Beyond the God Particle

by Leon M. Lederman

  Now, think of what a bizarre situation that is—Yukawa had theoretically predicted the pion, but no one had seen the pion, and no one would see it until 1947. Anderson and Neddermeyer found the surprising new particle—the muon—coming from the cosmic rays, and it had almost the exact mass that Yukawa predicted for the pion. The muon confused the heck out of everyone, as it turned out not to be the pion. But the muons Anderson and Neddermeyer had observed, unbeknownst to them, were the by-product of pions that are readily produced (and rapidly decay into muons) at very high altitudes in the atmosphere!8

  Now, the very fact that a muon can make it to the surface of the earth is, in part, a miracle of Albert Einstein's theory of relativity. We know that a muon is unstable, and it almost always decays within about two millionths of second (into an electron plus two neutrinos). This is actually, approximately, its “half-life”—after about two millionths of a second, there'll be about half as many muons as you started with, then in another two millionths of a second, a quarter as many, then an eighth, and so on.9 Muons are produced about ten to twenty miles up in the atmosphere in cosmic ray collisions. So a simple calculation shows that if a muon traveled as fast as possible, at the speed of light c, then in t = 2 millionths of second, it would only travel about ct = 0.6 kilometers, less than a half mile. So, we wouldn't expect many muons to make it to the surface of the earth before they had decayed.

  But Einstein told us that, for particles approaching the speed of light, time slows down. The slowing of time is observed by we who are sitting at rest on the ground watching the high-speed muons. The amount of slowing down of time that we observe is the amount by which the lifetime of a muon will be lengthened due its traveling near the speed of light. This effect, called “time dilation,” is easily computed: we take the energy of the muon and divide by its mass (times the speed of light squared, that is, we divide by mc2). So, if a muon has an energy that is 20 times its own rest mass energy, mc2, then it will have its lifetime extended by a factor of 20. With enough “lifetime-extending energy,” the high-energy muons can easily reach the surface of the earth ten miles below. The arrival of muons at the earth's surface is one of the many stunning confirmations of Einstein's theory of relativity. Kooks and others who want to challenge and demolish Einstein's theory of relativity, please take note: Relativity is a prime example of a “theory” that has become “fact”!

  Alas, the pion cannot travel far enough to arrive at the surface of the earth to be detected. It too is unstable, but it decays in a mere one hundredth of a millionth of a second—that's a hundred times shorter lifetime than that of a muon. We would need super-energetic pions to be produced with sufficient energy to lengthen their lifetimes by 2,000 times to get them to the surface of the earth—the effects of relativity simply aren't enough to help cosmic ray pions get down to the earth's surface.

  And, there's another big difference between pions and the muons that prohibits the former from making it down to the earth's surface. For the very reason that it holds the atomic nucleus together, a pion interacts very strongly with protons and neutrons. This means that when a cosmic ray makes a pion in the thin upper atmosphere, the pion is quickly reabsorbed by protons and neutrons in further collisions with atoms of nitrogen or oxygen. This, more than anything, cuts off the number of pions in cosmic rays observed at sea level. You have to go way up into the atmosphere to detect them.

  Nonetheless, in 1947 the charged pions, produced by cosmic rays, were finally found by a collaboration of scientists at the University of Bristol in England.

  10 Photographic plates were placed for long periods of time at high altitudes on mountains, first at Pic du Midi de Bigorre in the Pyrenees and later at Chacaltaya in the Andes Mountains. Here the photographic plates were directly hit by the primary cosmic rays, and after development, the plates were inspected under microscopes. This revealed the tracks of electrically charged particles. Pions were first identified by unusual double tracks, where one incoming track would suddenly shift direction into another outgoing track. The scientists were actually seeing the charged pion as it decayed into the muon, plus an invisible neutrino.

