Beyond the God Particle

by Leon M. Lederman

  Please reread the previous paragraph. This is what directly leads us to the Higgs boson.

  The original paper of Sheldon Glashow on the Standard Model of electromagnetic and weak interactions defined the basic structure of the weak and electromagnetic gauge symmetries and introduced the W+, W–, Z0.5 However, Glashow needed masses to explain the physical world, so he “put them in by hand,” knowing this was a serious problem but thinking a solution would come later. This, therefore, was not yet a mathematically complete theory, and it wasn't understood if it could ever be made compatible with the principles of quantum mechanics at the time.

  In 1967 Steven Weinberg wrote what has become an iconic paper of the Standard Model, “A Model of Leptons.”6 He took Glashow's theory and proposed a clever remedy to the problem of mass, focusing only on the electron and its neutrino. He was inspired by the paper of Peter Higgs, but had to refine Higgs's idea to make it work. In the end, Weinberg had engineered a kind of “superconductor” that made the W+, W–, and Z0 bosons heavy, while the photon remained massless. He also showed how the masses of all the matter particles, electrons, muons, the top quark, even ultimately neutrinos, could be explained. Without Weinberg's idea it would not be possible to have a consistent theory of mass for any of the elementary particles.

  Even after Weinberg launched his paper, many people had reservations about whether the theory really was truly mathematically consistent, and the idea didn't catch on immediately. It took the super heroic efforts of Gerard ‘t Hooft and Martinus Veltman to show that it was indeed a workable and useful theory, and to show us how to use it correctly.7 This opened a scientific discovery floodgate, and the “gauge theory revolution” began. A number of key refinements and major extensions were required to accommodate the quarks and the strong interactions. The rest was up to the theorists to compute the various predictions for physical processes, and to the experimentalists to measure these things and test the theory. It has proved to be a stunning success.

  ENTER THE HIGGS BOSON

  Recall that our problem is to make a massive muon march, oscillating L-R-L-R-L-R, even though each time L changes to R the weak charge changes from –1 to 0. How do we do it? As the muon simply sits at rest it is rapidly “oscillating” L-R-L-R…its weak charge is also oscillating: –1 0 –1 0…. The weak charge is flickering on-off-on-off. The mass of the muon seems to destroy the neat conservation law of the weak charge. The Standard Model must either be wrong—or something new is happening to rescue it.

  Graham: “So, let me ask a simpler question: Is there any way, or any process, even if it's only theoretical gibberish, in which an L muon can convert to an R muon and still conserve the weak charge?”

  In fact…yes! There is…and this is the key! If we introduce a new kind of boson that has the same weak charge as the L muon, a boson that also has weak charge –1, then the L muon could “convert” to such a boson, plus an R muon. When the initial L muon has weak charge –1 and converts to the R muon with weak charge 0, plus the new boson that has weak charge –1, the overall weak charge remains the same since –1 = 0 + (–1). The required space-time picture is shown in figure 6.22.

  Figure 6.22. Muon Coupled to Higgs Boson. An incoming L muon with weak charge -1 converts to a recoil R muon with weak charge 0, plus the Higgs boson with weak charge -1 and spin 0. The process has a “coupling strength” gµ. It unites the L muon with the R muon. The Higgs boson must carry a weak charge equal to that of the L muon, so the weak charge is conserved. The Higgs boson must also have spin 0 to conserve spin angular momentum.

  The properties of our new boson are completely dictated by this process (this is explained in detail in the caption of figure 6.22). Since the L muon is converting to an R muon, maintaining a constant spin direction, the new boson must have zero spin. Note that since the L muon and R muon have the same electric charge, –1, the new boson must therefore have zero electric charge. And the key to the whole game, since the incoming L muon has weak charge –1 and the outgoing R muon has weak charge 0 is that the new boson must have weak charge –1. Voilà! We have completely spelled out the properties of the new boson. We have done exactly what Weinberg did in his 1967 paper. We have introduced a new theoretical particle, a spin-0 boson, that carries weak charge. We call this the Higgs boson.

  BUT WHAT ABOUT MASS?

