Beyond the God Particle

by Leon M. Lederman

  But how does nature perform this grand marriage of L and R that gives us mass, the things we see in the world around us, the world of things moving slowly or at rest, having time to think and experience?

  In a simple world in which there are only muons interacting through electromagnetism (this is called “quantum electrodynamics,” or “QED” for short) we can easily perform this happy marriage and still respect the vaulted law of the conservation of electric charge. That is, there is nothing special about mass in QED. This can be done because the R muon has the same electric charge as the L one. For the muon, as well as for the electron and all electrically charged matter particles, when we include the effects of electromagnetism, there is a perfect symmetry between L and R—“parity” becomes a symmetry and L and R are otherwise indistinguishable—they have the same electric charges.

  From Alice's point of view, she might encounter the L and R muons on the table in her parlor and then see the mirror reflection of L and R, but by observing only their electric charges, she would see no difference between the mirror L and R in the looking-glass house, because L and R have the same electric charges. Theoretical physicists introduced the mass of the muon, or of the electron, into their equations “by hand” in the theory of QED—there was no need for a Higgs boson in electromagnetic theory.

  But, as we described in chapter 3, parity was discovered experimentally not to be a symmetry when the weak force is involved. The experiment of Lederman and his colleagues in 1957 demonstrated for the first time that parity was violated both in the weak interaction decay of the pions of Yukawa and of the muon itself—pretty good for a weekend's work! It was astounding news—the weak processes are not invariant under the parity—the looking-glass house through the mirror has different laws of physics than in Alice's parlor on our side of the mirror. This means that if Alice looks closely enough at the L muon, she will see something quite different than for the R muon.

  THE WEAK INTERACTIONS

  It's been almost 70 years since Enrico Fermi wrote down the first descriptive quantum theory of the “weak interactions.” At that time, these weak forces were backstage, the feeble forces seen at work in nuclear processes such as beta decay. Only later was it understood that they are critical to the burning of the sun and provide the gunpowder of nature's largest explosion since the big bang, the supernova. Supernovas make the heavy elements found in the universe and especially here on Earth. Without the weak force in nature we wouldn't be here.

  So, we're going to fast-forward through history. The weak forces were later found to be very similar in structure to electromagnetism. Like the photon of electromagnetism—the particle that jumps back and forth between charged particles and creates electric and magnetic forces—the weak interactions also involve new particles, called W+, W–, and Z0. These are similar to the photon, and the quantum jumping of W+, W–, and Z0 between matter particles causes the weak forces.

  Just as the particles that “feel” electromagnetism all have electric charges, the matter particles that feel the weak force have “weak charges.” Unlike the photon, however, the W+, W–, and Z0 are very heavy particles, and this suppresses their jumping back and forth between particles that have weak charges, so the weak forces become very weak. Initially, the W+, W–, and Z0 were only theoretical discoveries, but they ultimately defined a big part of the architecture of what we now call the Standard Model. These developments were led by theorists Sheldon Glashow, Abdus Salam, and Steven Weinberg, and the theory was perfected into a workable quantum theory by Gerard ‘t Hooft and Martinus Veltman, all of whom shared well-deserved Nobel Prizes for their heroic effort.

  The weak interactions are welded, or “unified,” with electromagnetism in the Standard Model. In the utopian world in which we can turn off all the masses of all particles, the W+, W–, and Z0 would also become massless and are essentially indistinguishable from the photon, γ. The “symmetry” of the Standard Model is precisely the idea that, when they are all massless, these four particles can be viewed as one “uber-particle” with four parts (technically it's 3 + 1 parts, but we'll not get into the delicacies of this distinction). We now know how to effectively turn off mass: just make things travel as closely as you can at the speed of light. It's a little hard to do, but that's almost what happens at the LHC when these heavy particles are produced. And, indeed, we see in our experiments that at ultra-high energies, or for extreme short distances and short time scales, the symmetry of the Standard Model works down to every last detail. There are many predictions of the Standard Model that have been tested experimentally, and we haven't found a single glitch yet.

  Developing the Standard Model constituted a revolution in particle physics that occurred in the early 1970s, at about the time quarks, the tiny particles that make up the proton and neutron and pion, were first glimpsed in experiments. This was the decade when it became both theoretically and experimentally established that all forces in nature are governed by the overriding symmetry principle, called gauge symmetry. This was known to govern electromagnetism and gravity and could now be extended to the weak interactions and the strong force among the quarks.

  HOW DO THE WEAK INTERACTIONS WORK?

  Let's return to our “space-time” diagrams. In figure 6.20 we show a greatly magnified view of how a muon decays, as Fermi would have described it in his primitive theory of 1935. The heavy muon is at rest and it moves forward in time. Suddenly, it disintegrates into a low-mass electron and two neutrinos. We write symbolically for this process:

  In Fermi's day the neutrinos were considered to be the same species of particle (one is a particle, the other an antiparticle), and the overthrow of parity had yet to be discovered.

