Beyond the God Particle

by Leon M. Lederman

  It turns out that it is a theoretically necessary condition in quantum mechanics that, if we want the total probability of all possible outcomes for a given process to add to one, then the combined operations of CPT must indeed be an exact symmetry. If we combine C, P, and T, at least at the present level of experimental sensitivity, we do appear to have an exact symmetry of the world, CPT. There has been no experimental evidence of CPT violation, and many people consider it to be very unlikely. So—if Alice jumps through the C mirror, then the P mirror, then the T mirror (in any order), she gets back home!

  If CPT failed as a symmetry, then over time probability would not be conserved. This undermines the notion of probability in quantum theory, and we would have to significantly modify it. That is, the probability for anything to happen under any circumstances would either exceed or be less than one! Nevertheless, we must ask, if the violation of CPT were very, very tiny, would we have noticed? It is, after all, an experimental question.

  Let's step back and reflect on the situation. There are many questions we do not have answers to. The devil is always in the details, and physics is an experimental science. And, if there's one thing we have should have learned from history by now: rare processes, processes that may probe up to a 100 times or more beyond the LHC, may lead us to new physics. New discoveries could radically change our entire view of nature may be lying just beyond our current reach.

  According to our modern scientific version of “genesis,” the universe emerged from a plasma of the elementary constituents of matter: quarks, leptons, gauge bosons, and perhaps many other hitherto undiscovered particles furiously swarming about at extreme temperatures and pressures in an embryonic warped and twisted space and time. Space itself exploded, driven by the raw energy of the constituents of the universe, as described by the equations of Einstein's general theory of relativity. As the universe and its constituent plasma expanded, it cooled and condensed, ultimately transforming itself into a uniform gas of hydrogen, some helium, and relic particles of electromagnetic radiation, neutrinos, and some unknown(s) that are referred to as “dark matter.” Primordial quantum fluctuations in the density of these relic particles may have been transmitted, through gravity, to the hydrogen gas cloud, leading to its collapse, and the formation of the galaxies and the first “protostars” of the early universe. These monstrous stars were the parents of all the later heavy elements, the planets, and the solar systems to come, including our own sun.

  All the atoms heavier than helium, such as carbon, oxygen, nitrogen, sulfur, silicon, iron, etc.—the stuff of our own solar system, rocks, and our solid and wet planet; the stuff of life itself—were created within the gigantic protostars. The heavy elements were cooked by the process of nuclear fusion, within their cores, bound by immense gravitation, deep within these super-massive stars. These heavy atoms became the raw ingredients of the modern universe, without which there would be no structure. Eventually, by the parentage of the protostars, the sun and planets formed, and the special conditions on Earth led to the subtle and gradual evolution of life and of human beings. The true scientific story of our heritage is richer than any fables, and it is more mysterious and bizarre in its reality.

  In order for this to work, somehow the heavy elements must become liberated from the cores of the super-massive protostars in which they were formed. Indeed, the nuclear furnace interiors of these monstrous stars eventually poison themselves. Filling with iron, the most stable atomic nucleus, they can no longer burn by nuclear fusion. The protostars then begin to collapse. Commanded by gravity, they cave inward upon themselves. No longer opposing gravity with the intense radiation of their nuclear engines, a sudden and rapid change occurs deep within their cores. There, the atoms of iron, supporting the entire weight of the massive hulk against the collapse by gravity, like the hull of a sinking submarine, give way and implode. The iron atoms are squeezed, subject to enormous pressure and density. This instantaneously creates a new state of matter, never before present in the universe—solid neutrons.

  We've come a long way from Democritus, and we've learned that atoms consist of electrons, outwardly orbiting the compact nucleus that defines the center of the atom. The nucleus is made of protons and neutrons. When a protostar reaches its last stage of collapse, the electrons and protons in its core are squeezed together, merging within one another. A new set of physical processes, normally silently lurking in the background shadows of the everyday world around us, suddenly jumps to the fore. These are the weak interactions, the lowly radioactive decays that were not previously observed until Henri Becquerel's work in the 1890s, and they quickly convert the squeezed protons and electrons into neutrons. This produces, as a by-product, an explosive blast outward of elementary particles, the neutrinos. The dominant process of the weak interactions that destroys the monstrous protostars takes the form:

  or, “proton plus electron converts to neutron plus electron-neutrino.” It's just beta decay slightly rearranged.

