﻿ ﻿Welcome to the Subatomic Zoo - The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics - Robert Oerter

# The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics - Robert Oerter (2006)

### Chapter 7. Welcome to the Subatomic Zoo

The changing of bodies into light, and light into bodies, is very conformable to the course of Nature, which seems delighted with such transmutations.

—Isaac Newton, Opticks

How do you find out what something is made out of if you aren’t allowed (or able) to open it and look inside? Imagine you are given what looks like a Nerf ball. Your mission (should you choose to accept it) is to find out what’s inside, without squeezing it or cutting it open. The only things you are allowed to do are weigh it and shoot BBs at it. When you weigh it, you find it weighs too much to be Nerf foam all the way through—it weighs as much as a baseball. Next, you buy a BB gun and start shooting at the ball. You find that most of your BBs get stuck inside, and the ones that scatter off don’t form any kind of informative pattern. You go back to the store and buy a more powerful BB gun. Now you start to see regular patterns in the BBs that fly off the ball.

It’s time to stop and think. What are the possibilities? Your ball may be an actual baseball, covered with a thin layer of Nerf foam just to confuse you. What sort of pattern of BBs would you expect to see if that were the case? At very low power, BBs would penetrate the Nerf layer but bounce off the baseball’s outer skin. At higher power, most of the BBs would penetrate the baseball and get stuck there. At very high power, the BBs would rip straight through, perhaps being deflected to one side or another in the process. Another possibility is that, instead of a baseball, there’s a much denser object embedded in the Nerf, say, a steel ball. In this case, we would expect that at low power the BBs get stuck or slightly scattered. At high power, they would go right through the Nerf and scatter off the hard center. In fact, by looking at the paths of the BBs that fly off and tracing them backward we can find out how large the central object is. There are still other possibilities we need to consider. What if there was more than one hard object embedded in the ball? Scattering would be more confusing. There would still be a low-power region where BBs mostly get stuck. At higher power, the BBs could bounce off one of the hard objects, or it could ricochet between several of them before exiting the Nerf and flying off into the distance. The patterns would be harder to identify. Still, we can imagine that with enough BBs and a little ingenuity, we could deduce the number and size of the hard objects.

This is, more or less, the situation that the elementary particle physicist faces. Back in 1909, Ernest Rutherford had pioneered this approach by firing alpha particles (which we now know to be helium nuclei—two protons and two neutrons) at a thin gold foil. The scattering pattern surprised him. From what he knew about the density of gold and the thickness of the foil, he had expected the alpha particles to pass through the foil with only a small amount of deflection. Instead, he found that some of the particles came right back toward the source, as if they had bounced off of a brick wall. “It was quite the most incredible event that has ever happened to me in my life,” he said. “It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”1 In order to explain this unexpected result, Rutherford proposed that the mass of the gold atom wasn’t evenly spread throughout the volume of the atom. Rather, the atom had a small, hard core that held 99.95% of the mass of the atom. This is like the second model in the Nerf example; the hard core is the nucleus of the atom, composed of protons and neutrons, and the remaining 0.05%, the Nerf foam, is the electron cloud.

This model is similar to the solar system, with the nucleus where the sun would be. The sun contains 99.9% of the mass of the solar system. Instead of the electrons being in orderly planet-like orbits, however, they must be spread out in orbitals as required by quantum mechanics (and by QED). It would be another 50 years before physicists would take the next step and probe inside the proton and neutron to discover their structure. As we will see, that structure is something like the third model in the Nerf example; three hard objects called quarks, and a cloud of “glue” that holds them together.

The process of firing particles at other particles and looking at what flies out has been compared to taking two Swiss watches and smashing them together, then trying to deduce how they work by looking at the gears and jewels that fly out. The actual situation is both better and worse than that. On the one hand, the proton structure is much simpler than a watch. It is built of just three quarks, plus the glue that binds them. On the other hand, we’ve never actually detected any of the “gears”—the quarks. Instead, when you smash two “Swiss watches” together—two protons, say—you find that two alarm clocks and a grandfather clock fly out. But let’s go back and tell the tale from the beginning.

