Beyond the God Particle

by Leon M. Lederman

  Bohr realized that, in their state of rapid circular motion about the nucleus, electrons would radiate away all of their energy in the form of electromagnetic waves very quickly. Like the swoop of a seagull into the sea, the electron orbits would quickly shrink to zero, within a tenth of a millionth of a billionth of a second. The electrons would spiral down into the nucleus. This would make the atom, ergo all of matter, chemically dead and the physical world as we know it impossible. The exact classical equations of electricity, due to Maxwell and based upon Newtonian physics, spelled disaster for the atom. Either the model had to be wrong, or the venerable laws of classical physics had to be wrong.

  Bohr applied himself to understanding the simplest atom—the hydrogen atom—which would have a single electron in orbit around a positively charged nucleus consisting of a single positively charged particle called a proton. Thinking about the new quantum ideas that were in the air, that particles are also waves, young Bohr was led to propose a very novel idea. He argued that only certain special orbits can ever happen for electrons in atoms because the motion of electrons in these orbits must be like that of waves. These are like the natural wavelike motion of a ringing bell or a Chinese gong, with a dominant lowest tone, or mode, and a sequence of “overtones” or “harmonics.” The lowest mode, what we mostly hear when the bell tolls, would be the one with the least amount of energy, corresponding to the wave motion where the electron is moving closest to the nucleus. In this lowest orbit the electron cannot radiate away anymore energy, because this is the state of lowest possible energy for the electron motion—the electron has no lower energy state into which to go. This special orbit is called the ground state. This is one of the hallmarks of quantum theory: atoms cannot just collapse into nothingness and are actually supported by the quantum wave motion, leading to the existence of a ground state, the state of lowest possible energy.

  In three papers published in 1913, Bohr articulated his audacious quantum theory of the hydrogen atom. Each of the atom's magic harmonic orbits is characterized by a certain energy. An electron emits a definite amount of radiation when it “jumps” from an orbit of higher energy down to one of lower energy. It emits a photon, the particle of light, whose energy is given by the difference of the energy of the two orbits. With billions of atoms doing this at the same time, we see bright and unique colors for the emitted light, the photons all having exactly the same energies. Bohr put his theory to work and calculated the wavelengths of all the emitted photons, the colorful “spectral lines,” seen in a spectroscope from hot glowing hydrogen gas. His formula worked perfectly! Electrons now moved in “Bohr orbits,” or “orbitals,” within the atoms.

  None of this made the slightest sense in the familiar framework of Newtonian-Galilean physics. It required sweeping changes in our understanding of physics and the further development of the radical new ideas of quantum mechanics. In any case, atoms were indeed seen, by now, to be made of still smaller objects: the electrons and the atomic nucleus, and the rules of motion, the relevant laws of physics, were now totally new and totally quantum mechanical.

  QUANTUM WAVES AND COSMIC RAYS

  The quantum wavelike behavior of all matter was established within the first several decades of the twentieth century through numerous experiments, and the quantum theory was cobbled together (see note 3). By accelerating particles, we can shrink their quantum wavelengths. The overall characteristic “size of the atom” is determined by the “Bohr radius,” which is the size of the quantum wave of the electron ground state of hydrogen and is about 0.000000005 centimeters (0.5 × 10–8 cm). The atomic nucleus is very much smaller, about one-hundred-thousandth the size of the Bohr radius. To explore these much smaller distances required much more energetic probes. High-energy particle accelerators would not arrive on the scene until the 1950s.

  Nature, however, provides one extremely high-energy source of particles. These are very energetic cosmic rays that bombard Earth coming from deep outer space.11 The cosmic rays are produced by violent processes in distant star systems, such as supernovae, pulsars, and active galactic nuclei. They are steered on the voyage to Earth by galactic magnetic fields, and their sources generally cannot be identified. The energies of cosmic rays extend way up beyond the highest energies of any particles we have ever seen or produced in the laboratory, higher than the LHC itself. The highest-energy cosmic rays ever detected have about 100,000,000,000,000,000,000 electron volts of energy (That's 1020 eV; for comparison the LHC design energy is 14 trillion eV, or 1.4 × 1013 eV), but these cosmic rays are extremely rare, only one of them passing through one square mile of sky every century! However, cosmic rays of energies up to about 1,000,000,000,000 eV (1,000 GeV; that's 1,000 Giga-eV, and 1 Giga = 1 billion) are sufficiently abundant that they can be put to good use to act as scientific probes—even to discover new particles.

