“Who ordered that?” – a quote attributed to physicist, I. I. Rabi, on hearing of the discovery of the muon, a particle that nobody wanted.
9.1 Alice in Nanoland
Ever since her visit to Gödel-land, Alice had been restless, and unable to concentrate on her school lessons. She pined for another dose of similar excitement, so much so that her mother became concerned for her health, and decided to take her on a visit to Aunt Elspeth, the white witch of the nor’-nor’-east.
Elspeth examined her niece closely, and then reached for two bottles of pills. “Alice has my blood”, she explained. “She will never be satisfied with the humdrum. She craves adventure.”
“But she’s only a child,” objected Marigold, Alice’s mother.
“These red pills will make her shrink, so that everything around appears different. I mean, really shrink! An ant will look as big as a dinosaur, and will be just as dangerous. It’s totally awesome. But be careful.”
“She’s too little for anything like that.”
“The green pills will bring her back to normal size.”
“Elspeth, you’re not listening to me.”
Marigold’s protests were too late, because Alice had already snatched the red container, and began swallowing pills, one after the other, as if they were chocolates. Marigold grabbed a second red container, and then the green one, and popped the red pills in an attempt to keep up with her daughter.
At first Marigold thought that the world about her was growing. The nearby table was now so big she could no longer see over the top. Her sister was a huge giant, with a silly grin on her face, who was waving a hand as big as a side of beef at her. Only Alice seemed at all normal, except for a gleam of rapture in her eyes. She was clearly enjoying herself, more than she had done for many months.
Their shrinkage was now accelerating. Down they went through a forest that Marigold realised must be the nap of the carpet. As they got smaller, they were surrounded by minute animals propelling themselves around by various mechanisms. Some sort of microbe, perhaps, thought Marigold. When was this going to end? How many of those confounded pills had they eaten?
Finally, the shrinkage slowed and stopped. Alice took hold of her mother’s hand. Her sense of adventure only went so far. “Yuk! What are those ugly things?” asked Alice, pointing at a group of large, blurry structures, just to their right.
“I don’t know,” replied Marigold, her voice wavering with fright.
“Molecules, of course. Don’t they teach you anything in school these days?” Marigold and Alice started in unison, and turned to see a little bald-headed man, about a third as tall as Alice, staring at them.
“Who are you?” they asked, as one.
“Felix Abernethy Quantum, Ph.D., F.A.P.S., R.M.V., at your service. I can see this is your first visit to Nanoland. There’s nothing to be afraid of – if you’re careful. I come here all the time. It makes for a nice outing.”
“Oh, really,” said Alice, as she noticed a continuous flashing of ultrafast, very small particles flying in all directions. “What happens if one of those things hits us?” At that very moment, Marigold was indeed struck. "Mom, mom, are you all right?”
"I’m fine. Just a tickle. It doesn't hurt at all.” She began to giggle. Moments later Alice was also hit, and then Marigold again, and soon they were both laughing themselves silly. “We should have brought the fly spray. They’re peskier than mosquitoes.”
“They’re neutrinos,” said Dr Quantum. “So small that it's hard to know if they’re matter at all. And they have no electric charge. That's why they don't hurt. They can even pass right through the earth without affecting anything."
“Oh, my gosh,” cried Alice, squeezing her mother’s hand tightly. With her free hand she pointed to a neutrino that appeared to be undergoing some sort of change, turning into a similar, but uglier, version of itself.
“Yes, there are three different types of neutrino, and they can change from one to the other,” explained Dr Quantum.
“Why only three?” asked Alice. “Why not four, or five, or a thousand?”
“Don’t ask so many …” began Marigold, before Dr Quantum silenced her with a gesture.
“Three seems to be a very special number. There are also three members of the family of leptons, three generations of quarks, and three quarks make up a baryon."
“What’s he talking about, Mom?” Before Marigold could think of a suitably evasive reply, Alice was tugging her arm and pointing at a large spherical blob, surrounded by a shimmering aura.
“I see you’ve found a hydrogen atom,” said Dr Quantum. “Those are electrons buzzing about. Careful, don’t get too close now.”
“That thing in the middle. I can see something moving inside it. It’s pregnant.”
“It’s a proton, and those are quarks inside it.”
Alice began to giggle. “Cottage cheese. So, it ate too much quark for dinner last night, did it?”
“No, those are a different type of quark, with funny names like up and down, strange, charm, top and bottom. And there are other little things in there as well, called gluons, because they stick everything together.”
“Look, there’s another one, only a bit different. And over there, a big group of them, both sorts. They’re having a party, with that shimmery cloud stuff all around them.”
“It’s another type of atom. Carbon, I think. It has a centre made up of protons, and other particles called neutrons.”