Our modern understanding of the nuclear forces grew via a complex process of development spanning about 40 years. In order to keep track of the main ideas through the twists and turns of that history, it may be useful to keep in mind the following outline. The history of the “strong nuclear force” can, in retrospect, be broken into three stages:

■ Isospin Theory, 1930-1960

■ The Eightfold Way, 1961-1973

■ QCD, 1974-present

A New Force of Nature

It was only in 1662 that the ancient Greek atomic hypothesis was revived by Robert Boyle. Boyle noticed that a gas, such as air, could be compressed, which implied there was some empty space in between the parts making up the gas. In the early 1800s, Joseph-Louis Proust, John Dalton, and other early chemists made use of the atomic hypothesis to explain why chemical reactions always occurred in fixed proportions. For instance, if you take one gram of hydrogen and 8 grams of oxygen, it will combine completely to make 9 grams of water. This can be explained by supposing that one atom of hydrogen combines with one atom of oxygen, and that each atom of oxygen is 8 times heavier than a hydrogen atom. This clearly is not the only solution: We now know that oxygen is 16 times heavier than hydrogen, and that two hydrogen atoms combine with each oxygen atom to make water (H20). It took much work for chemists to sort through the possibilities, but by 1869 Mendeleev had a reasonably good chart of atomic weights—the first version of what we now call the periodic table of the elements.

By 1935, physicists had an explanation for Mendeleev’s periodic table. The “uncuttable” atoms had been cut and found to consist of protons, neutrons, and electrons. The electrons were bound to the nucleus by the electric force, operating according to the laws of quantum mechanics (later quantum electrodynamics, or QED). The only remaining question: What holds the nucleus together? The protons, positively charged particles, were crammed into a space 1/100,000th the size of an atom. Positively charged particles repel each other, so the nucleus would fly apart if there was no other force holding it together. If only they could nail down the nature of the nuclear force, physicists thought, they would have a complete and fundamental understanding of matter.

“Science,” said Robert Millikan in his Nobel acceptance speech in 1924, “walks forward on two feet, namely, theory and experiment. Sometimes it is one foot which is put forward first, sometimes the other, but continuous progress is only made by the use of both.” In 1931, Dirac had stunned the physics community by predicting the existence of a new particle, the positron, which the experimenters then confirmed. Theorists came up with two more surprises during the 1930s.

The first surprise was triggered by the need to explain an experimental result that seemed to violate nearly every law of physics. The phenomenon is called beta decay; it is a form of radioactivity in which the nucleus emits an electron (then known as a beta ray) and changes to a different element. The simplest example is the decay of a free neutron (that is, one not bound in a nucleus). This free neutron gets converted to a proton, and an electron is emitted. Now, electric charge is conserved in this reaction. The neutron has 0 charge before the decay, and the proton and electron have +1 and -1 charge, so afterward the total charge is still 0. But everything else is screwy. For instance, spin. A neutron has spin 1/2, like the proton and the electron. But there is no way for initial spin to equal final spin—we can add two spin 1/2 particles to get spin 0 (by having one spin-up and one spin-down) or spin one or minus one (both spins in the same direction). But there is no combination that gives spin 1/2 for the total spin. So angular momentum apparently isn’t conserved.

Energy apparently isn’t conserved, either. A neutron is more massive than a proton and an electron combined. The extra mass should show up as kinetic energy (remember E = mc2) of the proton and electron. Think of this extra energy as the gunpowder in a rifle cartridge. If two cartridges have the same amount of gunpowder, the two bullets will come out of the gun with the same speed, and therefore the same energy. Since the mass difference is always the same in any beta decay, the electron should always come out with the same energy. Instead, experiments found that the electron’s energy was spread over a wide range. Initial energy, it seemed, did not always equal final energy.

Some physicists took this to mean that the sacred law of energy conservation had broken down. Wolfgang Pauli thought of a solution that seemed only slightly less radical—that a new particle, with spin 1/2 and no electric charge, was produced in the decay. How little confidence he had in this scheme is shown by the fact that he mentioned the idea in a letter to friends (he was explaining that he would not be at an upcoming physics conference because he wanted to enter a dance contest happening at the same time) and then let the matter lie. Several years later, in 1934, Enrico Fermi picked up the idea and published a paper showing how the new particle, dubbed the neutrino (or little neutral one), explained the range of energies seen in beta decay experiments. (For reasons we will learn later, physicists decided to re-name the new particle the antineutrino, and call its antiparticle the neutrino.) We will talk more about beta decay in Chapter 9.