  Typically, cosmic rays, mostly protons and some heavy atomic nuclei, collide with the nuclei of nitrogen and oxygen high up in the earth's atmosphere, perhaps 10 to 20 miles up. These collisions smash the nuclei apart and send other particles as debris downward, into the atmosphere. This typically generates a plume of electrons from all of the subsequent ionization and more collisions of debris particles with other atoms. Long-term exposure to this radiation would be harmful, but we are protected by the atmosphere at ground level. Occasionally some new particle could, in principle, be produced, and it might be detected all the way down at the surface of the earth, provided it is a deeply penetrating particle. Some experiments place detectors high up on mountaintops or in balloons to try to detect less deeply penetrating particles.

  From the 1930s, and even beyond the 1950s, when particle accelerators finally became available, most of the early discoveries of new elementary particles came from cosmic ray experiments. And, to this day, cosmic rays continue to serve us well in providing information that is hard to obtain from accelerators. Most recently, the masses of neutrinos were established using cosmic rays as neutrino sources in 1995 (see chapter 10).

  The energy stratum of the nucleus is measured in terms of millions to hundreds of millions of electron volts. To unravel the nucleus required probes of hundreds of millions of electron volts, so people in the 1930s and 1940s turned to exploit cosmic rays.

  THE MYSTERY DEEPENS: WHAT HOLDS THE ATOMIC NUCLEUS TOGETHER?

  By the mid-1930s, building upon Rutherford's discovery and the new quantum theory, it was realized that the atomic nucleus is composed of particles called protons and neutrons. The proton and neutron are very similar particles, each having about the same mass, but there is a big difference: the proton has a positive electric charge, while the neutron is electrically neutral. Hydrogen has the simplest nucleus that consists of a single proton, but all heavier nuclei are made of combinations of protons and neutrons, just as molecules are made of atoms. For example, the normal helium nucleus contains two protons and two neutrons.12

  Nuclei, like helium containing two or more protons, can only be held together by a very strong force—which is simply called the strong force. This nuclear-binding strong force has to be ultra-strong because the protons each have positive electric charges and therefore repel one another electrically. The nucleus of an atom like helium would instantly fly apart unless an overwhelmingly strong force compensated for this electrical repulsion and bound the protons, together with the neutrons, into the compact nucleus. Indeed, a nucleus like uranium, with 92 protons, is very unstable because of the enormous repulsive electrical forces of so many protons. Uranium therefore has many isotopes, such as U233 (where 233 = 92 protons + 141 neutrons), U235 (92 protons + 143 neutrons), U238 (92 protons + 146 neutrons), etc. Notice that we can package more neutrons into uranium because they are electrically neutral, and even help the binding together of the 92 protons. The strong force is about 10,000 times stronger than electromagnetism, and it can hold nuclei together up to about 100 protons.

  Very heavy nuclei with lots of protons are generally unstable due to this elect
ric repulsion. They undergo fission (spontaneously break apart) into lighter nuclei.

  Forces, in our quantum world, are actually generated by particles. The force between two objects, like a proton and a proton, is caused by lighter particles that jump to and fro between the two protons. The repulsive electrical force is caused by the jumping of photons, the particle of light, back and forth between the protons. The strong force had to be due to something else.

  A particle responsible for the strong force was predicted by the Japanese physicist Hideki Yukawa,13 in 1935, based upon the known properties of the atomic nucleus. Yukawa reasoned that the force of electromagnetism is comparatively long range—the electric force between charged particles decreases “slowly,” by the inverse square law (it falls like 1/r2 where r is the distance between the two particles). This inverse square law arises because the photon is a massless particle and can easily jump between nearby or distant electric charges. The force of electromagnetism is also somewhat feeble, because the “jumping probability” in quantum theory involves a small number, essentially the (square of the) electric charge (see the Appendix). This gives rise to the electric force that binds electrons to the positively charged protons in the nucleus.

