Beyond the God Particle

by Leon M. Lederman

  THEY DID IT WITHOUT COLLIDERS?

  Everything we have discussed to this point represents a fabric of some of the richest scientific discoveries in history—and none of it was done with high-energy particle colliders! Nature did all the work for us—it gave us unstable radioactive nuclei and cosmic rays as sources. The physics of beta decay led us to the discovery of the weak interactions and was all done in comparatively “low-energy” experiments, where nature furnished us with a “rare process.” By patiently studying the details of matter, we could infer the deeper structure of nature that is the weak interactions.

  Fermi's summation of the weak forces in his theory shows how the relevant high-energy scale of 175 GeV (or equivalent short-distance scale of about 1/10,000,000,000,000,000 centimeters) could be anticipated as early as 1935. It would be 25 years until Glashow would propose the W+, W–, and Z0 bosons in the context of the symmetries of the Standard Model, and until Weinberg would show how a Higgs boson could break those symmetries. The actual structure of the weak interactions was not probed directly by colliders until the discovery of the W and Z bosons at CERN in 1985, and of the Higgs boson of 2012. So, from Becquerel to the Higgs boson discovery at CERN, the weak interactions have been at the core of physics research for almost 120 years.

  What we have learned is that many of the great scientific advances in the twentieth century came by looking at the details of rare processes. Particle accelerators are generally either the colliders, operating at the highest energies, or smaller machines that produce many collisions, but each at a lower energy. Both offer pathways to discoveries.

  For example, we now know that there are three different kinds, or “flavors,” of neutrinos (see Appendix). Leon Lederman, Mel Schwartz, and Jack Steinberger demonstrated this in 1962 at the Brookhaven National Laboratory in Upton, New York, using a particle accelerator that provided a secondary beam of muons. With enough muon decays they showed that neutrinos are produced with distinct identities, by detecting the “muon-neutrino,” which is a different particle than the “electron-neutrino.” The key to the success of such an experiment is to have a very large number of particles available or a high statistics experiment. This required an intense source of sufficiently energetic protons to make muons, but not necessarily a very high-energy collider. With the subsequent discovery of the tau lepton, we now know there are three distinct “flavors” of neutrino.”15

  THE RARE WEAK PROCESSES

  Let's isolate the process of beta decay and examine it in greater detail:

  At the level of quarks and leptons, the decay of the neutron, if viewed under an extremely powerful microscope, resolves into an individual “down” quark decaying to an “up” quark plus the emission of a W– boson. However, the W– boson is so heavy that this process can only happen by way of Heisenberg's uncertainty principle for a miniscule moment in time, allowing the energy to fluctuate by a large amount. The W– then quickly converts into an electron plus a neutrino (see fig. 9.34). It is this extreme mass of the W– that makes a weak interaction process very feeble, relying on the big quantum fluctuation in time and energy. The heaviness of the weak gauge boson is, in short, why the weak forces are weak.

  This is the defining property of a “rare process.” Rare processes involve something at very short distances over very short time intervals and occurring as a “quantum fluctuation.” Becquerel couldn't observe the W– boson directly in a radioactive beta decay, but by measuring beta decay in detail we could later theoretically infer its existence. With Fermi's theory we could actually infer the scale of weak interactions, of 175 GeV, and eventually write down a more precise theory, called the Standard Model, which told the future collider physicists exactly where to look. Physics is like the game “Clue” (also known as “Cluedo”). With enough indirect evidence from rare processes we could say, “It was Colonel Mustard in the Library with the lead pipe” who did it!”16

  FIGURE 9.34. Beta Decay at Quark Level. At the level of quarks and leptons, and gluons binding the quarks inside the neutron and proton, we glimpse the process of a neutron decay, , which involves the quark transition, through the exchange of a W boson. The W is so heavy that it is not produced as a real particle, but it is created for only a tiny instant of time (we call it a “virtual particle”), allowed in quantum theory by Heisenberg's uncertainty principle. The improbable quantum fluctuation makes the weak force very “weak.” A free neutron has a half-life of about 11 minutes.

  There are a vast number of rare processes that are part of the Standard Model. Many of these have not yet been seen yet in experiments because they are so difficult to observe. And many rare processes are suggested by theories that attempt to go beyond the Standard Model. These effects can show up in two ways, either as inconsistencies in the rates for certain rare process or as tiny effects that are forbidden by the Standard Model. What other tales might rare processes tell us about nature?

  THE OTHER LOOKING GLASSES

  As we've seen, until the mid-1950s, physicists believed that parity was an exact symmetry of physics. Thus, the world of Alice through the looking glass would be indistinguishable in any physical process from our own world. The question of parity (P) nonconservation in the weak interactions was first raised by two young theorists, T. D. Lee and C. N. Yang, in 1956.17 Parity symmetry was practically considered to be an obvious fact in nature and had been used for decades in compiling data on nuclear and atomic physics. The breakthrough of Lee and Yang was the idea that the reflection symmetry—parity—could be perfectly respected in most of the interactions that physicists encountered, such as the strong force that holds the atomic nucleus together and the electromagnetic forces together with gravity. But Lee and Yang proposed that the weak force, with its particular form of beta-decay radioactivity, might not possess this mirror symmetry.