The second theoretical surprise came from Hideki Yukawa in 1935. Yukawa had been struggling with the nature of the nuclear force holding the protons together. Several years before, Heisenberg had suggested that the nucleus was held together by an exchange of some particle among the protons and neutrons, rather like the electric force is carried by exchange of (virtual) photons. Yukawa realized, as Heisenberg had, that the particle being exchanged could not be an electron, for the same reason as in beta decay—the spins wouldn’t add up. Finally, after hearing about Fermi’s theory of beta decay and the invention of a new particle, Yukawa decided to assume the nuclear force was caused by the exchange of some particle, which came to be called the pion (pronounced “pie-on,” as in the Greek letter pi), and then figure out just what the required properties of that particle would be.

In beta decay, a neutron turns into a proton, and an electron and an antineutrino are produced. Yukawa began with the same basic idea—namely, that a neutron could turn into a proton by emitting a negatively charged particle. The inverse reaction must also be possible: a proton turns into a neutron and emits a positively charged particle. That meant that the pion must come in two versions, a negative pion (called the pi-minus) and a positive pion (the pi-plus). Because the proton and neutron both have spin 1/2, the pion (in both versions) must have spin 0. The mass of this new particle can be estimated very simply. In Yukawa’s theory, the nucleus is held together by virtual pions in the same way that electrons are bound to atoms by virtual photons. For this to work, the virtual pions must live for about 7x10-24 second— the time it would take a particle traveling at the speed of light to cross the nucleus. Recall, though, that virtual particles live on borrowed time: the time they can survive is limited by the Heisenberg uncertainty principle, which states that the uncertainty in energy and time are related by the equation ΔE Δtħ . Because the pion has some mass m, it needs to borrow energy E = mc2. Using the time 7×10-24 second for Δt in the uncertainty principle, we find that the pion mass should be about 200 times the electron mass. Yukawa rather hesitantly suggested that such a particle, with charge +1 or -1, no spin, and mass intermediate between an electron’s mass and a proton’s mass, should be sought in cosmic ray showers.

On a Mountaintop

As theorists struggled with the seemingly intractable problems of beta decay, the nuclear force, and the infinities in quantum field theory, experimenters were going up in balloons and climbing mountains. Their purpose was not recreational; they were trying to understand the nature of cosmic rays. By 1935, it was known that these mysterious rays came from the sky, consisted of charged particles, and were capable of penetrating several feet of lead. It was suspected (correctly) that, whatever the primary rays from space were, they interacted in the atmosphere to create many different types of particles.

Experiment again moved to the forefront of physics. Its ascendancy would last through the 1940s, 1950s, and 1960s, as a whole zoo of subatomic particles was discovered using a variety of increasingly sophisticated techniques. The bewildering array of exotic, short-lived particles would only find theoretical explanation in the 1970s with the development of the Standard Model.

It was Carl Anderson, the famed discoverer of the positron, who in 1937 won a tight race to claim discovery of a charged particle with mass, “larger than that of a free electron and much smaller than that of a proton,” in fact, about 200 times the electron’s mass. People assumed immediately that this was Yukawa’s pion—but they were wrong. As the carriers of the nuclear force, pions ought to behave dramatically differently when traveling through matter than when traveling through empty space: They should be quickly trapped by a nucleus, which should then break apart in a shower of neutrons and protons. Two young Italians, working in a basement with scavenged supplies, decided to test if the new cosmic ray particles had the right properties. It was 1944, and Rome was occupied by the Germans. The city was falling apart around them. Still, Marcello Conversi and Oreste Piccioni managed to prove that these new particles lived more than 2 microseconds (2×10-6 seconds), much too long to be Yukawa’s pions.

The new particles were found to have spin 1/2, and didn’t seem to interact strongly with anything. Any particle that was produced in the upper atmosphere and that interacted strongly with the nucleus would have plenty of opportunity to do so on its trip down to sea level, as it would pass the nuclei of many air molecules on the way. It would be scattered many times and eventually captured by a nucleus. Therefore, it would have scant probability of ever reaching sea level. Because the new particles were detected in abundance at sea level after passing through miles of atmosphere, they couldn’t have a strong nuclear interaction. After the war, Conversi and Piccioni teamed up with Ettore Pancini and conducted an experiment that settled the matter. They decided to look for the expected nuclear interactions by measuring how quickly the particles were absorbed in carbon rods. Instead of being rapidly absorbed by the carbon rods, the new particles decayed in the same way as in the atmosphere. This meant that their rate of capture by the carbon nuclei was a trillion times slower than that predicted for Yukawa’s pions.