  On the other hand, an atomic nucleus is very small, a typical radius of about 0.0000000000001 centimeters (10-13 cm), about one hundred thousand times smaller than the electronic orbits that define the chemical size of the atom. This arises in part because of the much larger masses of protons and neutrons than electrons, but also by the strength of the strong force that overcomes the electric repulsion between protons. Furthermore, the nucleus is quite compact, requiring that the particle of the strong force need not produce a long-range or inverse square law force (which would have been detected outside the nucleus), but rather it is a short-range force. Yukawa realized that this required a new particle that could hop back and forth between protons and neutrons, causing the strong force, and the new particle would need to have a mass of about 100,000,000 eV (100 million eV, or 100 MeV; see note 4) to account for the short range of the new force.

  Figure 2.2. Forces Arise as the “Exchange of Particles.” The force between two particles arises from the “exchange of particles.” Two electrons, or any electrically charged particles, interact by exchanging photons, which are the particles of light. A proton and neutron strongly interact by exchanging pions.

  This is a tall order, but it certainly pointed the particle searchers in the right direction. And remarkably, in 1936 a particle with a mass of 100 MeV, called the muon (pronounced mew-on), or µ, was discovered in 1937. It seemed to be the thing predicted by Yukawa, but people soon realized that the muon was a case of false identity—the cops had arrested the wrong guy. The muon was discovered by using cosmic rays that (somehow) produced it 10 miles up in the sky. The muons then traveled to the surface of the earth where they could be detected. The reason the muon was initially thought to be the particle Yukawa had predicted (called the pion [pie-on], or π) was because it had Yukawa's predicted mass. But the muon did not interact strongly enough with protons and neutrons to be a pion since it could travel all the way to the earth's surface (muons only interact electromagnetically, or through the weak force). This new particle definitely was not the agent of the strong force, as predicted by Yukawa. In fact, the muon seemed to be a mere carbon copy of the electron but 200 times heavier, with a lifetime of about 2 millionths of a second (whereby the muon “decays” into an electron and a pair of neutrinos).14

  Almost all pure physics research was interrupted by World War II, as the world's scientists were redirected to serve military needs. The quest for Yukawa's pions could resume only after the war. In the meantime humans had conquered the atomic nucleus, with its strong force—and unleashed its fury.15

  In 1947, the pions, predicted by Hideki Yukawa to explain the strong nuclear force, were finally discovered by using cosmic rays. This vindicated Yukawa's ingenious theory, for which he later won the Nobel Prize in 1949.

  The pions arrived in three types, distinguished by their electric charges, π+, π–, and π0, where the superscript refers to the particle's electric charge. We often refer to π+ and π– as the “charged pions” and π0 as the “neutral pion.”1 The strong force, which welds the protons and neutrons together to build the atomic nucleus, arises as Yukawa had theorized through the “exchange of pions,” hopping back and forth between protons and neutrons as quantum fluctuations. The picture of the atom and its nucleus was now complete.

  Soon there would be particle accelerators, and numerous “elementary particles” emerged from experiments. Most of the multitude of new objects were strongly interacting, that is, they “felt” the strong force, and they interacted strongly with the pions, protons, and neutrons. It was also discovered that the proton, the neutron, the pions, and the long list of new strongly interacting particles, were not point-like objects but actually had finite sizes of about a hundredth of a trillionth of a centimeter. In the extreme cases some new particles were discovered that had lifetimes as short as the time it took light to transit their finite diameters. The nascent world of particle physics was never more confusing and chaotic than in the 1950s as the first higher-energy particle accelerators came online.

