Weinberg from Harvard in the US and Abdus Salam from Imperial College, London independently realised that it would help in their attempts to build a unified theory of the weak and the electromagnetic forces, based on a single underlying ‘electroweak’ force. One apparent stumbling block on the road to this unification was that the carriers of the weak force, the W and the Z particles, appeared from experimental evidence to be as massive as a moderate-sized nucleus; on the other hand, the photon, the carrier of the electromagnetic force, was clearly massless.
This difference in mass is evident in the apparent relative strengths of the two forces. The weak force, in its effects in radioactive beta decay, for example, is at least 1000 times weaker than the electromagnetic force; moreover, the weak force is limited to distances smaller than a neutron or proton, while the electromagnetic force has an infinite range. We can understand this if the carrier particles of the weak force are heavy: the heavy particles cannot be so readily exchanged, so the force appears weaker and limited in range.
The Higgs mechanism proved to be exactly what Weinberg and Salam needed. It allowed the electroweak theory to retain its basic symmetry between electromagnetic and weak interactions, while giving the W and the Z particles their masses and at the same time leaving the photon massless. At very high energies, the masses of the W and the Z particles are relatively unimportant, and the theory reveals its true symmetry, the weak carriers being in effect massless, just like the photon. It is only at lower energies, such as exist in the everyday world, that the symmetry is hidden, or appears to be broken, as the masses of the weak carriers become important, and the weak and the electromagnetic forces appear to have different strengths.
Predictions confirmed
In 1971, Gerard ‘t Hooft at University of Utrecht discovered that the Higgs mechanism has another important role in electroweak theory. Through its extra interactions, it cancels out meaningless infinite values that otherwise exist in the theory. The ‘t Hooft discovery proved that the theory is self-consistent and so has to be taken seriously. Now, 20 years later, large amounts of experimental data that agree with the theory’s predictions have established the unified electroweak theory as a major component of the Standard Model.
Because the Higgs mechanism makes electroweak theory respectable, it is clearly a crucial part of the Standard Model. Moreover, within the model, the same mechanism gives masses not only to the W and the Z particles, but also to the quarks and the leptons – the particles of matter.
These particles all have masses because they interact with a Higgs field. How massive a particle is depends on how strongly it interacts with the Higgs field. The photon has no mass because it does not interact with the Higgs field; the W and the Z particles do interact with the Higgs field, and so appear massive. In a sense, the Higgs field slows down the W and the Z particles, which is giving them a mass.
There is, however, one major problem with this discussion so far: as yet there is no experimental evidence for the Higgs mechanism. In particular, there is no evidence for even one Higgs boson – the minimum required in any variation of the theory. This is one of the gravest weaknesses of the current version of the Standard Model, so searching for evidence for the Higgs mechanism is now a key feature of research in particle physics. Higgs-like fields have also been incorporated into the latest cosmological theories of the evolution of the Universe.
In the late 1940s, George Gamow proposed the idea that the Universe is expanding from an initial ‘hot big bang’. However, during the following decades the conventional theory became beset by a number of difficulties. In particular, it was impossible to explain how the microwave background – the radiation left over from the heat of the big bang – could be as uniform across the Universe as measurements indicate, smooth to 1 part in 100 000.
This smoothness implies that all the Universe we observe today must have been at the same temperature at the time when the radiation ceased to be in equilibrium with the primordial matter – about 300 000 years after the big bang. And this in turn implies that all the observed Universe must have been in close, thermal contact at this time. But from the measured rate of expansion of the Universe, we know that when we observe the sky in opposite directions, we are looking at regions of space that were too far apart to have had no way of knowing about each other 300 000 years after the big bang, even if they communicated at the speed of light. So how could they have had the same temperature?
Clues from the big bang
In 1980, Alan Guth suggested a variation of the big bang that seemed to resolve this and several other problems. He proposed that early in its history, only 10 -35 seconds after the big bang, the Universe evolved through a period of rapid (exponential) expansion known as ‘inflation’, in which its size doubled every 10 -34 then abandoned. Just so. The region became North Americ seconds. This would, among other things, inflate small regions of the very early Universe to produce huge uniform volumes, such as that of our present observable Universe. Since 1981, the ‘inflationary scenario’ has been reborn several times, but the basic idea remains that the early Universe underwent a period of very rapid expansion.
The current hypothesis for producing inflation requires the existence of a Higgs-like scalar field, very early in the history of the Universe. The assumption is that, in some small region of the Universe, this field settled into an almost stable state analogous to the ball bearing on top of the bump at the base of the wine bottle. In other words, the potential energy in this part of the Universe was not the smallest possible. Such a state is called a ‘false vacuum’, in contrast to the ‘true vacuum’ which corresponds to the lowest energy state. At this stage, the energy density of this particular region of the Universe would be determined by the potential energy of the false vacuum, and as long as the region remained in this state – on top of the bump – its energy density would remain constant as the Universe expanded. The equations of general relativity tell us that this would mean that this small part of the Universe would have expanded exponentially, or in other words, inflated.
A small fluctuation would have been enough to cause the region to ‘roll over’ from false vacuum to true vacuum – to provide the slight nudge needed to knock the ball bearing off. Once on its way to the true vacuum state, this region of the Universe would have continued to expand slowly, as in the standard big bang theory, to become what we observe as the Universe today. And the energy released from the false vacuum would have been converted into all the matter and radiation we observe.
This inflationary scenario has become such an attractive version of cosmology that it is vitally important that its basic ingredients are proven and properly understood. The key feature is the existence of the false vacuum state, and this in turn depends on the existence of a scalar, Higgs-like field. Cosmologists and particle physicists, therefore, have a common interest in discovering if there really do exist in nature scalar fields of the kind that Higgs and others proposed.
