Beyond the God Particle

by Leon M. Lederman

  Unfortunately, the discovery of a Standard Model Higgs boson seems to have no obvious correlation with this hypothesis. We see no clue, at the moment, as to how to solve the riddle of the Higgs boson mass itself in a manner such as QCD generates strong mass. Nature has consolidated all of the quark and lepton and W and Z boson masses into the Higgs boson field, but the Higgs boson remains a black box—it does not yet tell us anything deeper about the origin of the electroweak mass scale, or equivalently, about its own mass.

  FINALE

  The most important next step for our science is the LHC run, scheduled to begin sometime around January 1, 2015, yielding possible major and dramatic new physics results in 2017 or so. Hopefully the LHC, when it comes back online, will reveal new particles and new phenomena, and the next layer of the onion will finally come into view.

  Without such a revelation, without new targets for future colliders, can we rationally ask our government for a multi-billion-dollar high-energy particle collider at this time? The answer may be: we shouldn't.7 It may be irrational and irresponsible to do so given that we have no indications of what new physics to pursue with such a machine. It would be a costly shot in the dark. Rather, we must wait until 2017 and continue reliably slugging it out at the LHC, participating actively in future machine and detector upgrades. There's still lots to learn from the LHC.

  However, here in the US, we have a golden opportunity to penetrate deeply into the fog of the highest energies with a different, cost-effective approach, the approach of Becquerel, the Curies, and Rutherford, back in the earliest era of our science. We can now roll up our sleeves and build a smaller, few-billion-dollar machine, called Project X. With Project X, as we have seen, we could simultaneously probe nature for indirect hints as to what lies at energy scales 100 to 1,000 times beyond the LHC, while also collaborating actively in the energy frontier effort at the LHC. Project X could help to solve major global challenges, such as ridding the world of plutonium and providing clean nuclear power, as well as yielding rich scientific discoveries. It may ultimately lead us to the next-generation particle collider, first with a relatively small Muon Collider Higgs factory, using the powerful Project X beam to provide the requisite muon source. Later we could upgrade to a multi-TeV Muon Collider to provide point-like probes of any interesting new targets at the highest energies. This approach is staged, economical, and sensible. This is a most sensible evolutionary program that would allow the full benefit of advanced-technology R&D to provide much-needed “exogenous inputs” into our economy This, we believe, is our best pathway forward, beyond the Higgs boson.

  Experiment will always be the ultimate arbiter, so long as it's science we're doing. So far, regarding the Higgs boson there's not a hint of new dynamics. While we all expected that a major revolution was coming to the science of elementary particle physics, immediately with the discoveries at the LHC few expected a single Standard Model Higgs boson. So far the major revolution hasn't happened.

  So what does this imply for the future? What else remains to be understood that can be understood? What, perchance, is not dreamt of in our philosophies? What generates the Higgs boson mass? Has the LHC missed something? Surely, there have to be some clues somewhere. Or maybe we're just not being clever enough? Are we misunderstanding what nature is telling us? We're working on it.

  Please stay tuned for the all-important LHC results in 2017 or so. And let's roll up our sleeves and get started on Project X!

  THE STRONG INTERACTIONS

  By the mid-1960s, a vast array of strongly interacting particles was produced in many experiments at the many new accelerator labs. The number of new particles surpassed the number of atomic elements. Almost all of these various new particles were cousins of the proton, the neutron, and the pion—the components of the atomic nucleus. These particles were unstable, some having comparatively “long lifetimes” of a hundredth of a millionth to a tenth of a millionth of a billionth of a second (10-8 to 10-16 seconds), while others had ridiculously short lifetimes, about 10-23 seconds, not much longer than the transit time of light across their diameters. As these new strongly interacting particles proliferated, only one tool could be brought to bear to try to make sense of them—symmetry.