  Indeed, as we've seen, parity violation was discovered experimentally in 1957 by studying the pion and muon weak-interaction decay in detail. Independently, the effect was seen by Madame Chien-Shiung Wu, using another technique in nuclear weak-decay processes. This was astounding news—the weak processes are not invariant under the parity (P) symmetry operation. Later it was shown that the parity violation of the weak interactions is a property of the fact that only L-handed particles participate in weak interactions, while their R-handed brethren do not. This in turn ultimately mandates the existence of the Higgs boson so that particles can march L-R-L-R through space-time and thus acquire mass.

  Let us think a little more about space and time symmetries. Think about viewing the laws of physics by watching a movie. Parity symmetry would say that you cannot tell if the movie was taken by the camera looking directly at the scene or by viewing the scene reflected though a mirror. For example, the weak decay of a pion or a muon would not appear to us to be consistent with our known laws of physics if the camera is viewing things as a reflection in a mirror. L is exchanged with R, and we would see only R particles participating in the weak interactions in the mirror, not our world, where only L particles do.

  But now let's try something different. Let's run the film backward through the projector. This is easy to do with a DVD player nowadays by pressing the “reverse” button. We have all seen, with amusement, the pie fly off Uncle Bert's face or brick towers un-collapsing and jumping back into their original positions. Unlike the world viewed through the mirror, it seems very easy to proclaim that you're watching a film that is running backward through the projector. We can therefore imagine a new kind of Alice mirror, a kind of “time looking glass” or “time mirror,” in which we are always viewing things moving backward in time. Alice would find the world through the time mirror apparently quite different than her own. We'll call it “T.”

  However, when we examine up close simple or fundamental systems in the time mirror, such as two billiard balls colliding on the pool table, it becomes harder to tell in which direction in time the movie is progressing. The motion we see, forward or backward, viewed through the
time mirror, as two billiard balls approach and bounce off one another recoiling into different directions on the table, appears not much changed. It's hard to tell if we're looking through the time mirror, T, or not. The forward-in-time collision on our side of the time mirror seems to respect the same microscopic laws of motion as the backward-in-time collision on the other side of the time mirror. The microscopic laws of motion of simple systems are evidently the same, whether they are run forward or backward in time.18

  This is called “time-reversal symmetry.” But just as parity seemed to be a symmetry until we encountered the weak interactions, we might ask, “Is time reversal a fundamental symmetry of nature and therefore valid for the elementary particles?” Does the world through the time mirror have the same laws of physics as does ours? Or like parity, is it a broken symmetry?

  The answer is that the weak interactions, which violate parity, also violate time-reversal invariance at a much weaker level. To see this, we need yet another mirror—the antiparticle mirror.

  CPT

  We have already noted that mirror symmetry, designated by “P” for parity, is not a valid symmetry when it comes to processes involving the weak forces. Furthermore, as we have seen, there exists yet another discrete symmetry operation, called “T,” which reverses the flow of time, that is, we can replace t → –t in all of our physics equations, swap initial conditions with final ones, and get the same consistent results.19

  Yet another symmetry now arises given the existence of antimatter: it consists of replacing all particles by antiparticles in any given reaction. This is called C or “charge conjugation.” This symmetry would imply that there is an analogy to Alice's mirror called an antiparticle mirror. When Alice falls through her parlor mirror, P, she enters the world in which all parities are reversed (all “lefts” become “rights” and vice versa). When Alice falls through the “antiparticle mirror,” C, all the particles of all matter are turned into antiparticles and vice versa. We have seen that the laws of physics are slightly different through the parlor mirror—parity is a broken symmetry. So, naturally we ask, are the laws of physics the same through the antiparticle mirror? For example, would anti-hydrogen, consisting of an antiproton and an antielectron (positron) have the same identical properties, e.g., energy levels, sizes of the electron orbitals, decay rates, and spectrum, as does the ordinary hydrogen atom?

  If C is a valid symmetry, then an antiparticle must behave in every respect identically to its particle counterpart, provided we replace every particle by its antiparticle in any given process. But this makes no reference to the spins of the particles, which have to do with P. In the pion decay, the produced muon always has positive helicity, i.e., it is always produced as an L particle (negative helicity) in the weak interaction, but its mass flips it into R (positive helicity) so the process can occur and conserve angular momentum. If we perform a C operation on this process, we get the antiparticle process, π+ → μ+v0, where all particles are now replaced by antiparticles, but the spins all stay the same (we went through the C mirror, not the P mirror). Therefore, the helicity of the anti-muon in the antiparticle process would still be positive, or R (spin is still aligned with direction of motion).