  Recall that the pions come in three charge species, π+, π–, and π0. The neutral pion decays very quickly, in about one tenth of a millionth of a billionth of a second (that's 10–16 seconds), into two very energetic photons, called gamma rays, π0 → γ + γ. This rapid rate of decay occurs because it involves the electromagnetic interaction. But the negatively charged pions decay into muons plus antineutrinos: π– → μ– + anti-ν0 (and the corresponding antiparticle process involves a positively charged pion decaying into an anti-muon of positive charge and a neutrino, π+ → μ+ + ν0). The charged pions live about 0.00000001 (that's 10–8) seconds.

  The charged pion decays are examples of “weak interactions.” The “weakness” of the weak interactions makes the charged pion decay more slowly than the neutral one (the weak force at low mass scales of pions and muons is much more feeble than the electromagnetic force, which is why no hints of it were observed at all until the late 1890s), and therefore the charged pion has a longer lifetime than the neutral pion.11 As we'll see shortly, these weak decays of the pion into the muon revealed the stunning property of nature that ultimately led us to the Higgs boson.

  So, you see, the scientists who worked all of this out in the 1930s and 1940s had quite a few puzzles to solve (see note 10). There is a lot of physics involved with muons and pions. Once these particles were established and their detailed properties were ferreted out of the many experiments, they became the tools to take us deeper into the fabric of nature. And the plot thickened.

  THE MUON IS NATURE'S PERFECT GYROSCOPE

  A remarkable feature of the muon is that it provides us with a nearly perfect elementary gyroscope. Indeed the muon has spin, and the spin of a muon, once it's produced, is very stable. The spin and its electric charge causes the muon to become a magnet. So we can place muons in magnetic fields, make them go in circular orbits, and the spin of the muon will “precess” or slowly change direction, much like a toy gyroscope in the gravity force of Earth (see the Appendix under “Spin” heading).

  Welcome to the quintessential quantum property of “spin.” Any rotating body has spin—a top, a CD player, a ballerina or figure skater, the earth, the washing machine basin on the rinse cycle, a star, a bicycle wheel, a black hole, a galaxy—all have spin. So, too, do most quantum particles, molecules, atoms, nuclei of atoms, the protons and neutrons in the nucleus, the particle of light (photons), or electrons or muons, the particles inside of protons and neutrons (quarks, gluons), the electron, etc., all have spin.

  A notable exception is the pion, which has zero spin. But while large classical objects can have any amount of spin, and can stop spinning altogether, quantum objects have “intrinsic spin” and are always spinning with the same total intrinsic spin. An elementary particle's spin is one of its defining properties. We can never halt a muon from spinning, else it would no longer be a muon. We can never make a pion spin, hence it would not be a pion anymore.

  When we say that an object spins in a particular direction, we are referring to the axis about which it spins. Consider a toy gyroscope. Now to define the “spin direction” of the gyroscope, we take our right hand and curl our fingers in the direction of motion of the spinning mass of the gyroscope. Our right hand's thumb then points in what we call the “spin direction.” Similarly, we can define the spin direction of a muon.

  Figure 3.4. Spin of a Gyroscope. The direction of the spin (angular momentum) of a gyroscope is defined by the “right-hand rule.” We curl the fingers of the right hand in the direction of the spinning limbs of the gyroscope. The spin (vector) points perpendicular to the plane of the spinning gyroscope. The assigned direction of the spin is the direction of the thumb of the right hand.

  It is, however, one of the weird results of the quantum world that the spin of a muon is always either “up” or “down,” once we choose any directio
n along which to measure the spin. So, if we choose the direction of measurement to be “east,” the muon will always be observed to have exactly “east” pointing or “west” pointing spin. East-pointing spin would be spin “up” along the east direction; west-pointing spin would be spin “down” along the east direction. Quantum mechanics allows only these two possibilities, up or down, for the observed spin of an electron or a muon (or an electron, a quark, a neutrino, a proton, etc.) when measured along any axis in space.