“What else is there to see?” Alice’s attention was beginning to wander. After all, she was only a little girl. Suddenly there was a huge explosion, and two dazzling flashes of light sped off in opposite directions. “Wow!”
“That was an annihilation. It happens sometimes when there’s antimatter about. You’d better watch out for bosons. Especially the Higgs boson. If he grabs you, you will get very heavy indeed.”
“Come on, Alice,” said Marigold, becoming apprehensive about their safety. “It’s time we were getting back. She held up the container of green pills, but Alice showed no interest.
“Are there any things smaller than these, Dr Quantum?”
“I don’t know,” said the little bald man, his face reddening with embarrassment at being forced to make such an admission. “Not just me. Nobody knows.”
Suddenly Marigold realised what her daughter was thinking. She knew that cheeky expression only too well. “Alice, no. Stop. You mustn’t. Alice!” Too late, she grabbed at Alice’s hand. It was empty, and the little girl was already shrinking, on her way to another domain, where not even Dr Quantum, with all his great scientific knowledge, could tell her what to expect.
***
If we leave Alice, and her reluctant mother, chasing excitement in their search for the ever smaller, we must realise they are only emulating the physicists of the 20th Century, whose penchant for the infinitesimal extended the range of physics deep into the subatomic domain. In so doing, they opened up a new world of great beauty, and considerable complexity, which we shall explore in the remaining Sections of this Chapter.
9.2 The Particle Zoo
As we have seen in Chap. 8, at the end of the 19th Century, physicists were quite happy with their understanding that, together with electrons and photons, the world was comprised of atoms, bound into molecules, and that these molecules made up all of the vast variety of matter that surrounds us. There were those, such as Rutherford, who were dissatisfied that so many different types of atom existed, and believed that perhaps atoms themselves might be composed of something smaller. Rutherford’s experiments, described in Chap. 8, showed that atoms were indeed constructed of neutrons, protons and electrons, and it was believed that at last the fundamental particles had been obtained. Everything of importance had been learned, or so they maintained.
Perhaps this arrogance was an example of hubris, an offence in Greek mythology that is a challenge to the gods, for it certainly brought a swift retribution down on the heads of the perpetrators. Within a decade or two, this cosy little clique of four fundamental particles (including the photon) had to be expanded to include a plethora of new arrivals, some coloured and flavoured, some charmed and others downright strange. (This may seem an unusual collection of adjectives to associate with particles, but as we shall see in later Sections, physicists working in this field love to choose curious names.) So widespread had this influx become, rather like a horde of gate-crashers storming a dinner at the Athenaeum Club, that Willis Lamb joked in his 1955 Nobel Lecture: “the finder of a new elementary particle used to be rewarded by a Nobel Prize, but such a discovery now ought to be punished by a 10,000 dollar fine."
The term Particle Zoo was coined to describe the new state of affairs. As a consequence of the random order in which the discovery of these new particles occurred, we will abandon here any attempt at chronology, and instead arrange the particles post factum into groups depending on their nature.
9.3 The Four Forces
We saw in Chaps. 7 and 8 that two of the fundamental forces of nature, gravity and electromagnetism, can be explained, the former by Einstein’s theory of Relativity, and the latter by Quantum Electrodynamics. These forces described all of the known physics up until the time Rutherford and his co-workers upset the classical applecart with their discovery of the atomic nucleus. Their experiments showed that these nuclei are comprised of electrically charged protons and uncharged neutrons, both with masses approximately 1837 times that of the electron.
The protons, being positively charged, experience a strong mutual electrostatic repulsion. Some new force must therefore be overpowering this repulsion and holding the nucleus together. This force was given the somewhat unimaginative name, especially considering the flamboyant nomenclature prevalent today in particle physics, of strong nuclear interaction. The natural question that immediately follows is: “what produces this interaction?” We saw in Chap. 8 how the electromagnetic interaction is generated by the exchange of photons. In analogy, Japanese physicist, Hideki Yukawa, proposed in 1935 that the strong interaction was the result of the exchange of as yet undiscovered particles between the nucleons (i.e., between neutrons and protons).
However, a major difference exists between the electromagnetic and strong nuclear interactions. The fact that the nuclear force is not observed in everyday phenomena, despite the great strength it must have to hold the nucleons together, is evidence that it has a short range. In the quantum theory of fields, the mass of a carrier particle associated with a force is related to the range of that force. (See Appendix 9.1.) The requirement that the new force be of such short range, i.e. of the order of a few femtometres1, implies that, unlike the photon, the carrier particle will not be massless. Indeed, its mass could be predicted reasonably accurately. Yukawa named the hypothetical particle a “meson” (which is Greek for “intermediate”) because its mass was expected to lie between the mass of an electron and that of a proton.