  At the instant of the collapse of the core of a protostar, the weak interactions have stolen the show. The innermost core of the star is compressed into a ball of pure neutron matter, extremely compact, perhaps only ten miles in diameter, and yet as massive as our sun, but a trillion times more dense. The neutrinos, however, stream frantically outward from the core. As the neutrinos burst forth, they exert extreme pressure on the dense, hulking outer parts of the protostar—the outer shell of the star explodes. This marks a supernova—the most intense and spectacular explosion to occur in the universe, after the big bang.1

  It is remarkable and ironic that this ferocious “mother of all explosions” involves the lowly neutrino, an elementary particle that would seem otherwise to be the most inert and inconspicuous of all particles. Out blast the neutrinos, taking with them all of the outer matter of the star, and all of the newly synthesized elements, producing a brilliant flash of light, many thousands of times brighter than all of the stars shining within a single galaxy. The outer shell of the body of the protostar, containing all the elements from hydrogen to iron, is blown out into space, making a gigantic cloud, or “nebula” from which future and second-generation stars and solar systems (and us) will form. A dense spinning neutron star, or perhaps a black hole, is left behind. This is the tiny remnant of the pure neutron core of the protostar that was blown inward in the mighty supernova explosion, a few miles in diameter, spinning on its axis faster than once per second, but with a mass greater than that of our own sun.

  Over time, the nebulae of gas and dust and debris, now containing the heavy elements—the cindered remains of the many deceased protostars in their violent fates—accumulated and encircled the galaxies. This gave the galaxies a new and grandiose shape: that of gossamer spirals with their outreaching and enveloping spiral arms. In the outer spirals of the galaxies were born the offspring of the protostars, the second generation of smaller, yellowish stars, like our sun, together with the comets, asteroids, moons, and planets. These were composed of the gas and the rocky and metallic remains of the protostars.2

  The existence of everyday matter, the existence of the planets and the world we inhabit today, the existence of life and our very existence owes to the violent annihilation of these anonymous protostars that died in the ferocious oblivion of their supernovae, billions of years ago. All of our “everyday matter” was cooked together within these monstrous conflagrations. This process of heavy-element formation is ongoing throughout the universe even today. Many smaller large blue giant stars exist today, shining with the light of the fusion of almost pure hydrogen and helium, dwelling within the inner recesses at the centers of galaxies, detonating from time to time. In otherwise dim and distant galaxies millions of light-years away, the supernovae light them up for a moment, flashing in the dark, distant universe like fireflies in the night. And some stars within our own galaxy, and not too distant from Earth, perhaps the unstable and dying Eta Carinae (eta kar-in-i), will one day brighten our own sky with their catacl
ysmic finales.3

  THE PARTICLES WITH THE SMALLEST MASSES

  Neutrinos hold a certain fascination because they are so weakly coupled to matter that they are very hard to detect, particularly at low energies. They are only detectable through the weak interactions. There are more than a hundred trillion neutrinos passing through your body every second, mainly from the sun. The sun emits neutrinos copiously as they are associated with the nuclear fusion processes that generate sunshine and the synthesis of atomic elements. These neutrinos pass freely through the earth, so your neutrino bath is harmless and continuous, and doesn't depend (much) upon day or night, whether the sun is up or has set.

  Neutrinos come in three types, or “flavors.” These are called “electron neutrino,” “muon neutrino,” and “tau neutrino” (sometimes we just call them 1, 2, and 3). They are named for their closest relatives in the weak interactions, the electron, the muon, and the tau leptons. This pairing of charged lepton (e.g., the electron) with its neutrino (electron neutrino) is part of the symmetry of the Standard Model (see Appendix).