  Much was learned since Fermi's original paper in 1935 up to the time of the Standard Model revolution in the early 1970s. Today we know (again, thanks to Leon and his friends and their work on a different experiment, which won Leon the Nobel Prize) that there are actually two different kinds, or “flavors,” of neutrinos involved here. One of these is associated with the electron and is called the “electron-neutrino.” Another is associated with the muon and is called the “muon-neutrino”; today we know of a third neutrino associated with the τ lepton, called the and τ-neutrino.1 But the main thing we want to examine is precisely how this process occurs at extremely short distances. In fact, the weak interaction of the muon that produces its decay is an “indirect process,” where the W boson is only evident at an extremely short distance over a miniscule period of time. To see this we need to crank up the magnifying power of our microscope by a quite a bit.

  Figure 6.19. Fermi's Theory of Muon Decay. Muon decay is depicted in the Fermi theory of weak interactions, ca. 1935. Here we see the process µ– → e– + vµ + anti-ve. Using the measured lifetime of the muon of about 2 millionths of a second, we can calibrate the strength of the weak interactions, and we can infer the “energy scale of the weak interactions” to be about 175 GeV. This turns out to correspond to the strength of the Higgs field in the vacuum.

  In figure 6.20 we show how the muon decays as it would be seen at the magnification of the Fermilab Tevatron or the LHC (this isn't exactly how it's done, but the metaphor holds; processes exactly like this were seen in top quark decay at the Tevatron when the top quark was discovered in the mid-1990s and are now “bread-and-butter” physics at the LHC).

  Figure 6.20: Muon Decay in the Standard Model. We examine the muon decay under a powerful microscope, which shows how it appears in reality as described by the Standard Model. We see in the process µ– → e– + vµ + anti-ve that a muon converts into a W boson and a neutrino. There is insufficient energy for the W boson to become a real particle in this process, so this only occurs as a quantum fluctuation, for a brief instant of time, as allowed by Heisenberg's uncertainty principle. The W boson instantly converts to the electron and antielectron neutrino, W– → e– + anti-ve. This is a suppressed quantum fluctuation causing the weak interactions to be “weak.” By partic
le physics standards, the muon lifetime of 2 millionths of a second is a very long time.

  Here we see a sequence of events. We start with our massive muon at rest. Then at event (A) the muon converts to a muon-neutrino and a W– particle. Note that the negative electric charge of the initial muon has gone to make the negatively charged W–, so electric charge is conserved, as it must be. The W– then instantly converts into the electron and an antielectron neutrino at event (B). Again, electric charge is conserved.

  “Wait a minute,” says Graham, “aren't you swindling us with this small mass, muon particle converting into the monster heavy W–? This must grossly violate the conservation of energy!” Indeed, the W– boson has a mass that is almost a thousand times greater than the muon (the mass of the muon is only 0.105 GeV, while the W– boson has a mass of 80.4 GeV). Graham is right! There is no way that a muon can convert to a neutrino plus the ultra-heavy W– boson and conserve energy. What is happening here? Why does an “indirect process” exist with an ultra-heavy W– boson existing for only a fleeting instant of time?

  This is an example of one of the great wonders and chestnuts of quantum theory, called the Heisenberg's uncertainty principle. The time interval between the creation for the W– from the muon, and W– converting into the electron is extremely short (about 0.0000000000000000000000001 seconds, or 10-25 seconds). Heisenberg tells us that, as a consequence of quantum theory, energy is a fundamentally uncertain quantity during extremely short time scales. In fact, he tells us exactly by how much.2 For that miniscule amount of time, the amount by which the energy is uncertain is equivalent to the mass of the W– boson in Einstein's formula E = mc2. Therefore, the uncertainty principle allows the W– to exist, but only for a tiny instant of time. This is called a “quantum fluctuation.”

  However, this requisite, large “quantum fluctuation of certainty of the energy” needed to momentarily evade energy conservation causes the resulting process to be very improbable—it is a “rare quantum fluctuation.” This is why the overall process is a “weak interaction.” In fact, the amount by which the overall decay of the muon is suppressed, since it requires a big quantum fluctuation in energy, is a factor of about one trillionth (or 10-12) compared to what would happen if the W– could be replaced by a massless particle like a photon, which would require no quantum fluctuation in energy at all (the photon, however, cannot convert a muon into its neutrino since it must conserve electric charge and can only convert a muon into a muon). The only way the muon can decay is through this highly suppressed process involving the heavy W– boson that converts a muon into a muon-neutrino.

  But let us examine the “conversion” of the muon into a neutrino plus a W– boson in still greater detail. Recall that the world of Alice through the looking glass is fundamentally different than ours because of the violation of parity. If we examine figure 6.21 we see why. The muon comes marching in, L-R-L-R-…as all massive particles do, oscillating between L and R. At some instant, while the muon has oscillated into an L particle, it can convert into the W– boson and the neutrino. The neutrino is effectively massless (it has a mass that is less than 0.00000001 times the muon mass, so it behaves like a massless particle), and an L muon-neutrino emerges, almost on the light cone. The point is that W– boson interacts with the L muon and with the L neutrino.