In Chap. 8 we introduced the concept of an intrinsic angular momentum, or spin, associated with fundamental particles. As Planck found to be the case for energy, this angular momentum is quantised, which means it comes in multiples of an elementary basic unit. (It need not concern us here what the actual value of this unit is2; suffice it to say that it is very small.) Experimental physicists, excited by the new field opening before them, were soon busy populating the particle zoo. The new particles they discovered could be divided into two classes, known as bosons and fermions, differentiated by the value of their spins. Bosons, named after Indian physicist Satyendra Nath Bose, possess a spin of integer or zero units. On the other hand, Fermions, named after Italian physicist Enrico Fermi, possess half odd-integer (i.e. 1/2, 3/2, 5/2, etc.) units of spin. As we shall see later, this difference results in some important differences in the properties of these particles. Armed with this information, experimentalists began combing cosmic ray data for evidence of the proposed meson.
One can imagine the excitement when a new particle, dubbed the mu meson, was discovered by Carl Anderson and Seth Neddermeyer at Caltech in 1936. (Carl Anderson also discovered the positron, so if Willis Lamb’s suggestion above had been in effect, he would have become severely impoverished.) The elation soon turned to disappointment when the newcomer turned out to be a fermion, not a boson, as anticipated from Quantum Field Theory. In fact, the particle appeared not to participate in the strong interaction at all. It therefore lost its status as a meson, and led to the disgruntled comment by Rabi at the head of this Chapter. It is now called the muon. The pi meson, or pion, which is now recognised as the real Yukawa particle, was discovered in 1947 by Cecil Powell. As a consequence, Yukawa was awarded the Nobel Prize in physics in 1949, and Powell joined him a year later.
(We shall see later that the particle emitted in this decay, for reasons of symmetry, is actually an anti-neutrino, the anti-particle of the neutrino.)
The neutrino3 was originally proposed by Wolfgang Pauli when he realised that without some new particle to carry away excess angular momentum in beta decay, conservation of angular momentum was not possible. The neutron is a fermion, with a spin of ½. The proton and electron are also fermions with spins of ½. Without the presence of a neutrino (a fermion with a spin of ½) it would not be possible to balance the angular momenta before and after the decay process. Pauli chose what he considered the lesser of two evils. Rather than violate the law of conservation of angular momentum, he invented a new particle, a fermion with zero, or near zero, mass. Not that his action left him with a clear conscience: “I have done a terrible thing,” he admitted. “I have postulated a particle that cannot be detected.” He was, however, wrong: the neutrino has since been detected, and about 100 trillion of them pass through our bodies every second.
As is often the case in physics, the discovery of a new entity can have implications that no one has foreseen. The weak interaction was found to have a unique characteristic that differentiates it from the other three forces in a way that was not detected, and largely not even suspected, for two decades.
In the last Chapter, we stated that the laws of physics have a symmetry with regard to the reversal of time. If we watch a video of two balls colliding on a billiard table, we cannot tell if the video is running forwards or backwards. We also cannot tell whether the video has been left-right reflected, i.e. whether we are actually watching a mirror image of the collision. This is because all the laws of classical physics are symmetric with respect to these types of interchange.
This symmetry can manifest itself in many ways. For instance, suppose we wish to communicate to another intelligence in a faraway galaxy, and tell them that we drive on the left-hand side of the road4, how can we do it by words alone? Concepts such as left or right are mere conventions, and classical physics does not offer us any experiment that we could ask our far-off friends to perform which might help them distinguish left from right. The weak interaction, however, provides us with a solution. An experiment to measure the spin of the electrons emitted in beta decay, a process that involves the weak interaction, will show an asymmetry that enables us to define the left and right directions unambiguously [1].
It is also interesting to note that complex biological molecules have a left-handedness, which may be a consequence of their all being descended from an original left-handed molecule aeons ago. Chemicals manufactured in the laboratory normally have equal numbers of left and right-handed molecules. It is worth debating whether extra-terrestrial life, if we discover it sometime in the future, will display a similar left-handedness in its constituent molecules.
As its name suggests, the strength of the weak interaction is much less than that of the strong interaction, by a factor of approximately 10-6. (Because the weak force decays much more quickly with distance than the strong force, this factor is hard to define precisely.) It is also only about 10-4 times as strong as the electromagnetic interaction. Its range is of the order of 10-18 m, which is 1/1000 that of the strong force.
Following the same methodology used by Feynman in QED, and by Yukawa for the strong force, Sheldon Lee Glashow, Abdus Salam, and Steven Weinberg in the 1960s independently proposed a scheme for the weak force, analogous to QED. However, a particular symmetry requirement could only be met if the electromagnetic force were also included into their scheme. The result is a composite electroweak interaction. This development generated great excitement at the time, as it was seen as the first step towards a Theory of Everything, an overarching theory, uniting all four forces into one. This was the goal pursued in vain by Einstein for the latter half of his life. It seemed the journey he had been seeking had at last begun, and excitement was in the air.