  If you don't think this is weird, then you didn't understand what we just said! A gyroscope can, at any time, have any fraction of its spin pointing east, like 29 percent, or 3 percent, or -82 percent, but an electron or muon is always 100 percent east (“up”) or 100 percent west (“down”)—and that's weird (this is a quantum property of spin–½ particles; see Appendix).

  Spin (or, more generally, angular momentum) is a conserved quantity such that the total spin of an undisturbed isolated system remains forever constant. Frisbees® are a popular application of the principle of the conservation of angular momentum. Pilots, however, must always avoid the dreaded “flat-spin,” where they can inadvertently get an airplane spinning like a Frisbee, and the conservation of angular momentum makes it very difficult to recover control of the airplane.

  The two spin states of the resting, or slowly moving, electron or muon are easily related: we can simply rotate the muon and one spin (e.g., “up”) flips into the other (“down”). It's not hard to flip the spin of an electron, in part because it is so light in mass. However, for the heavier muon these “spin flipping” effects are greatly suppressed. Once created, the muon spin will stay the same unless it encounters a strong magnetic field or experiences a really hard collision. A muon that is simply losing energy by softly scattering with electrons in a material medium will tend to preserve its spin orientation faithfully. The muon can be stopped in matter and still retains the original spin. In most experiments at low energies, the muon is a wonderful gyroscope, with very good “memory” of the spin it had when it was produced.

  The existence of spin raises some fundamental questions. Recall that defining the direction of spin of a gyroscope involves using your right hand, curling the fingers in the direction of motion, and then pointing the thumb in the direction of spin. But how does nature know that it's the “right hand” and not the “left hand” that defines spin? Clearly nature doesn't care about the foolish-looking person (me) who is staring at a gyroscope, holding up his right hand as his thumb points up to the moon. As far as nature is concerned, it could just as well be his left hand. There must be a symmetry here—you should be able to consistently define spin with your left hand and the laws of physics should be the same—left should be as good as right and vice versa. That equality of properties of L and R is called “parity.”

  PARITY

  Now if you'll only listen, Kitty, and not talk so much, I'll tell you all my ideas about looking-glass house. First, there's the room you can see through the glass—that's just the same as our drawing room, only things go the other way. I can see all of it when I get upon a chair—all but the bit behind the fireplace. Oh! I do so wish I could see that bit!”12

  So said Alice, before she fell through the looking glass on the mantel of her Victorian parlor to get a better view, where she had climbed to see if there was also a fire in the fireplace of the “looking-glass house.” She tumbled into a new world in which the normal laws of physics were suspended—chess pieces muttered and roamed about the countryside, Humpty-Dumpty took a great fall, and “all mimsy were the borogoves, and the mome raths outgrabe.”13

  What do we see in a mirror? We see a different world, alphabetical letters reversed, the sunlight entering windows into a room that almost looks the same as ours, yet reversed, and our own image, as we are accustomed to it, but not as others see it, with that freckle and the part of the hair on the wrong side, but more or less the same. It all comes down, ultimately, to one thing—“things go the other way,” as Alice said—left and right are reversed.

  This left-right reversed world through the looking glass is otherwise hardly changed at all. Were we astute observers of everything that happened in this world, as methodical as Newton in trying to understand its rules and laws, what would we conclude? Would we find any difference between the laws of nature in the mirror world compared to the laws of nature in our world? Or is the “dual” world through the looking glass equivalent to ours in its most fundamental laws of physics? Would we truly find this to be a symmetry—that only the superficial things, left and right, are reversed, yet the laws of nature otherwise remain the same?

  Many things are the same when viewed through a mirror. A ball with no markings looks the same in the mirror. We say that such things are “invariant under reflection.” But there are also many things that are not invariant under reflection. For example, our left hand, under reflection, becomes a right hand. Right and left hands are distinct from one another. This happens because there is a sense in which we can curl our fingers relative to the position of our thumb. This relative curling sense of the fingers and the placement of the thumb defines left and right handedness.