  Throughout this time, the poor muon seemed to be an oddball, an almost uninvited guest at the dinner table.2 The muon has a mass about 200 times that of the electron. It “decays” (through the weak interaction) into an electron and two very difficult to observe particles called neutrinos, living a mere two millionths of a second when at rest in the laboratory. Otherwise, the muon seemed to play no particular role in anything else, pointless in the fabric of nature. Its serendipitous and seemingly random appearance had elicited the famous quip by I. I. Rabi, “Who ordered that?”3

  Figure 3.3. The Atom, Pion Exchange, and the Atomic Nucleus. An atom consists of the cloudlike motion of electrons about a dense nucleus containing protons and neutrons. The nucleus is held together by the exchange of pions that hop back and forth between the neutrons and protons.

  We could retrace the long and winding road taken by particle physics from 1947 onward. There followed the era of the 1950s and 1960s when powerful new accelerators and various national laboratories came along. At one time there was a new energy frontier particle accelerator every few years or so, and a plethora of new “particles” and particle phenomena were discovered. Yes, we could stroll down memory lane and recount all of the history and structure of the Standard Model. Your eyes might glaze over, your eyelids becoming heavy. Rather, we'd like to veer off that traditional litany and do something a little different. We want to hop, skip, and jump to the Higgs boson as quickly as we can, to actually delve in and try to explain it to you in a way that is as close as we can get to how physicists understand it.

  Indeed, by the time physicists understood the details of the forces of nature, in particular the “radioactive” transmutations between these particles that involve the “weak force,” it was soon realized that some kind of “Higgs boson” was a necessity. This realization mainly came from the work of one of the architects of the Standard Model,4 a theorist named Steven Weinberg (see chap. 1, note 14). There was no other way to make particles behave the way they do, and simultaneously to have mass, without something like a “Higgs mechanism.” Remarkably, one of the key ingredients to this revelation, the ingredient that mandated the theoretical existence of a Higgs boson, was revealed by the lowly muon (in concert with the charged pion, which also decays through the weak force into a muon and a neutrino). The pion and muon decays provided the major clue about the weak forces of elementary particles that would lead directly to the Higgs boson. It was in an almost incidental way that the muon revealed the essential aspect of the weak force that ultimately legislates the Higgs boson into existence. The unexpected and uninvited guest at our table, the muon, was actually a gift—perhaps this is the answer to Rabi's question as to why the muon was “ordered.”

  We also think that
in the not-too-distant future humans will use the muon as a powerful practical tool, much like we use everything we discover in nature. In fact, muons are already providing themselves as new diagnostic tools that scientists use to study nuclear and atomic processes. In some quarters there is a fervent albeit long-shot hope that the muon might ultimately provide the catalyst needed to unleash the ultimate energy source—nuclear fusion—through a process known as “muon-catalyzed fusion.”5 And we believe our favorite laboratory, Fermilab (or some other laboratory in another country, if the US government doesn't get its act together), will someday build a new type of high-energy particle collider—one that will literally rank as the most sophisticated thing humans ever built—a machine that collides muons—the Muon Collider.6 There are many reasons why this is very good ideas—so let's now pop open some champagne and celebrate…

  THE LOWLY MUON

  As we've seen, people were expecting to observe the pion, with a mass of about 100 MeV, to confirm Yukawa's theory that explained the strong force between the neutron and proton and that holds together the atomic nucleus. Instead, Carl Anderson and Seth Neddermeyer, at Caltech in 1936, found the muon in the debris of cosmic rays that bombard the surface of the earth.7 Muons are produced in the upper atmosphere when primary, very energetic cosmic rays from outer space collide with nuclei of atoms in the thin air. But even that story has a peculiar twist.

  How are muons produced in these collisions? Remarkably, we know today that pions are, indeed, immediately produced by the cosmic rays hitting atomic nuclei in atoms of nitrogen and oxygen in the earth's upper atmosphere. This happens because the pions are strongly coupled to nuclei (they are the glue that holds nuclei together, after all), and the cosmic rays are essentially protons colliding with other protons and neutrons in the nuclei of atoms in the atmosphere—at the high energies of cosmic rays, this process readily ejects pions. The pions then rapidly decay into muons (and neutrinos) within about a hundredth of a millionth of a second.