  We're almost there. I can just taste those rainbow trout that we'll soon be catching at the mountain lake once we put our fishing gear into action. It's just another 50 feet…take a deep breath. The grandest peak of all will soon come into view.

  What do we mean by “boson”? For reasons that are deep and profound and have to do with quantum fields and relativity, there is a remarkable difference between matter fields, like electrons and muons and quarks, etc., and things we call the force carriers, the “bosons.” Matter particles are called “fermions” after Enrico Fermi. For no reason connected to their namesake, they are recluses and like to keep away from other fermions (Fermi was quite outgoing and personable).

  Fermions like to avoid one another. We can never get two fermions into the same quantum state—they are forbidden from doing this. This is a deep principle and has to do with the weird quantum attribute of spin.8 This property was discovered in the process of understanding atoms, and without it there would be no chemistry—all atoms would collapse down into different forms of the chemically inert helium—the universe would forever be one big gas bag of non-interacting helium-like atoms.

  Bosons are named after the Indian physicist Satyendra Nath Bose, who was a friend of Einstein.9 Bosons are gregarious particles (unlike their namesake, who was kind of shy). Bosons love hot tubs. They all pile into the same quantum state together whenever they can. In fact, whenever bosons start to pile into the same state, one of them yells “Party's on,” and pretty soon a gazillion bosons end up in the same state. You've seen this phenomenon in the dramatic instance of a laser beam, where many photons, which are each bosons, pile into exactly the same state of motion with the exact same frequency and wavelength of light, making a mysterious and intense beam of light.

  But there's a more mundane example. Any old electric or magnetic field is just a very large and indefinite number of photons dancing around in a small set of quantum states. This is called a “classical coherent state.” The quantum particle aspect of this becomes so blended that all we see is a large macroscopic wavelike field, and it is described by Maxwell's classical equations of electromagnetism. The blending into a coherent or “collective” state masks the quantum nature of the photons that make up the field. The same is true of the radio waves delivering text messages to your iPhone®. These are large aggregates of photons that behave “collectively” like one big field, doing exactly what bosons love to do.

  THE HIGGS VACUUM

  Weinberg realized that this bosonic “piling on” into one big collective state could also happen to the Higgs boson. We need only create an enormous “Higgs field” that permeates the entire universe. This field is similar to the magnetic field of the earth, in that it is composed of the Higgs bosons acting collectively, while magnetic fields are composed of photons acting collectively. However, magnetic fields have a well-defined direction in space—defined by the direction the compass needle points—we call a magnetic field a “vector field.” The Higgs field, on the other hand, just has a value—measured in energy—it has no direction in space. We call it a “scalar field.”

  Why would the universe have such a field? There is again a clever idea that the particle theorists borrowed from the study of materials—in this case the phenomenon of ferromagnetism. An iron magnet will spontaneously magnetize when it is cooled. The magnetic field seems to pop out of nowhere, but it is actually coming from the trillions and trillions of atoms inside the iron magnet. Each atom has a spin and is a little magnet itself. For iron, when it is cooled, these atomic spins all line up and point in the same direction. This creates a large magnetic field.10

  While magnets are co
mplicated in detail, we can understand iron in a simple way through a plot. The point is that the energy of the iron is reduced the more the atoms’ spins are aligned. This comes from the complex interactions of the atoms with each other in the iron material. If we have misaligned atoms, or random atomic spins that have no net alignment, we have a state of higher energy. The state in which all atomic spins are aligned has much less energy, and for some particular amount of alignment, or “magnetization,” we get the lowest energy state. The magnetic field then appears spontaneously.

  Figure 6.23. Magnetic Potential. The energy of an iron magnet as function of its magnetization shows that the minimum energy occurs for a nonzero value of the magnetization. This is why magnets form a stable state with a nonzero magnetic field.

  Figure 6.24. The Higgs Potential. We can adapt the principle of an iron magnet to the vacuum energy of the Higgs boson. The energy of the vacuum has a minimum for a nonzero value of the Higgs field. This causes the vacuum to develop a nonzero Higgs field everywhere throughout space. The parameters are tuned to produce a Higgs field strength in the vacuum of 175 GeV, the value that is inferred from Fermi's theory of the weak interaction and the muon lifetime.