Four massless carrier particles are required for the new interaction. Three of them were given the name Intermediate Vector Bosons and are represented by the symbols W+, W-, and Z0. The fourth is the photon. A problem immediately arose in that the short range of the weak interaction implied that the carriers W+, W-, and Z0 had to be very massive, of the order of 650 times the mass of the pion. Some mechanism is therefore required that gives mass to the three intermediate vector bosons, but not to the photon. This process was resolved by the assumption of another unseen field, the Higgs field, that is assumed to pervade all space. Interaction of the Higgs field and the electroweak force results in mass being attributed to the intermediate vector bosons. The Higgs field also has a carrier particle of its own, the Higgs boson. With these extra assumptions, the electroweak theory seemed complete, and experimental physicists began their search for all four bosons.
The Large Hadron Collider (LHC) in CERN, the instrument used for the discovery of the Higgs Boson. Image courtesy of CERN (Image released by CERN under Creative Commons (2013) https://home.cern/news/news/cern/cern-releases-photos-under-creative-commons-licence (accessed 2020/06/3))
If the unification of the weak and electromagnetic interactions into the electroweak interaction represented the first step towards a Theory of Everything, it remains unfortunately the only step. So far, no unification has been achieved with the strong interaction. The weakest of the forces, gravity, also remains very much on the outer. As we have seen in Chap. 7, the theory of relativity interprets gravity as arising from a distortion of the geometry of space-time, and a quantum theory of gravity, analogous to QED, has not yet been found.
9.4 Sorting the Particle Zoo
Now that we have gained an insight into the role played by the four forces in the subatomic domain, it is time to return to the Particle Zoo, with a view to sorting out the exhibits that industrious experimentalists were rapidly discovering and attempting to classify. The advent of powerful new accelerators in the 20th century provided physicists with access to particles with energies that had hitherto been unattainable. So many “fundamental” particles turned up in experiments that it was soon realised that not all could be truly fundamental; many of them were probably constructed from other smaller units.
This suspicion was strengthened when the proton was examined more closely. We saw in Chap. 8 how electrons behave like tiny magnets when placed in a magnetic field. The strength of this behaviour is determined by the electron’s magnetic moment, and its prediction to astonishing accuracy is one of the triumphs of QED. However, when, in the nineteen-thirties, measurements were made of the magnetic moment of the proton, the theoretical and experimental results were in mutual disagreement by hundreds of percent. This was soon recognised as evidence that the proton has internal structure of its own. The proton is not a fundamental particle, and like Alice in Nanoland, we must go to an even smaller domain, to search for the most basic constituents of nature.
The reader can probably guess one path physicists might take to further progress: follow the example of Rutherford in the atomic domain, and smash two particles together to see what eventuates. A high energy analogue of the Rutherford experiment described in Chap. 8 was carried out at the Stanford Linear Accelerator (SLAC) in California in 1970. Protons were bombarded with very high energy electrons5. The distribution of the electrons after the collision indicated the presence of internal structure in the proton [2]. There could be no doubt now: the proton definitely was not a fundamental particle.
Trying to get some sort of order into the assemblage of particles that had turned up in their collision experiments became a priority for particle physicists in the last half of the 20th century. We will not follow the history too closely, but rather attempt an overview of the currently accepted situation, and highlight any outstanding problems.
We have already indicated that particles can be divided into two groups, fermions and bosons, depending on their intrinsic spins. This division is important, because fermions satisfy the Pauli Exclusion Principle (see Chap. 8), while bosons do not.
However, there are other classifications that are important in attempting to sort out our zoo. Just as a visitor to a normal zoo might expect the big cats (lions, tigers, etc.) to be in a different area from the bears and insects, so physicists have arranged the particles into leptons and hadrons. The hadrons are themselves subdivided into baryons and mesons. We will treat these various groups separately, and see what their differences are.
Leptons
Leptons are particles that interact only via the electroweak interaction, and not the strong interaction. (We will not consider gravity further in our discussion of particles.) The name comes from the Greek root leptos, meaning “slight”. This name is now somewhat inappropriate, as since the name was first adopted, leptons more massive than protons have been discovered, but no one has yet succumbed to the urge to change the name.
Leptons are truly elementary particles, having no internal structure. According to the Standard Model, all leptons are point particles; their volume is zero. What this means exactly is complicated by the Heisenberg Uncertainty Principle, which requires the particle wavepacket to occupy a non-zero volume. Physicists discuss the intrinsic “size” of a particle, i.e. the size of its internal structure, rather than the size of its wavepacket. Leptons have no internal structure, so their “size” is zero. Experimental evidence shows the electron to be smaller than 10−18 m, or at least 1000 times smaller than a proton.