The new particle had the wrong spin, the wrong lifetime, and didn’t interact strongly with the nucleus. It wasn’t Yukawa’s pion—that much was certain. It came to be called the muon (denoted by the Greek letter mu, µ), and physicists came to think of it as a sort of overweight older brother for the electron. Here was a coup for the experimenters and a curve ball for the theorists. No one knew why there should be another particle just like the electron, but heavier. The curmudgeonly I. I. Rabi groused, “Who ordered that?”

Through the end of the 1940s and into the 1950s, cloud chambers continued to be built at higher and higher altitudes to take advantage of the greater flux of cosmic rays. Particle physics became a sort of extreme adventure sport: long days in cramped quarters while the storms blew outside, skiing on the glaciers in good weather, and, not infrequently, death in the crevasses. Detection methods were improved. Geiger counters were added to the cloud chambers, so that the chamber would be triggered and a photograph taken only when a particle was detected by the Geiger counter. A new technique was developed using photographic emulsion, essentially a type of camera film with an extra-thick layer of chemicals that could be left on the mountains for months at a time, then developed and examined microscopically for particle tracks. With this method, a track as short as a millionth of a centimeter could be seen.

With the new techniques, experimenters kept coming up with new surprises. A particle was discovered with spin 0, and mass about 270 times the electron mass, which would occasionally be seen colliding with a nucleus and producing a spray of particles—a clear sign of a strong interaction. Moreover, these particles were only detected on mountaintops, not at sea level; further proof of a strong interaction with the nucleus. Once again, physicists thought they had bagged Yukawa’s pion. This time they were right.

New, strange particles that left V-shaped tracks started showing up in the cloud chambers and emulsions. When a decaying particle is electrically neutral, it leaves no track in the cloud chamber (or emulsion), so the tracks of the particles produced in the decay seem to come from nowhere. In 1950, one such decay was shown to produce a proton and a pion. This was a shocker. The decaying particle, called the lambda-zero (λ0), must be more massive than a proton and a pion combined.

By 1955, there were particles called kaons (K+, K-, K° ), sigma-plus (Σ+), sigma-minus (Σ-) and xi-minus (Ξ-), some lighter, some much heavier than the proton. The subatomic zoo was growing larger and more confusing each year.

Thanks to Schwinger, Feynman, Dyson, and many others, QED, the theory of electrons, positrons, photons, and their interactions, was in good shape by 1950, and theorists were taking another look at the nuclear force. It occurred to more than one person that the nuclear force might behave somewhat like QED. After all, the electric force in QED was carried by photon exchange, as we have seen. In Yukawa’s theory, the nuclear force was carried by pion exchange in a similar manner:

Here a neutron emits a pi-minus, turning into a proton. Then, a nearby proton absorbs the pi-minus and turns into a neutron. Thus, the nuclear force arises from pion exchange, just as the electric force in QED arises from photon exchange. To make this scheme work, theorists found they had to introduce a new concept, which they called isospin.

The isospin concept was introduced in analogy to an electron’s spin. The electron has spin 1/2, and by the rules of quantum mechanics, it can be in one of only two states when placed in a magnetic field. The direction of the spin arrow is determined by the right hand rule: curl the fingers of your right hand in the direction the electron is spinning and the direction your thumb points is the direction of the spin.

Using this rule, the electron’s spin is up, or +1/2, when it is in the same direction as the magnetic field and down, or -1/2, when it is opposite to the field. The down state has more energy than the up state, so it is possible for an electron with spin down to flip to spin up, emitting the excess energy as a photon.