  We use this idea, theoretically, to make our Higgs field fill the vacuum. A vacuum in which the Higgs field is zero is simply “engineered” to be a state that has a higher energy than one in which the Higgs field has a nonzero value. Theorists know immediately how to do this: one simply relabels figure 6.23 for an iron magnetic, replacing “energy of the magnet” by “energy of the vacuum,” and “magnetization” by “Higgs field.” In this way we get the (now-famous) “Higgs potential” shown in figure 6.24. The preferred value of the Higgs field is just the location on the x-axis of the minimum energy point of the potential. This is the value the Higgs field will have throughout all of space. We can determine what it must be from Fermi's original theory. It is an energy and has a value of about v = 175 GeV. Voilà!

  Katherine: “But once we have filled the vacuum with an enormous Higgs field, why can't we just go out in our backyard and pluck a Higgs particle from the vacuum? Why do we need the LHC at CERN?”

  Figure 6.25. Higgs Field Fills the Vacuum. Higgs bosons form a field in the vacuum, represented by the circles, much like photons can form an electric or magnetic field. The Higgs field contains an indefinite number of bosons and an indefinite weak charge. A Higgs boson particle that undergoes a quantum fluctuation into a state of zero energy and zero momentum can “disappear” into the field (or “appear” from the field). The vacuum becomes a reservoir of weak charge.

  Very good question, but it has a simple answer. The photon, which makes large electric and magnetic fields, has zero mass, so it isn't too hard to pluck a photon out of a large electromagnetic field. For example, we can have a source of light, like a laser beam, that is full of photons and that looks very coherent, as though there are no particles there. But we can also spread the beam out and make it very dim and put a “photon counter” or photo-cell hooked up to a computer, and we then see “tick…tick, tick…tick….” as individual photons are counted. We've thus plucked the photon particles out of the laser beam. These are very low-energy particles that can easily be detected by a sensitive detector. In fact, that's exactly what the silver halide crystals in an old photographic emulsion do: they react to individual photons as particles and when developed, give us a pretty picture, like Ansel Adam's view of the Grand Tetons.

  And, indeed, the Higgs field that permeates the universe implies that Higgs bosons, as particles, are lurking inside the vacuum. However, the Higgs boson particles that collectively make up the Higgs field are very heavy particles. It takes a big sledgehammer to knock one out of the vacuum, and that's exactly what the LHC is doing.

  But there's something else really interesting about the Higgs field—its existence means that the vacuum is full of weak charge. Recall that the Higgs boson must have a weak charge of –1 because it couples to L (–1 weak charge) and R (0 weak charge). The Higgs field throughout space means that the vacuum has become an enormous reservoir full of weak charge. We can borrow weak charge from the vacuum and, in so doing, turn a lowly R muon into an L muon. And an L muon can dump its weak charge into the vacuum and become an R muon. Eureka! We now see how the muon gets its mass by flipping from L-R-L-R. The flip involves a certain “coupling strength” of the muon to the Higgs boson, called gµ. The mass of the muon is then determined: it is simply mµ = gµ (times) 175 GeV.

  The problem of giving the masses to the elementary particles is solved! The vacuum is an enormous reservoir of weak charge. R particles that have no weak charge absorb the weak charge from the vacuum to become L particles. L particles that carry weak charge dump their charge into the vacuum to become R particles. Since the great reservoir of weak charge, the Higgs field, fills all space for all time, the masses of the elementary particles are generated throughout all space and time. The gauge symmetry, i.e., the conservation of weak charge, is still in effect, operating at the microscopic level.

  Figure 6.26. Muon Mass from the Higgs Field. The Higgs field, together with the coupling of the Higgs bosons to all particles, as in figure 6.22, gives rise to mass. The L muon can convert to an R muon and radiate a zero-energy Higgs boson that disappears into the field and carries away weak charge. In the figure the multiple arrows show the flow of weak charge out of the vacuum as R converts to L, then back into the vacuum as L converts to R. This also happens for electrons, the other leptons, and the quarks.