Leptons come in three generations, each containing two flavours, so that we have six flavours in total. (We must now make our acquaintance with the somewhat flowery terminology of particle physics, where words do not have the same meaning as they do in everyday life. Particle physicists have adopted the attitude of Humpty Dumpty: “When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means just what I choose it to mean — neither more nor less” [3].) A flavour is akin to the species of an animal in a normal zoo, and has nothing to do with our sense of taste.
Table of Leptons
Generation | Name | Symbol | Antiparticle | Chargea | Massb |
|---|---|---|---|---|---|
1 | Electron | e− | e+ | −1 | 1.0 |
1 | Electron neutrino | νe |
| 0 | Small, but non-zero |
2 | Muon | µ− | µ+ | −1 | 206.8 |
2 | Muon neutrino | νµ |
| 0 | Small, but non-zero |
3 | Tau | τ− | τ+ | −1 | 3477.5 |
3 | Tau neutrino | ντ |
| 0 | Small, but non-zero |
As can be seen, Pauli’s chimerical particle, the neutrino, now comes in three flavours. In the Standard Model, the neutrinos are massless. However, this is no longer believed to be the reality. A thirty-year old puzzle was why the number of neutrinos arriving on the earth from solar nuclear reactions was only about one third that expected from theory. The solution, which earned Takaaki Kajita of Japan and Arthur B. McDonald from Canada the 2015 Nobel Prize in physics, is that the missing neutrinos escape detection by changing flavours on their journey to the earth. This ability to change flavours requires the neutrinos to have a non-zero mass, however small that may be. These observations induce a sense of humility, as they reveal that the Standard Model, despite its great success, cannot be the complete theory of the fundamental constituents of the universe.
To distinguish leptons from other particles, physicists introduced a new quantity, called the lepton number. All the leptons in the above table have a lepton number of +1, and all the anti-leptons −1. Particles that are not leptons (e.g. neutrons, protons, etc.) have a lepton number of zero. Physicists believe that the lepton number is conserved during particle interactions (i.e. the sum of the lepton numbers before the interaction is equal to the sum of the lepton numbers after the interaction.)
The superscripts give the electric charges of the individual particles, and we see that the sum of the charges on the right-hand side is equal to zero, which is the same as the charge of the neutron on the left-hand side. Similarly, the lepton numbers, 0, 1, and −1 respectively, of the three particles on the right-hand side, sum to zero, which is the lepton number of the neutron. Both electric charge and lepton number are therefore conserved in this process.
The ability of a neutrino to change its flavour has led to the question being asked: is a neutrino its own antiparticle? (This is not as absurd as it may sound. Photons and gluons—to be encountered soon—are their own antiparticles.) In this case, lepton number may not be conserved in particle decays.
A final question springs to mind when surveying the table of leptons above: why stop with three generations? (This is the question Alice posed to Dr Quantum in our opening story.) How do we know that there are not more, heavier leptons, waiting in the wings to be discovered in the future, as our accelerators reach to ever higher energies? The same question can be asked when we come soon to examine quarks. The answer is the same in both cases: we don’t know. However, fourth and higher generations are considered unlikely. Their presence would result in slight changes to predictions of electroweak theory that are not observed. Also, any extra fermions would interact with the Higgs boson, modifying its properties so that it would not have been detected. The observation of the Higgs boson, with the properties it has, is evidence that there are only three generations. Statistical analyses at CERN and the Humboldt University of Berlin exclude the presence of a fourth generation with a 99.99999% probability [4].
Hadrons
It is now time to consider the other large family of fundamental particles, those interacting by means of the strong interaction6. They are known as hadrons, and as we have seen, have two main subgroups, called baryons and mesons. Unlike leptons, hadrons are not truly elementary, in the sense that they are themselves composed of smaller particles called quarks.
The name “quark” was coined by physicist, Murray Gell-mann, when he noticed the sentence: “Three quarks for Muster Mark” in James Joyce’s book, Finnegan’s Wake. At the time he believed that there were three quarks occurring in nature. Now it is known that there are six, and they have been given the rather uninspiring names: up (u), down (d), charm (c), strange (s), top (t) and bottom (b). For a while, “truth (t)” and “beauty (b)” were floated as possible names for the last two, but banality ultimately prevailed. Most physicists pronounce “quark” to rhyme with “Mark”; Gell-mann pronounced it “kwork”.