  For many years it was thought that neutrinos were massless particles, that they only come in a left-handed variety (and their antiparticle would therefore be right-handed), and that they do not couple to the Higgs boson. If particles are massless, then there is no L-R-L-R march through space-time. Massless particles are either pure L or pure R and always travel at the speed of light. However, in the past few decades, we have learned that neutrinos do, in fact, have miniscule masses, but they are masses that are extremely hard to measure, and hence they are very feebly coupled to the Higgs boson. To this day the neutrino masses have been detected but not precisely measured. However, neutrinos also exhibit a dramatic phenomenon associated with their masses: they “oscillate,” between their various flavors (electron, muon, or tau) as they propagate through space.4

  The neutrino masses, just like those of the other leptons or quarks, involve the Higgs field filling all of space. As you have learned, this leads to a “forced march”—the familiar L-R-L-R—where now the L and R are two distinct neutrino “chiralities” of “left” (L) and “right” (R). Each time a neutrino takes a step in the march, however, it very slightly changes its “flavor” identity. That is, if we go through one complete cycle, L-R-L, an L muon neutrino will end up as mostly an L muon neutrino, but it will pick up a little bit of electron neutrino or tau neutrino. So after many such steps the identity of the original muon neutrino has changed, and it has accumulated a significant probability of becoming a muon neutrino or a tau neutrino. (Likewise, if we “launch” an electron neutrino or a tau neutrino it, too, will similarly change identity.)

  It would be as if every time your pet hamster took a step in his hamster wheel, he acquired a miniscule quantum probability of being a mouse. After many rotations of the hamster wheel you might find that he had morphed completely into a mouse. After some more running, perhaps he morphs into a rat. No doubt, you would become quite curious about this phenomenon, as have physicists become fascinated with neutrinos.

  And, of course, this raises various questions: Does a mouse also morph back into a hamster? What does a rat morph into, a hedge fund manager? (Sorry, we couldn't resist that one.) Are there possible morphs other than mice, rats, and hamsters? Do things work in reverse as they do forward in time (time-reversal invariance)? Do left-handed hamsters behave the same way as right-handed ones? You can easily see the large multiplicity of questions we are interested in with regard to neutrinos.

  In studying the weak interactions, we encountered the L neutrino (or R antineutrino). Only the L neutrino “feels” the W bosons and participates in weak interactions. Only later, with very sensitive experiments did we encounter neutrino mass, and therefore the march of the L into the R neutrino through the interaction with the Higgs boson. But—wait a minute—for such a long time we thought neutrinos were massless, so we didn't ever have to worry about the R neutrinos. Now we find neutrinos have masses, so if we make an L neutrino in a weak interaction, then what is the R neutrino into which it steps in the mass march?

  Here is a mystery involving neutrinos that we don't encounter with electrons, or muons, or quarks. It's a little tricky—we have to do some bookkeeping—but it isn't too hard, so hang in there. We've learned that the phenomenon of mass always requires an L-R-L-R march, whereby, e.g., an L electron converts to an R electron, which converts back to an L electron, and so on. The L and R electrons are two different particles that become independent of each other if we turn off the effects of mass (which is what happens as they approach the speed of light, from a stationary observer's perspective). Furthermore, both the L and R electrons must have the exact same electric charge of –1 since electric charge is conserved.5

  Because of the foundational constraint—the conservation of electric charge—we wouldn't dare hypothesize that the R electron is just the anti–L electron, that is, the R positron in disguise. Indeed, the anti–L electron, or R positron, has right-handed chirality (its spin is counter-aligned with its velocity at the speed of light—it's the absence of L in the vacuum, hence R). But the R positron has an electric charge of +1, so it cannot participate in a L-R-L-R…march, since the electric charge would then oscillate in time: (–1)…(+1)…(–1)…(+1)…hopelessly violating the conservation of electric charge. No way! The L and R electrons, and also the L and R positrons, are all distinct particles—the lowly electron involves a total of 4 different particles, or 4 components; the same is true for the other charged leptons, muon and tau, and for quarks as well. This 4-component system of a spin-1/2 particle is called a “Dirac particle.”