  In 1957, shortly after the overthrow of P, the symmetry C was tested directly through experiment. When the experiment was performed, the helicity of the anti-muon in pion decay was not R, rather it was found to be L. Therefore, the symmetry C is also violated, together with P in weak interactions, such as the decay of pions and muons.

  The reason is not hard to see if you remember Dirac's sea. You'll recall that the L part of the muon couples to the weak interactions, while R does not. But antiparticles are holes, representing the absence of negative-energy particles in the Dirac sea. So, we would expect that if L has –1 weak charge, a hole would have +1 weak charge. But a hole is the absence of L and must therefore be R. So, for antiparticles we would expect that the R anti-muon couples to W bosons while the L anti-muon (the absence of R, which had weak charge 0) does not. Don't worry if you find this a bit confusing—it is, and it requires some practice to get it straight, and maybe a Tylenol® afterward. But it turns out that it would be hard to have it otherwise; when we reverse particle with antiparticle we naturally reverse parities.

  So, naturally, there arose the conjecture that, perhaps, if we simultaneously reflect in a parlor mirror, P, and then go through the antiparticle mirror, C, i.e., change particle to antiparticle, that this combined symmetry may be exact in nature. The combined symmetry operation is called “CP.” Upon performing CP to the negatively charged left-handed muon, we get a positively charged right-handed anti-muon. In the pion decay, π+ → μ+v0, the produced muon is indeed left-handed, so CP has turned out to be a symmetry of the pion decay. We now seemed to have deeper symmetry, which connected space reflections with the identity of particle and antiparticle. In summary, CP symmetry says: Jump through Alice's parlor mirror, which reverses parities, P, then jump through the antiparticle mirror, which changes all particles to antiparticles, C (the order is immaterial, CP is equivalent to PC), and we seem to get back to a world equivalent to our own.

  But—the world is often much more enigmatic than humans are led to believe. In 1964, in a beautiful and extremely well-executed experiment involving some other interesting particles called neutral K-mesons (again, this is an accelerator-based experiment where “intensity,” or many, many produced K's, is more important than high energy), it was shown that CP is not conserved, that is, CP is also not a symmetry. The physics of weak forces is not invariant under the combined operations C and P. If you go through the P mirror and the C mirror, you do not come home, but rather you end up in a world with different properties than our own.20

  The details of the origin of this breakdown of the symmetry, CP, has come to define a frontier of physics for the past 50 years. There remain many unanswered questions, such as “Do neutrinos in their peculiar flavor oscillations interactions also display a violation of CP symmetry?” (See the next chapter.) We still do not know how this will play out, but we have since learned that if CP were indeed a perfect symmetry of nature, our universe would be so totally different that we, our solar system, stars, and galaxies, would probably not exist. Nor would you be reading this book. So, it's a good thing for us that CP as a symmetry of nature is actually violated.

  CP violation tells us that a particle and an antiparticle do behave in slightly different ways. In fact, CP violation is a prerequisite to explaining yet another enigmatic question: “Why does the universe seem to contain only matter and no antimatter?” If we go back to the initial instants of the big bang, when the universe was extremely hot (hotter than any energy scale ever probed in the lab), cosmological theory would predict equal abundances of matter and antimatter. However, with CP violation, some ultra-heavy-matter particles could have decayed slightly differently than their antiparticle counterparts. This miniscule asymmetry could have favored, at the end of the decay sequence, the production of a slight excess of the normal matter (hydrogen) over the antimatter (anti-hydrogen). Then, as the universe cooled, and all the remaining matter and antimatter annihilated each other, this slight mismatched excess of matter remained. The slight mismatched excess of matter is us and everything we see in the universe.

  The problem is that, while we need CP violation to explain the fact that the universe contains matter and no antimatter, we don't think we have yet discovered the particular CP-violating interactions that produce this effect. The CP-violation effect, first seen in neutral K-mesons, now seen in other particle decays, remains an intriguing hint of much more to come, but it cannot explain the matter–antimatter asymmetry. This issue is being studied aggressively around the world. And the answer may ultimately come from the lowly neutrino, if indeed neutrinos display CP violation. The devil is in the details. We have reached the frontier—we don't know the answer to this question.

  DOES ANY COMBINATION OF MIRRORS TAKE US HOME?

  Alice now h
as three mirrors to jump though. There's her parlor mirror, which flipped parities, P. There's the time-reversed mirror, T, which runs things backward in time, and there's the antiparticle mirror, C, which flips all matter into antimatter. Is there a sequence of mirrors we can jump through that will get us back home to the same world in which we live?

  Quantum mechanics makes probabilistic predictions for the outcome of events. When we flip a “fair” coin, we have equal probability of getting heads or tails. But even with an “unfair” coin, the sum of the probabilities of getting heads or tails in a coin flip is one—the sum of all probabilities that anything should happen must add to one, or else we are not able to talk meaningfully about probability—the quantum theory would fall apart if this were not so. What would it mean that the probability of heads in a coin flip is 2/3, while tails is also 2/3? How can the total probability be 4/3?