At first, considerable effort was expended trying to detect free quarks in cosmic rays and accelerator data. Quarks have an electric charge of 1/3 or 2/3 that of the electron, which should make them distinctive. Despite a few false alarms [5], it is now generally accepted that quarks are confined within the hadron, and cannot be seen on their own. We shall discuss this idea further shortly.
In a conventional zoo, it is customary to put a label on the animals’ cages bearing the names of the beasts within. For instance, the tigers’ cage would have the tag: Panthera tigris tigris if it contains a Bengal tiger, or Panthera tigris sumatrae if there is a Sumatran tiger lurking somewhere back in the shadows. The three Latin names are the genus, species and sub-species of that strain of tiger. In our particle zoo, quantum numbers serve the same purpose, i.e. they enable us to differentiate between particles. (We have already encountered the lepton number, which is one example of a quantum number.) Unlike the Latin scientific names of animals, however, they also limit the interactions that particles can engage in, via various conservation laws.
Very early in nuclear physics, in 1937, a quantum number called isospin was introduced by Eugene Wigner, in analogy with ordinary spin, to distinguish protons from neutrons. Particles that are affected equally by the strong force, with similar properties, apart from their charge (e.g. neutrons and protons), are considered to be different states of the same particle. They are said to have different isospin. Later, physicists introduced the additional quantum numbers of baryon number, charm, strangeness, topness, and bottomness to distinguish the newer members of the particle zoo. Not all physicists had Gell-man’s erudite knowledge of literature to draw on when choosing names. A table of the six quarks and their associated quantum numbers is included in Appendix 9.2.
We are now almost in a position to see how the individual hadrons are put together. However, simply forming all possible combinations of the known quarks would result in far more hadrons than are actually observed. Clearly there is another selection process at work here. This involves what has been called colour, although it has nothing to do with the visual colours that we know so well.
Just as the electromagnetic (or more correctly, the electroweak) force binds the electrons to the atomic nucleus, colour (or the colour force) binds the quarks together inside a baryon, e.g. inside a proton or neutron. The mediating carriers for this force are the gluons. They are called gluons because they are the source of the glue binding the quarks together.
Giant leaf-tail gecko, Uroplatus fimbriatus, clinging to glass. Image from Tom Vickers (Wikimedia Commons, public domain. https://commons.wikimedia.org/wiki/File:Uroplatus_fimbriatus_(3).jpg (accessed 2020/6/8))
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In the Standard Model of Particle Physics, remnants of the colour force extend outside the boundaries of the neutrons and protons. It is this residual force that produces the strong nuclear interaction that is responsible for most of nuclear physics, including the destructive power of nuclear weapons.
Within the hadron, the colour force is unlike the other forces, and does not drop off with distance. This property is responsible for the confinement of the quarks within the hadron, and is the reason no free quarks are observed in laboratory experiments. Indeed, the colour force, produced by the exchange of gluons, is so strong that quark-antiquark pair production will occur before the quarks can be separated. However, at short separation distances the colour force is weak, and the quarks can move freely, until they start to get too far apart. Then the colour force kicks in and brings them back together, rather like a sheep dog rounding up lambs that have strayed too far from the flock.
Colour is the analogue in the colour force to charge in the electromagnetic force. However, whereas two values were needed for the electric charge, denoted by convention “positive” and “negative”, three values are needed for the colour. These three values of the colour “charge” have been given the names of the three primary colours: red, green and blue. Clearly the colour charges have nothing to do with visible light, or the perception of colours. They are just another example of the Humpty-Dumpty influence that we mentioned earlier.
Without the existence of colour, the Pauli Exclusion Principle would not allow, for instance, two up quarks to be present inside a hadron. However, if each up quark is of a different colour, they are non-identical, and therefore can be present together.
Having got our heads around the basic concepts of the Standard Model, we are now at last in a position to see how hadrons are put together. There are some limitations on how these particles are constructed. First, only “colourless” hadrons exist in nature. These may be baryons comprising three quarks of the three different colours (in the same manner that white light is produced by combining the three primary colours of red, green and blue light), or mesons made from a quark-antiquark pair. Antiquarks have an anticolour, so that a quark-antiquark pair is colourless. In addition, as no particles with fractional electronic charges exist in nature, baryons must have an electric charge that is an integer multiple (disregarding the sign) of the electronic charge. As they are fermions, they must also have half-odd integer spin.
Now would seem to be an appropriate time to introduce a table of hadrons, showing how they are all constructed from their constituent quarks. However, thanks to the diligence of experimental high-energy physicists, there are literally hundreds of them, and studying such a list would, for the non-specialist, be about as entertaining as reading the Greater London Telephone Directory, or perhaps even Whitehead and Russell’s Principia (see Chap. 3). For illustrative purposes, we discuss here only the proton and the pion, as examples of a baryon and a meson.