According to the isospin concept, the neutron and the proton should be thought of as two different states of the same particle, called the nucleon. The nucleon has isospin 1/2, which means it can exist in two different states. If the nucleon has isospin down, or -1/2, it is a neutron. If its isospin is up, or +1/2, it is a proton. By flipping its isospin, it changes from one state to the other, emitting (or absorbing) a pion in the process. In the case of the electron in the magnetic field, the photon, with spin 1, makes up for the difference between the spin-up (or +1/2) state and the spin-down (or -1/2) state. Analogously, the pion, with isospin 1, makes up for the isospin difference between the neutron and the proton. You should not think of isospin as having an actual direction in space. Unlike spin, isospin lives in a fictitious space, an “internal” direction that has nothing to do with the three-dimensional space in which we move. In the case of spin, the words up and down compare the spin direction to the magnetic field direction. In the case of isospin, the words up and down are used merely for convenience. There is no direction in physical space to compare with the isospin direction. The quantum mechanical rule is that isospin, like spin, must change in whole-number steps, so a particle with isospin 1, like the pion, can exist in three different states: isospin +1, isospin 0, or isospin -1. The +1 and -1 versions correspond to Yukawa’s pi-plus and pi-minus. Isospin theory requires a third version, the neutral pi-zero, in addition.

If it sounds weird that an electron can spontaneously emit a photon, as in QED, then the idea that a neutron can spontaneously transform into a proton by emitting a pion seems downright bizarre. It is as if a Great Dane could be walking down the street and then spontaneously transform into a Weimaraner and a Siamese cat. Indeed, Yukawa’s pion theory wasn’t received enthusiastically at first. The discoveries, first of the muon and then of the pion itself, fired a frenzy of activity directed at understanding the pions and the nuclear forces. As Yukawa’s theory began to prove its worth, the bizarre transformations it required of its particles came to seem natural and unobjectionable to physicists. Eventually, this sort of transformation became a basic feature of relativistic quantum field theory.

Building a Better BB Gun

As more and more strange and inexplicable particles were being discovered in the cosmic ray data, experimenters became impatient with waiting for something interesting to fall from the sky. How much better it would be to have a machine that produced high-energy particles! Then you would know what particle was coming in, when it was coming, what energy it had to start with, and you could be prepared to look at the results, in a way that was impossible with cosmic rays. Fortunately, a particle accelerator is easy to build. In fact, chances are you have one in your house. It’s called a TV.

In order to accelerate particles, you need the following:

1. A source of particles

2. A way to speed them up

3. A way to steer them

4. A target for them to hit

In your TV, the particle source is called a cathode. It’s similar to the filament in a light bulb: a little wire you heat up by passing electric current through it, which spews electrons in all directions.

Because electrons are charged particles, all you need to accelerate them is an electric field, which is provided by connecting a voltage source to two metal plates ([2] in the diagram). After passing through a hole in the positive plate, the electrons are steered by two more pairs of plates that bend the beam in the up-down or side-to-side direction (3). The target is the phosphorescent material on the inside of the TV screen, which glows when struck by the electron beam, producing a tiny glowing dot, which forms part of the TV picture (4). The inside of the TV tube is devoid of air so that the electrons won’t be scattered before hitting the screen. The particle accelerators that were being built in the 1950s (and are still being built today) are basically the same as a TV. The main difference, of course, is that the particles need to be accelerated to much higher energy in order to get anything interesting out of the collision with the target. There are two ways to do this.

One possibility is to use multiple acceleration stages, and daisy-chain them so that the particles coming out of one stage immediately enter the next stage and get accelerated some more. The whole thing is enclosed in a tube with a very high vacuum. You can keep this up as long as your budget will allow. This type of machine is called a linear accelerator. The Stanford Linear Accelerator Facility (SLAC, for short) is the largest such machine. It started operating in 1967 and was considered a monster machine—two miles long, that being the largest they could make it on Stanford University’s grounds—both by the physicists and by the local communities. For most of the machine’s length, microwaves provide the acceleration. The particles (electrons and positrons, in the case of SLAC) surf along on the microwaves and pick up additional energy. For a linear accelerator like SLAC, steering is limited to keeping the beam straight and focused—as narrow as possible so that the maximum number of particles hits the target. The target at SLAC in the early days was usually liquid hydrogen. Hydrogen is a particularly simple target: it has just one proton and one electron; there are no neutrons to confuse matters.