  How do we know that W bosons interact only with L particles? Go back and reread Leon's account of the discovery of parity violation (chapter 3). It was observed that muons decayed (see figures 6.19–20) in such a way that the electron coming out moves in the general direction of the spin of the muon (getting the details of this right is a little tricky). This also means that a direction in space is associated with a spin, and that always implies a preferred chirality, so the decay process violates parity3.

  This is the mysterious source of the parity violation in the weak interactions. It is connected intimately to mass and to the fact that every particle has two inner L and R chirality components. Only the L part of a quark or a lepton can convert to a W boson (and it's reversed for antimatter; only R antiparticles can convert to a W). Alice in the looking-glass house would see L and R swapped. So, she would see that the R muon is converting to the W boson, and her neutrino would be R, with its spin aligned with the direction of motion. But that is a different world than ours.

  AYE, HERE'S THE RUB

  So we're almost there. We've climbed a long way, but the beautiful mountain lake full of rainbow trout is still another hundred feet up. It's only a short climb from here. Take a breath, a swig of water, and let's continue. The first purple peak will soon come into view. We are about to see why a Higgs boson must exist.

  Figure 6.21. Chirality in Muon Decay. We examine figure 6.20 more closely to reveal that only the left-handed muon (and left-handed neutrino) converts to the W boson: µ– → anti-vµ + W–. Likewise, only the left-handed electron (and right-handed antielectron neutrino) is produced by the process W– → e– + anti-ve. The weak interactions involve only left-handed particles (and their right-handed antiparticles).

  The W+ and W– bosons are like photons. They couple to the L muon (R anti-muon) and L neutrino (R antineutrino) with a “weak charge.” In order to unify the W's with the photon and with the Z boson in perfect utopian symmetry, it is necessary that this charge be very much like the electric charge—weak charge must be conserved. In a more erudite manner of speech: “the defining gauge symmetry principle of the weak interactions is the conservation of weak charge, just like the conservation of electric charge defines electromagnetism.”

  Why must charges be conserved? What goes wrong if they are not? This is a deep question and has to do with the remarkable principle of “gauge symmetry” that underlies electromagnetism. It's actually implicit in the fancy name “electro-magnet-ism.” Essentially, it implies that all we can ever observe in nature about photons are electric and magnetic fields. Electric fields accelerate electrons, imparting energy to them, while magnetic fields bend their trajectories into circular motion. But the photon is actually neither an electric or magnetic field: it is something more basic. The photon is a wave of something called a gauge field. The gauge field cannot be directly observed. But gauge fields can readily produce electric and magnetic fields.4 Only the electric and magnetic fields produced by a gauge field can be observed. But if we observe an electric or magnetic field we cannot reconstruct exactly what underlying gauge field made it. And there are nonzero gauge fields that produce no observable electric or magnetic fields.

  Katherine exclaims: “So, an infinite number of different possible gauge fields can make the same electric and magnetic fields?” Yes. And that is the symmetry. Any two apparently different gauge fields that make equivalent electric and magnetic fields we say are “(gauge) equivalent” to one another. It's like a perfect wine bottle with no label—rotate the bottle about its axis of symmetry, and the wine bottle is now in a different position, but it looks exactly equivalent to the position we started with. We say the two positions of the wine bottle are “rotationally equivalent” to one another. Katherine: “Well, OK, that makes sense, I suppose. But in order to make it work for the wine bottle you had to make sure there was no label—no marks that allow you to tell you rotated the bottle. What's the analogy of that to gauge symmetry?” The short answer is that in order for gauge symmetry to work, the electric charge must be conserved. The total electric charge you start with must be the same as the electric charge you end up with (See our book Symmetry and the Beautiful Universe [Amherst, NY: Prometheus Books, 2007] for a much more detailed discussion of gauge theories).

  It also turns out that the gauge symmetry principle is intimately related to quantum theory. Without the quantum waves that describe electrons and other charged particles, together with photons, the gauge symmetry seems awkward—there's no electron wave to “transform” under the gauge symmetry—there's no “representation” of the gauge transformation, like the wine bottle that rotates when we do a rotation transformat
ion in space. It was as if electromagnetic theory, created by wizards in the nineteenth century, was waiting and begging for the quantum theory to come along and make it whole. And, if you try to modify electromagnetism to make the gauge fields directly observable, the whole structure of the quantum theory breaks down and becomes a heap of rubble. The key to cloaking the gauge field—making it unobservable while the derived magnetic and electric fields are observable—is the conservation of electric charge. But now we encounter the weak interactions with the three new gauge bosons, W+ W– and Z0 and all particles now have weak charges. Again, as in electromagnetism, we find that the weak charge, like the electric charge, must also be conserved.

  The weak charge of the L muon is –1 (in some units). But the parity violations experiment tells us that the weak charge of the R muon is zero. L particles have weak charge while R particles do not. So now the marching L-R-L-R-L of a massive muon (or electron or top quark—any other matter particle will do) creates a problem. As L turns into R, the weak charge of the muon changes from –1 to 0. The weak charge is evidently not conserved for a massive muon sitting at rest, minding its own business, and oscillating between L and R. Mass breaks the vaulted gauge symmetry, which we have now extended to include the W+, W–, and Z0 bosons. But without conserved charge, the gauge theory collapses into charred remains.