The quark structure of the proton
The astute reader may have noticed, by referring to the Table of Quarks in Appendix 9.2, that the sum of masses of the three individual quarks comprising the proton amounts to no more than 1% of the proton mass. The remaining mass comes purely from the motion and confinement of quarks and gluons [7], in accord with the equivalence of mass and energy that we discussed in Chap. 7.
The quark structure of the π+ meson
The remaining members of the particle zoo can be explained in a similar fashion from conglomerations of quarks, and the observance of appropriate conservation laws for charges and quantum numbers.
Gluons
Before quitting our zoo, we should say a little about the final components of the Standard Model, the unfortunately named gluons, carriers of the colour (or interquark) force. Gluons carry out the same role for the colour force between quarks as photons perform for the electromagnetic interaction between electrons. However, they are also carriers of the colour charge, unlike photons, which do not carry the electromagnetic charge. They are massless, like the photon, but unlike the photon, they are never observed outside the confines of the hadron. They have spins of 1 unit, and are therefore bosons.
Gluons carry both a colour and an anticolour. This gives a possible nine combinations. An exchange of a gluon between quarks converts a quark from one colour to another. The analogy of this process with photon exchange has led to the name Quantum Chromodynamics (QCD) being coined for this aspect of the Standard Model.
9.5 Beyond the Standard Model
In the last chapter we have made much of the incredible agreement between QED predictions and experimental measurements for physics involving the electron-electron interaction. Naturally physicists hoped to achieve the same precision with the strong force analogue to QED, i.e. QCD. As we shall see, they have been only partially successful. Various reasons have been put forward for this, and suggestions made to extend the Standard Model. As this is currently a highly active research field, we should bear in mind that the situation can change very quickly.
Feynman diagrams for the exchange of carrier particles in the various nuclear interactions
In (a) the decay of a neutron by means of the weak interaction into a proton, an electron and an antineutrino is displayed. The process is mediated by the exchange of an Intermediate Vector Boson.
In (b) an example of the colour force in action is shown. A green quark and a blue quark swap colours by the exchange of a green-antiblue gluon.
The last example in (c) is the scattering of a neutron and a proton inside the nucleus by the exchange of a pion. This is the process that was proposed by Yukawa when he predicted the existence of the meson to explain the strong nuclear interaction between nucleons inside the nucleus. Now, if the strong interaction is interpreted as a residual interaction left over from the inter-quark colour force inside the nucleons, there is some doubt over the role, if any, played by pion exchange.
If physicists hoped for a level of agreement in QCD comparable to that of QED for the electron then they were disappointed. We have seen in Chap. 8 how accurate the QED prediction of the anomalous magnetic moment of an electron is. A similar calculation for the muon requires the inclusion of Feynman diagrams related to the weak interaction. In this case, the predicted muon anomalous magnetic moment differs from the measured value [8] by 3.5 standard deviations. (From probability theory, one expects 99.7% of measurements to lie within 3 standard deviations of the correct result.) However, the agreement is still to the eighth decimal place in the actual magnetic moment7. On the other hand, composite particles such as the neutron and proton have huge anomalous magnetic moments.
Another substantial disagreement between the Standard Model and experimental measurement is in the model’s prediction of the proton radius, where the discrepancy is enormous8. In this case, and also for the muon magnetic moment, physicists are reluctant to attribute the discrepancies to the Standard Model until all possible sources of error in the experimental measurements have been eliminated.
As well as the discrepancies mentioned above, there are some physical phenomena which are left completely unexplained by the Standard Model. For instance, gravity remains steadfast in its refusal to be accommodated in the same scheme as the other physical forces. Since Einstein, gravity has been interpreted as arising from curvature in the space-time fabric within which the other forces operate. This fundamental incompatibility between quantum mechanics and relativity is one of the major embarrassments of modern physics.
More recently, the growing evidence for dark matter and dark energy throughout the universe (see Chap. 11) proposes another challenge for the Standard Model. It might be expected that a theory of fundamental particles would provide an explanation for these two phenomena, but as currently constituted, the Standard Model has no relevant mechanism. In addition, a particle that has been around since the middle of the last century, the neutrino, has been found to oscillate between three different flavours. Such a characteristic requires the presence of mass, but in the Standard Model the neutrino is massless. This disagreement is not yet resolved.
Much has been made of the discovery of the Higgs boson as a triumph for the Standard Model. There are, however, other hadrons that are predicted at very high energies by the Standard Model, and have not yet been observed. In addition, “glueballs”, which are particles comprised solely from two or three gluons, but no other hadrons, are predicted. Their detection would represent a major coup for the Standard Model.