  TOO MANY FUNDAMENTAL PARTICLES

  The first order of business in any science, such as zoology or botany or epidemiology, is to classify things. This means that you make lists of everything you have observed and then try to put these items into general related categories. For example, we might list animals according to whether or not they have backbones (vertebrates and invertebrates). Within this category we make a sub-list according to whether they have scales, feathers, fur, etc. Then we look for patterns among the lists. Eventually we discover relationships, and we can then formulate theories of their origins and try to explain the myriad patterns.

  By the end of the 1950s there were three broad categories of “elementary” particles. First, there were a few non–strongly interacting matter particles (particles that don't participate in the strong interactions, that is, they do not interact with Yukawa's pions or any of their relatives). These were initially seen to be comparatively lighter-in-mass particles compared to the proton and neutron, so they were dubbed the “light ones,” which in Greek is leptons. The class of leptons contained the electron, the muon, and two very hard-to-observe particles called the electron neutrino, ve, and the muon neutrino, vμ. Much later, in the mid 1970s, another pair joined and completed this class of leptons, called the “tau,” τ, and the “tau” neutrino, vτ. Even though the tau is heavier, it shares the non–strongly interacting behavior of the electron and muon, and it fits into the lepton family.

  By the 1970s accelerator experiments had confirmed that leptons were point-like, or structureless, objects down to the smallest accessible distance scales, about a hundredth of a millionth of a billionth of a centimeter (10-17 cm). In addition to the leptons there were two other particles that are strictly force carriers and that fall into a special class we call “gauge bosons.” These include the well-known photon, the particle of light, and a hypothetical “graviton”—the particle of gravity.

  The remaining particles comprising the vast list of strongly interacting particles were called the “hadrons” or “strong ones.” All strongly interacting particles were found to have a finite nonzero “size” of about a hundredth of a thousandth of a billionth of a centimeter (0.2 × 10–13 cm). Various patterns began to emerge within that class of particles. Indeed, the patterns began to hint that hadrons are actually composed of smaller, more elementary objects deep down within another stratum that could not yet be resolved with the existing accelerator probes.

  For a long time there was considerable resistance to the idea of any further substructure within the hadrons. No matter how high an energy probe struck the proton, it was not possible to “smash it into smithereens.” All that happened was that other short-lived hadrons were produced in these collisions, and you ended up back with the original proton (or a neutron or pions) you started with. Evidently Democritus's idea of fundamental underlying “atoms” was breaking down with the discovery and properties of the hadrons. Very novel and Zen ideas emerged—perhaps hadrons are composed of each other in such a way that none is truly fundamental and yet all are? It was as if the world of hadrons were an Escher staircase, eternally going uphill, only to return again to the first step.

  Connected to this idea was the notion that hadrons are not made of point-like objects but are more like the consistency of putty—deformable and malleable rather than point-like and hard. One of the most intriguing patterns among these objects could be explained if it was assumed that, as the putty rotates rapidly, it becomes drawn out into a kind of putty “string.” Various quantum modes of motion of this “string” were studied, and it seemed to make sense—all of the hadrons could be explained as putty strings, and many of their properties were predicted and emergent from the idea. Thus was born, in attempting to explain hadrons, a ne
w type of dynamical quantum theory, the string theory.

  THE STRATUM OF QUARKS AND LEPTONS

  But the long list of “too many strongly interacting particles” led some physicists, most notably Murray Gell-Mann and George Zweig of the California Institute of Technology, to assert that these were not fundamental. The long list of hadrons had certain patterns, like the recurring chemical properties of atoms, and hinted at the existence of yet another layer of the physics onion. Yet there was a serious problem with the idea of another stratum of nature—whatever comprised the strongly interacting particles could never be set free from the particles they composed by any experiment. Even the most powerful of particle accelerators, producing the most violent collisions, never liberated any of the hadronic innards, and instead simply produced more and more of the unstable hadrons.