  However, neutrinos are different than quarks or leptons—they are electrically neutral—they have zero electric charge. It therefore becomes thinkable that an L neutrino can actually flip into its own anti–L neutrino, which has an R chirality. The point is that for neutrinos, because they have no electric charge, the one-step L-R flip can, theoretically, also flip (particle) into (antiparticle). It is as though the hamster at every step on his wheel flips into an anti-hamster and subsequently back again (and then there are also the mixings of flavor, the slight probability of flipping into an anti-mouse and an anti-rat and so on). A particle that flips into its antiparticle when it does the L-R step is called a “Majorana particle” (my-hor-AH-na). It's actually doing the “L-anti-L” step.6

  This is the neutrino mystery: we don't know if the masses of neutrinos are of the “Dirac form” (requiring 4 distinct components: L, R, anti-L, anti-R) or the “Majorana form” (requiring only L and anti-L). There may indeed be an independent R neutrino, and also the anti–R neutrino. The L-R-L-R march involves the flipping of an L neutrino, which we can produce in a weak interaction, into a “sterile” neutrino, R, which we only see because of the mass. In that case, neutrino masses are just like those of charged particles, and they are then of the Dirac form. However, it is entirely possible, and in fact very likely from a theoretical perspective, that an L electron-neutrino flips into its own anti–L electron-neutrino—the antiparticle is then the R state, and the mass is of the Majorana form.

  How can we tell if neutrinos have Dirac masses or Majorana masses? This is a really big question, one we hope to develop the tools to answer in the future. It may only be answered by seeing a particular, previously unseen, ultra-rare nuclear process called “neutrinoless double-beta decay.” Unfortunately, for lack of space we have to send you to another source to read more about this phenomenon.7

  Most theorists believe the observed neutrino masses will prove to be of the Majorana kind. The reason for this is a remarkable observation about neutrino masses in grand unified theories. In short, the idea is that at very high-energy scales, those of grand unification (about a trillion times beyond the LHC energy scale, or 1015 GeV), neutrinos are hypothesized to start out with the 4 ingredients of Dirac masses, that is, a distinct R neutrino exists for each flavor (with its corresponding anti–R particle). Such R neutrinos, however, would be “sterile,”
coupling only through the Higgs interaction (such as in figure 6.22) and through the gravitational interaction.

  But then the sterile R neutrinos could experience extremely high-energy and extremely weird processes that the other L neutrinos cannot. The reason is that the W boson coupling of conventional L particles constrains them in many ways. For example, suppose a “mini–black hole” underwent a quantum fluctuation and came briefly into existence at a tiny distance a trillion times smaller than the scales we have ever probed at LHC (or smaller still). The black hole is like a fish in the ocean, like a big fat grouper, that appears on the scene and eats a little fish, then disappears into the undersea gloom. The mini–black hole would see a lowly R neutrino and swallow it—poof! The R neutrino is gone, and the grouper then swims away and disappears. But the mini–black hole cannot swallow the L neutrino and then simply disappear, because the L neutrino has weak charge—it couples to the W boson. The W boson is like a fishing line attached to the L neutrino—when the grouper swallows it, it is now caught and can't swim away…there's still weak charge in the grouper's belly forbidding him from just disappearing. So, he spits the L neutrino back out immediately: “Ouch. I don't want to mess with those fishing lines,” says the grouper, and then he's gone.

  The effect of this would be that the mini–black holes interfere with the mass-generation mechanism of the Higgs boson for neutrinos. All the sterile R and anti–R neutrinos can be eaten by mini–black holes in quantum fluctuations, which in physics parlance gives them effectively a very large Majorana mass. But the Higgs boson can still cause L to convert to R as a big quantum fluctuation. This then causes the L neutrinos to acquire a very tiny Majorana mass. These are the neutrinos we would see, with the fish lines of W bosons attached to them—the L and anti–L neutrinos (the ones with weak charges). So, what we believe we are seeing, here in the land of broken symmetries, are effectively Majorana masses among the ordinary L neutrinos that are produced in beta decays.