One way to prove the existence of a Higgs field is to discover a Higgs boson. Unfortunately, the Standard Model makes no predictions as to how massive the Higgs boson or bosons should be. This is because the mass depends on the potential – in effect, the height of the bulge in the ‘wine bottle’ – and this is something we can discover only through experiment. The simplest possible structure for the Higgs field, used in the basic Standard Model, gives rise to a single, neutral Higgs particle. But there are also more complicated scenarios. One popular possibility incorporates the concept of ‘supersymmetry’. If this symmetry holds, then for all known particles with a spin of 1/2 there should exist heavier partners with spin 1, and vice versa. Supersymmetrical theories have a rich structure, giving rise to several Higgs particles, charged as well as neutral. Only through discovering one or more Higgs particles, or by proving conclusively that they do not exist, will a future theory emerge.
The search for Higgs particles is beginning in earnest with CERN’s latest machine, the Large Electron Positron accelerator (LEP), and will continue when the LEP is upgraded to higher energies. But even LEP II will give access only to the beginning of the trail – exploring masses up to about 80 gigaelectronvolts, or approximately 80 proton masses. The Higgs boson or bosons could have masses 10 times as great as this without violating any fundamental physical principles. To investigate the possibility of these higher masses requires a machine that probes much higher energies, in the region of 1000 gigaelectronvolts, (1 teraelectronvolt) and more.
The surest way that we know at present to reach such energies is with machines that collide beams of protons head-on. Protons contain quarks, and these can radiate W or Z particles through the electroweak force, just as they can radiate photons. (The photons we see as light are radiated by electrons, but at high enough energies protons can also radiate photons, which we can observe as synchrotron radiation, produced when high energy protons curve through magnetic fields.) In the collision of two quarks at sufficiently high energies, both quarks can radiate a W or a Z, which in turn can interact to produce a Higgs particle – an example of the interactions introduced by the Higgs mechanism that preserve the underlying symmetry. In other words, the Higgs particle would be the product of a collision between W or Z particles (see Figure 3).FIG-mg18174703.GIF
How to make Higgs particles
A machine to create Higgs particles in the collisions of quarks would need to accelerate the proton beams to more than 6 teraelectronvolts to ensure that the individual constituents of the protons have collision energies in the regions of 1 teraelectronvolt. This is the design energy of the Large Hadron Collider, proposed for CERN, so investigation of the Higgs mechanism is one of the unresolved areas of basic physics that this machine can begin to attack (‘A supercollider for Europe’, ¿ìè¶ÌÊÓƵrst on the upland, where ponds fed by rainfall dried, 27 July 1991). The same is true for the Superconducting Supercollider being built in Texas. This will collide protons at beam energies of 20 teraelectronvolts.
Searching for Higgs particles at these high energies will demand the greatest ingenuity from experimenters. One of the clearest ways in which a Higgs particle may manifest itself is through its decay back into two Z particles, which can in turn each decay into a lepton and its antiparticle. So the Higgs particle would produce a characteristic ‘signature’ of two lepton-antilepton pairs. A plot of the number of times such events happen against the total mass energy of the two pairs would reveal a peak corresponding to the mass of the unseen Higgs particle. However, experimenters will be searching among the debris from many competing processes for the proverbial needle in a haystack – indeed, only in 10 billion collisions is calculated to produce an observable Higgs particle. So physicists are already developing the technology they will need to be able to sift rapidly through the ‘hay’ in order to find the ‘needles’.
The Z-particle decay should reveal any Higgs particles with masses in a range from around 180 to 800 gigaelectronvolts. Other possibilities will be more difficult to find and will require the collection of much more data, but they should stretch the mass range to between 45 and about 1000 gigaelectronvolts.
The discovery of a Higgs particle will imply that the Higgs mechanism is the means by which nature endows particles with mass. Armed with this knowledge, we will be able to move on to the next big question regarding mass, which the Higgs mechanism does not itself address: why do the particles have the range of masses they do? In the present theory, the masses depend on the coupling of particles to the Higgs field, but this only defers the problem, for we do not know what the couplings should be; we can only determine them from the observed masses. The discovery of a Higgs particle would also imply that scalar fields, with the ‘wine-bottle’ potential energy characteristics, can exist in nature – good news for cosmologists as well as for particle physicists.
Even if no Higgs particles are found, there are bound to be new effects at energies in the region of 1 teraelectronvolt or below. Whatever the results of the next generation of high-energy experiments, we are assured some exciting discoveries about the fundamental nature of matter and, consequently, the Universe we inhabit.
Roger Cashmore is head of the department of particle and nuclear physics at the University of Oxford.
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What is a field?
In physics, the word ‘field’ describes the continuous distribution of some quantity across space and time: for example, temperature and pressure on a weather map, or the electric force in the region surrounding an electric charge. If we know the law that governs how the quantity varies in space and time, we can write down an equation that describes the behaviour of the field – a field equation.
For example, in the case of the electric field, we know from experiments that the force due to an electric charge follows an inverse square law, becoming smaller as the square of the distance from the magnet increases. This forms the basis for our mathematical expression for the electric field.
In quantum field theory, not only the forces between subatomic particles but also the particles themselves are described in terms of fields. At the quantum level, we no longer know the precise position of a particle at a given time, only the probability of finding it at a certain position. However, we can describe this probability in terms of a field. Similarly, we can think of the fields due to the forces acting at the subatomic level in terms of the ‘field particles’. The best-known field particle is the photon, which is associated with the electromagnetic field.