To get to even higher energy (and so probe even deeper into the proton), you might think of turning your beam around in a loop and sending it back through the accelerator, just like you might drive through the car wash twice to get your car extra-clean. This is the idea behind the cyclotron, invented in the 1920s by Ernest O. Lawrence at the University of California at Berkeley. Lawrence knew that he could use a magnetic field to get the electrons to loop around. The crucial realization came when he saw that each time the electron passed through the accelerator it would gain speed, but it would also swing out in a larger circle. Because it had farther to go, but was traveling faster, it would take the same time to go around, no matter how many times it passed through the accelerator stage. When Lawrence realized that the larger circle (of radius R) and faster speed (also proportional to R) cancelled out to keep the trip time constant, he ran around the laboratory, stopping people to tell them, “R cancels R! R cancels R!” This meant he could use a simple alternating current to provide the electric field.

Every time the electrons crossed the gap between the D-shaped plates, they got a small kick from the alternating electric field. By the time they returned to the gap on the other side, the electric field would have switched direction and they would receive another small kick. In this way, electrons would spiral out until they reached the outside edge of the D, at which point they would fly out in a beam. Lawrence’s first machine had 4-inch Ds. With an 11-inch version, he managed in 1932 to accelerate electrons to an energy of a million electron-volts. (An electron-volt is the amount of energy an electron gains when accelerated by an electric potential of one volt.) At this energy, the electrons are traveling at 90 percent of the speed of light. Because of special relativity, the cancellation that got Lawrence so excited no longer works, so to go to higher energies, physicists had to do things differently.

The largest particle accelerators in existence today are called synchrotrons. A synchrotron is essentially a huge circular tube with magnets surrounding it to bend the electrons (or other particles) in the correct path, and with one or more accelerating stages at various points around the circle. Because the size of the circle is fixed, the magnetic field must be increased each time the particles pass through an accelerating stage, to keep them from swinging out into a larger orbit and hitting the wall of the tube. One of the most powerful machines ever built is LEP (Large Electron-Positron machine) at the European laboratory CERN (European Organization for Nuclear Research), on the Swiss-French border near Geneva. It is 17 miles in circumference and accelerates electrons to 100 billion electron-volts. They cross from Switzerland to France and back again twenty thousand times a second; fortunately, they don’t need to go through customs.

To perform an experiment, you need to do more than smash particles together; you need a detector to measure the results. In the early days, the detectors were bubble chambers: vats of liquid helium in which charged particles left tracks. The tracks were photographed and the photographs carefully measured. The identity of each particle was deduced from the thickness, length, and curvature of each track. Modern detectors are much more complex and varied in design. In the most common setup, the detector surrounds the interaction region where two accelerator beams cross each other. The detector is built in multiple layers that attempt to extract all the important information about the collision. The complete onion-like structure is the size of a house.

For instance, the CDF detector at Fermilab consists of four main layers. The innermost layer is the vertex detector, constructed of thin silicon strips (somewhat like a computer chip) and designed to identify as closely as possible the location of the collision. The second layer is a large chamber crisscrossed with many exquisitely thin gold wires. This is the tracking layer. Whenever a charged particle passes near one of the wires, the wire’s electrical properties change, and a computer records the changes. A strong magnetic field bends the particle’s path; the curvature of the path helps identify the particle’s charge and momentum. The next layer is a stack of thin lead plates interspersed with photon detectors. This layer is called the calorimeter. It is a gauntlet the particles are made to run in order to measure their energy. An electron will only penetrate a few inches, whereas a heavy particle like a proton may penetrate a foot or more. A photon, being electrically neutral, will pass through the tracking chamber without a trace, but it will deposit its energy in the calorimeter. Muons, heavier than electrons but without strong interactions, will zoom through the tracking layer, pass entirely through the calorimeter, and be trapped in the outermost layer, specially built as a muon detector. Only neutrinos run the gauntlet and escape completely, without registering in any of the layers. Their presence can be deduced from the missing energy they carry away. Many of the particles of interest don’t live long enough to reach the tracking chamber. They can only be detected indirectly, by identifying the particles they decay into, and then working backward to find the energy, charge, and spin of the decaying particle.

A second method of identifying new particles looks at a whole series of scattering experiments, rather than an individual event. Experimenters tune their accelerator to a particular energy and simply record the total number of “hits,” or scattering events, in which a particle from the beam is deflected or transformed into other particles. They then increase the beam energy by a small amount and again count the scattering events. The graph that results shows a bump at the energy corresponding to the mass of the particle being created in the collision, as in the following graph, which depicts the data that revealed the existence of a particle known as the J/psi.