  Nonetheless, for a particular theoretical next layer of constituency of matter, whether real or purely mathematical, Gell-Mann introduced the term “quark.”1 In the early 1970s, through the theoretical insights of James Bjorken,2 the first “photograph” of the inner world of the proton was taken at the Stanford Linear Accelerator by scattering very energetic electrons off of protons, a process known as “deep inelastic scattering.” For the first time, the constituents of hadrons—the quarks—were seen. It was also observed that half of the constituents of the hadrons were something else—a mysterious electrically neutral component of these particles was detected. Could this be the “glue” that holds the quarks inside?

  Initially, almost comically, the theoretical force carriers that bind quarks within hadrons were dubbed “gluons.” Soon, however, by making a profound analogy with electric and magnetic forces generated by photons, a real theory of quarks and gluons, called “quantum chromodynamics” (QCD for short; QCD is a Yang–Mills gauge theory) took hold. Gluons joined the panoply of elementary particles and entered the list of bosons, like the photon and graviton. Gluons, indeed, generate the force that holds the quarks inside the strongly interacting particles.3

  FIGURE A.35. Table of Quarks and Leptons. This exhibits the “generation structure” of the matter particles, by which a pair of “up”-type and “down”-type colored quarks fit together with a pair of “electron” and “neutrino”-type leptons.4 In addition, there are the antiparticles, required by special relativity. Antiparticles have opposite electric charges and anti-colors, hence the blue quark has an antiparticle that is “anti-blue,” which acts like a combination of red and yellow. The neutrinos have extremely tiny masses, expected to be less than about 2 electron volts.

  As of today we have built many particle accelerators, some so powerful that we can clearly see the quarks and gluons deep inside the hadrons, like the nucleus inside the atom or the DNA inside of a living cell. The gluon force is not, however, like anything we have seen before. Unlike familiar electromagnetism, the gluonic force doesn't fall off like the inverse square law between two separated electric charges but is rather a constant force as we try to separate the quarks. This behavior ends up forbidding us from ever isolating the quarks. Quarks are confined forever inside of hadrons. In fact, the gluon force, when we rapidly rotate a hadron, becomes the putty-like string.

  TODAY: THE PATTERNS OF QUARKS, LEPTONS, AND BOSONS

  The elementary constituents of the hadrons are the quarks and gluons. Quarks and gluons are real, and their properties are measured, but they can never be set free from the prisons of the hadrons that they comprise. With quarks and gluons a more Democritus-styled explanation of the hadrons took hold, and this is the view that we have of them today. Quarks, like their sisters the leptons, are point-like and structureless matter particles.

  We often refer to the quarks and leptons as “the matter particles.” Each of these particles is a tiny gyroscope, each has spin 1/2 (see “Spin” below), in accordance with the rules of quantum mechanics. All the everyday matter in our world is essentially composed of the two quarks, the up and down (and gluons), and the one lepton, the electron. These quarks are distinguished by their electric charges and their masses. We always define the electron to have an electric charge of –1. In these units, the up quark (u) has an electric charge of +2/3, and the down quark (d) an electric charge of –1/3. The proton is therefore not an elementary particle but is rather a composite particle, built of three quarks in the pattern u + u + d (or uud). Adding up the electric charges of the constituent quarks, we see that the proton charge is +2/3 + 2/3 – 1/3 = +1. Similarly, the neutron is composed of u + d + d, and the corresponding electric charge combination is +2/3 – 1/3 – 1/3 = 0.

  Every particle in nature has a corresponding antiparticle. This was Dirac's famous discovery based upon unifying quantum theory with special relativity. The antielectron is the positron and has electric charge +1 and the same mass and spin as the electron. The antiquarks likewise have the opposite electric charges to their quark counterparts. We designate the anti-up quark as , and it has an electric charge –2/3, while the anti-down is , with electric charge +1/3.

  The pions are composed of combinations of a quark and antiquark. We easily see that there are four possible quark-antiquark combinations involving u, d, , and , which are d (–1), u (0), u (+1), d (0). In quantum mechanics, neutral particle states often become “blended” (added together in particular ways), and the resulting composite particles are

  The first three are the pions, and the fourth is called the “eta meson.” All four are known well from experiment, and their quark composition accounts neatly for the pattern. In fact, from the masses of the pions and other mesons, we can deduce the masses of quarks themselves.