Other forms of “exotic” particles have indeed been discovered, including pentaquarks and tetraquarks, composed of five and four individual quarks respectively. Recently it was announced by CERN that a tetraquark comprised of four charm quarks had been discovered [9]. It is a good candidate to test theories on whether the four quarks are tightly bound, or arranged to form two mesons, which are stuck together loosely in analogy to a chemical molecule.
Even though the Standard Model has had great success in establishing an order in the chaos of the particle zoo, it has fundamental limitations. We saw in Chap. 8 how Feynman lamented that the Fine Structure Constant cannot be calculated by physicists, but must be measured by experiment and inserted into the equations of QED. Philosophically this is quite unsatisfactory because even a comparatively small change in the value of this constant would result in a very different universe that would not support life as we know it.
However, the Standard Model has nineteen independent constants which have to be inserted into it arbitrarily. Examples of these constants are the masses of the elementary particles and of the Higgs boson, as well as constants, analogous to the Fine Structure Constant, which govern the strength of the various interactions. Such a degree of arbitrariness is clearly not appropriate, and physicists are continually searching for other approaches.
Two avenues that have been explored to extend the Standard Model are a Grand Unified Theory (GUT) and Supersymmetry. We have discussed these approaches briefly in Appendix 9.3. Both of these theories predict the existence of new particles. However, unfortunately these new particles are so massive that it is beyond the capabilities of existing particle colliders to produce them.
String Theory is another contender that has received a lot of attention in the research literature and in the popular media. It was first developed in the nineteen-sixties as a possible explanation of the strong nuclear force. It fell from favour as Quantum Chromodynamics became popular, but has found another life as a candidate for a Theory of Everything (TOE), perhaps the Holy Grail of physics (see Chap. 4). The attraction of String Theory is that it treats gravity on the same footing as the other forces, and can therefore be regarded as a theory of quantum gravity.
As the name might indicate, in String Theory “zero-dimensional” point-like particles are replaced by one dimensional “strings”. These may be either lengths of string, or loops of string. The properties of the particle (mass, charge, etc.) are determined by the vibrational states of the string. One of these vibrational states corresponds to the graviton, the long sought-after carrier particle of the gravitational field. Originally String Theory only included bosons, but has now been extended into Superstring Theory, to also include fermions.
Five different versions of String Theory were developed over the years until it was found that they were all variants of one overriding single theory, called M-theory. M-theory is formulated in eleven dimensions, which represents an improvement on the original bosonic string theory, which required twenty-six dimensions.
a A length of hose appears one dimensional when viewed from a distance. b When viewed close up, the two dimensional nature of the hose surface becomes apparent. The transverse dimension is “closed” because if one travels in this direction, remaining on the surface, one returns to the starting point
From a distance the hose looks one-dimensional, but as one gets closer, it becomes clear that the surface is two dimensional. One dimension lies along the length of the hose, and the second runs transversely around the perimeter. The second dimension is closed, because if an ant on the surface were to travel around the perimeter of the hose, it would finish up back at its starting point.
In the case of String Theory, the extra seven dimensions are thought to be closed into very tight circles. They are then unobserved in the same manner that the transverse dimension of the hose is not noticeable at large distances.
String Theory has been applied to many of the outstanding problems of physics, covering the full scope from fundamental particles to cosmic inflation (see Chap. 11). However, it attracts criticism because it can “explain” too much. As currently understood, it can describe around 10500 different universes. From this inconceivably high number of possibilities, there is surely one to describe our universe, no matter what it happens to be. If you want to play the lead role in the Royal Shakespeare Company’s next production of Hamlet, there is already a universe waiting for you in String Theory where that can happen. All experimental attempts to verify the theory must remain unconvincing if, no matter what result is obtained from the measurement, it can be explained by selecting the appropriate universe.
As we can see from the above arguments, although the Standard Model has achieved much in providing a framework for the interpretation of the particle zoo, it also has its limitations. Many physicists believe it is an interim step along the way to an understanding that will only be achieved when a better, less arbitrary, theory is discovered.
Since the time of Galileo, experiment and theory have each contributed equally to our understanding of the physics of our world. Sometimes experimentalists have discovered new phenomena that have challenged theorists to produce new theories to explain them, and sometimes theorists have told experimenters which experiments are critical to distinguish between competing theories. In the main, a happy partnership has existed between two groups of physicists with very different skill sets.
In the field of Fundamental Particle Physics, however, the cost of the accelerators needed to reach the energy regions now of interest to theorists has become so high that these machines strain the budgets of even the wealthiest of nations. There are so many other competing priorities for scarce resources that it is possible that the current generation of particle colliders is the last we shall see for the foreseeable future. If that is the case, it falls to theorists to find alternative ways to test their theories. This in itself represents a new challenge for the next generation of particle physicists.