The width of the bump, ΔE, tells the lifetime, Δt, of the particle via the Heisenberg uncertainty principle: Δt = E. If you stand in a shower stall and sing a scale, you find that certain notes resonate much more loudly. These resonant notes occur whenever the sound wavelength fits the size and shape of the stall. Incrementally stepping the beam energy is like singing a scale. Whenever the beam energy fits the mass of a new particle (according to E = mc2), there is a resonance: more scattering events occur. The drawback to the resonance method is that it reveals only the mass and the lifetime of the particle. To learn its other properties, spin, charge, isospin, and so forth, experimenters resort to the first method, examining individual scattering events.

Each time a new accelerator started up, new and heavier particles were discovered. Where did these particles come from? They were created from pure energy.

Remember that, according to Einstein’s E = mc2, energy can be converted into matter and vice versa. The accelerator pumps some particle, say, an electron, full of kinetic energy. The electron then smashes into a target—possibly a stationary one, like the vat of liquid hydrogen in the early SLAC experiments, or else another particle, a positron, for instance, that has been accelerated so that it meets the first electron head-on. The kinetic energy of the colliding particles is released, like sparks struck off when two rocks are struck together. Now a principle comes into play that has been called the totalitarian theorem: “Anything that is not forbidden is compulsory.” Applied to particle collisions, this means that anything can happen to the energy of collision, as long as it isn’t forbidden by the law of conservation of energy, or conservation of momentum, or of spin, or of charge, or by some other conservation law (possibly one we haven’t discovered yet). So if the colliding particles have enough energy to equal the mass, say, of a lambda-zero, then a lambda-zero must be produced at least some of the time, if its production is not forbidden by other conservation laws. If you had enough energy, you could, in principle, produce a Toyota the same way: pile a tremendous amount of energy into the collision of two objects, and some (infinitesimally small) fraction of the time, that energy will appear in the form of a Toyota. This is not a practical way to get a new car because, firstly, the energy needed is about that of a million nuclear bombs, and, secondly, most of the time the energy would get converted into less pleasant forms—heat, radiation, and massive destruction.

Now, suppose you are colliding electrons with positrons and you hope to produce a xi-minus, which has a charge of -1. To reach the energy you need, you are helped by the fact that the electron and the positron will likely annihilate, liberating the mass-energy of both particles as well as the kinetic energy. But there is a pesky conservation law in the way. You start out with an electron (charge -1) and a positron (charge +1 ): 0 net charge. You can’t produce a xi-minus unless you also produce a positively charged particle at the same time. So we could hope, for example, to produce a xi-minus and a proton together. (Of course, we would need to begin with enough energy to add up to the total mc2 of both particles.) But what if there is some other conservation law that prevents this possibility—say, conservation of isospin (if it really is conserved), or of some other type of “charge”? We can still hope to get some xi-minuses by starting with twice the energy we would need for one xi-minus, because we would then have enough energy to produce a xi-minus and its antiparticle, the xi-plus. Because the antiparticle has all its properties reversed, it will have the opposite isospin, and opposite values of any other possible “charges,” so that the total “charge” will always be 0 for any conceivable conserved quantity. In short, we can produce any particle that exists simply by pumping enough energy into the colliding particles.

All of these possibilities can be represented by the following Feynman diagram:

We see an electron (e-) and a positron (e+) approaching and colliding (left side of diagram). They annihilate, producing a photon (γ). The photon then produces a particle-antiparticle pair (X stands for the particle, X for its antiparticle). The two newly minted particles then move off in different directions.

As experimenters improved their techniques throughout the 1950s and 1960s, they discovered one new particle after another. The earlier shyness about declaring the existence of new subatomic particles wore off as the particle count ratcheted higher and higher. Physicists came to call it the subatomic zoo: the bewildering array of new particles with their different masses, spins, lifetimes, and decay modes. Around the turn of the century, it had seemed that three particles constituted all the matter in the universe: the proton, the neutron, and the electron. What had begun as a simple quest to explain the force that held neutrons and protons together had become a nightmare of confusion. Why were all the new particles necessary? In Rabi’s phrase, who had ordered them? What did they have to do with the nuclear forces? And who could bring order to them, now that there was such an amazing variety of them?

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