  Alas, aside from solving the conceptual problem of making mass while preserving gauge symmetry, the formula mµ = gµ (times) v, where v = 175 GeV/c2 tells us very little. The problem is that the Standard Model doesn't predict the value of gµ for us or the coupling of any other fermions to the Higgs boson, for that matter. All we can do is to go out and measure the mass of the muon, mµ, and from that we can determine gµ = mµ/v. The measured mass of the muon is about 0.1 GeV/c2, giving gµ = mµ/v = 0.1/175 = 0.00057. Likewise, the electron has a measured mass of about 0.0005 GeV/c2, and therefore the electron couples to the Higgs boson with coupling strength ge = 0.0005/175 = 0.0000028. The top quark has a measured mass of about 172 GeV/c2, and therefore has a coupling to the Higgs that is nearly 1, i.e., gt = 172/175 = 0.98. Here we've simply swapped the unpredicted masses of these particles for the unpredicted coupling strengths to the Higgs boson, gµ, ge, gt, etc. But the Standard Model, through the Higgs boson, also generates the heavy masses of the W+, W–, and Z0 bosons. These particles’ masses were predicted by the theory, and the agreement between experiment and theory is spectacular. We leave the job of constructing a more complete theory that predicts the origin and mathematical values of the Higgs coupling constants to a future, younger generation.

  We've arrived at the Rainbow Trout Lake, and we've just caught a big one. All particle masses, the L-R-L-R march through space-time, are due to the oscillation of L into R, and each time L turns to R it dumps a unit of weak charge into the vacuum via the Higgs field. And each time an R turns into an L it absorbs weak charge back out of the vacuum. That is the origin of mass. So, yes, Katherine, indeed you can “pluck a Higgs out of the vacuum,” but to make and study the Higgs boson particle directly requires the sledgehammer of the CERN LHC. Our entire world is sculpted by the grand Higgs field that surrounds us. It's a little spooky.

  LET'S TAKE A BREAK

  Breathe in the cool and pure mountain air. We've fast-forwarded through the entire twentieth-century physics to get here. We deserve a break and a few moments to soak in the serene beauty of the mountain peaks and our lovely lake. We've just filled our basket with rainbow trout, and it'll soon be time to start back down the mountain. In fact, we are at the pinnacle. We now understand what the Higgs boson is and how its field fills the entire universe and how particles undergoing their L-R-L-R march through space-time are absorbing and reemitting weak charge, to and fro, into the vacuum itself. It's happening before us and all around us as we linger. All of the
particles that make up our mountain, our lake, our trout, and us, are doing the L-R-L-R march and interacting with the grand Higgs-filled vacuum, dumping and absorbing weak charge as they go. And, on July 4, 2012, the experiments at the CERN LHC, finally confirmed to the entire world that it is true: The Higgs boson, the “particle comprising the Higgs field,” the particles that collectively make up this vast hot tub of a vacuum in the universe in which we live, has finally been seen in the laboratory.

  Our neighbors often ask, “So what do you folks do over there at Fermilab?” We would often tell them that “Fermilab has the world's most powerful microscope.” This was true until November 20, 2009.

  “The LHC is back,” the European Organization for Nuclear Research announced triumphantly Friday, as the world's largest particle accelerator resumed operation more than a year after an electrical failure shut it down.

  Restarting the Large Hadron Collider—the $10 billion research tool's full name—has been “a herculean effort,” CERN's director for accelerators, Steve Myers, said in a statement announcing the success. Experiments at the LHC may help answer fundamental questions…which deal with [the particles of] matter far too small to see.1

  The LHC was back after the challenging rebuilding process following its cataclysmic magnet explosion on September 19, 2008 (see chapter 1, under the heading “Oh, $%&#!”). At that time, the world's most powerful particle accelerator became the fully operational Large Hadron Collider (LHC) at CERN in Geneva, Switzerland. At that moment, a little-noted passage in history of profound significance had occurred: Europe became home to the world's most powerful microscope after nearly a century of US preeminence. The Fermilab Tevatron was switched off permanently on September 30, 2011. However, just as there are many kinds of microscopes, there are also many kinds of particle accelerators. Even today, Fermilab still operates many of the original onsite accelerators since the Tevatron shut down.