  Only particular combinations of quark composites are observed experimentally to occur. In nature we only find objects containing three quarks (called baryons), or three antiquarks (called anti-baryons), or objects containing quark plus antiquark (called mesons). So the question arises: What is the nature of the strong force that holds the quarks together inside of the hadrons?

  We find that each quark comes in “triplets.” That is, there are three up quarks, three down quarks, three strange quarks, and so on. The additional label is the “color.” Hence we say that there is a red up, a blue up, and a yellow up quark. This has nothing to do with visual colors of the rainbow but is a mnemonic description of the full symmetry of quarks.

  The color of a quark is hard to detect, because any observed particle that the quarks compose, a hadron such as the proton and neutron and mesons, always has a net color of zero. For example, at any instant of time, the proton contains uud, but one quark is red, another blue, and another yellow, making an overall color-neutral state.

  The antiquarks must be viewed as having anti-colors in the sense of the color wheel. So the anti–blue up quark is actually a red-yellow, or “cyan,” object. Therefore, we can make color-balanced mesons by combining pairs of quark and antiquark. This simple rule explains the forms of the bound particles that we see. However, it also gives the clue to the fundamental theory of the strong interactions.

  Figure A.36. Table of Gauge Bosons. These are also the known “force carriers” and all are defined by “gauge” symmetries.

  How do we establish that quark color exists if we can't see it? In fact, it was anticipated in the early days of the quark theory because of Pauli's exclusion principle. There exists a composite strongly interacting particle, whose properties Gell-Mann dramatically and precisely predicted in 1963. Experimentalists quickly confirmed the prediction at Brookhaven National Laboratory. This is the Ω–, “omega-minus,” and it contains three strange quarks, or sss. It is known that the quarks making up the Ω– must move in a single common quantum state, or orbital, but without quark color this would be strictly forbidden by the Pauli exclusion principle. Yet the Ω– does indeed exist. The only way out of this conundrum is the existence of quark color. If one s quark is red, the second blue, and the third yellow, making up the Ω–, then there is no problem with the exclusion principle. There are many other ways in which the number of colors
of quarks has been “counted” in experiment, and the result is always consistent with three.

  We can think of a quark as though it lives in a “three-dimensional color space,” whose three axes are labeled by the three colors. In this space, a quark can be thought of as an arrow (a vector) that can point in any color direction. If the quark is red, its arrow points along the red axis, if blue, then the blue axis, and so forth. However, in quantum theory the arrow can rotate and point in any direction. The color symmetry is just the collection of rotations that we can do to such a quark arrow (this is known as the “symmetry group SU(3)”).

  Now we generalize the subtle idea of “gauge symmetry,” which governs electrodynamics. For the electron, the symmetry requires the introduction of the photon. The electron becomes a quantum blend with the photon. Gauge symmetry then implies that by “shaking” (accelerating) the electron, we can cause the emission of a gauge particle, or gauge boson, called the photon. This gives rise to all of the electromagnetic properties of matter.

  But for quarks, we go further with this concept. We can rotate the quarks in color space, for example, we can rotate a pure red down quark into a blue down quark. We want this to be a “gauge symmetry,” and this requires that we have additional particles that “undo” the changes we make on the red quark, keeping the overall result invariant. To have a color-gauge symmetry, we need 8 new gauge particles, called gluons.5

  The physical gluons are emitted from the quarks when the quarks accelerate, like photons from electrons. But gluons carry off the old color of the quark and carry in a new color. So a gluon has (color + anti-color). So, when we turn a red quark into a blue quark, by emitting a gluon we simultaneously create a (red, anti-blue) gluon, so the net color is (red + anti-blue) + (blue) = (red), and therefore initial color of the quark is recovered.