  We thus see a basic property of reflections. Some things are the same thing under reflection, like spheres or label-free wine bottles (e.g., if our hands had no thumbs and the backside of each hand was the same as the front, then left hands would be identical to right hands and we would need only one kind of glove for each hand). Some things, like our hands, are different in the mirror world, and form a pair of mirror-image partners. If we reflect left, we get right, and vice versa. We refer to something that is different, or not invariant, under reflections as having “handedness.”

  It's not hard to make things with handedness. A box of screws from a hardware store will usually be “right-handed.” This means that a rotation of the screwdriver by the curling of the fingers of the right hand moves the screw forward in the direction of the thumb. Seen in the mirror, the right-hand rotation becomes left-handed, but the mirror image of the screw still moves forward, so the mirror-image screw is “left-handed.” A left-handed screw can just as easily be manufactured in a factory, and it is completely compatible with the laws of physics—nothing violates the laws of physics to make a left-handed screw, it just takes a special order from a manufacturer, such as “Please make us 10 dozen 8-32 left-handed screws.”

  At a more fundamental level, molecules generally have reflection symmetries. A molecule can be invariant under a reflection, such as H2O, which looks the same in a mirror. Or, a molecule can become a different one, having a mirror partner, when we reflect it in the mirror. A molecule that is the mirror image of another molecule is called a “stereoisomer.” A stereoisomer pair contains left (levo-) and right (dextro-) forms that swap identities by reflection in the mirror (like our left and right hands). That is, dextro-molecules are the mirror images of the levo-molecules, and vice versa. The dextro- (levo-) stereoisomers will have the exact same chemical properties when they are mixed into soup with other dextro- (levo-) stereoisomers. However, dextro- (levo-) isomers will have different chemical properties when they are mixed into soup with the mirror-image levo- (dextro-) isomers.

  This leads to the old story that when you first land on a distant world, Zzyxx, and are greeted by aliens who look exactly like you and are invited to a great feast with their leader, you find that you are hungry within a few hours. The food stuff on their world is entirely based upon levo-sugars, while ours is based upon dextro-sugars—we cannot digest or gain food nutrition from these mirror-image sugars. This is an accident of evolution at which, in the distant past, some organisms randomly evolved to eat dextrose on Earth and levose on Zzyxx. This fateful event propagated forward to all subsequent generations of organisms on the respective worlds. And after a moment's thought, we realize that this is a very good thing—we will not be eaten by the aliens on Zzyxx should they turn out to be cannibals!

  So, we might ask, “Are the laws of
physics invariant under the discrete symmetry of reflection?” Are the laws of physics in the looking-glass house, which differs only by exchanging right for left, really the same as ours? In other words, “Is parity a symmetry of the laws of physics?”

  Perfect parity symmetry, both literally and mathematically, would mean that upon viewing the world, including all of its physical processes, in a mirror, as if we were in Alice's looking-glass house, would reveal the same outcomes for experiments as in our world. In the mirror world we see physical objects move around, collide and interact, and obey the “laws of physics” that work on that side of the mirror. Are these exactly the same as ours? Is there any process in nature, let us say, in how something like a pion decays into a muon and a neutrino, or how a muon decays into an electron and neutrinos, that would be different in the mirror world than what we see in our world? It seems like such a simple idea, and such a natural one, that we might lull ourselves into believing that “yes, indeed, it must be that way! How could it not? Parity must be a symmetry of physics. What else could it be?”

  The pion is a “spinless” particle, meaning that it is a “spin = 0” particle—it has zero intrinsic spin. It can be considered as a perfect little sphere, like a tiny billiard ball, which does not appear to change in any way if we rotate it. The muon (and the anti-neutrino), on the other hand, has spin that is always “up” or “down” along any axis we choose to measure the spin. When a pion decays, the initial spin is zero, therefore the sum of the final spins of the muon and anti-neutrino must also be zero. That is, if we observe the outgoing muon with spin “down” along the east direction, then the anti-neutrino will have spin “up” along the east direction. This is the conservation law of angular momentum.