Knocking on Heaven's Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World - Lisa Randall (2011)

Part IV. MODELING, PREDICTING, AND ANTICIPATING RESULTS

Chapter 16. THE HIGGS BOSON

On the morning of March 30, 2010, I awoke to a flurry of e-mails about the successful 7 TeV collisions that had taken place at CERN the night before. This triumph launched the beginning of the true physics program at the LHC. The acceleration and collisions that had taken place toward the close of the previous year had been critical technical milestones. Those events were important for LHC experimenters who could finally calibrate and better understand their detectors using data from genuine LHC collisions, and not just cosmic rays that had happened to pass through their apparatus. But for the next year and a half, detectors at CERN would be recording real data that physicists could use to constrain or verify models. Finally, after its many ups and downs, the physics program at the LHC had at long last begun.

The launch proceeded almost exactly according to plan—a good thing according to my experimental colleagues, who the day before had expressed concerns that the presence of reporters might compromise the day’s technical goals. The reporters (and everyone else present) did witness a couple of false starts—in part because of the zealous protection mechanisms that had been installed, which were designed to trigger if anything went even slightly awry. But within a few hours, beams circulated and collided and newspapers and websites had lots of pretty pictures to display.

The 7 TeV collisions occurred with only half the intended LHC energy. The real target energy of 14 TeV wouldn’t be reached for several years. And the intended luminosity for the 7 TeV run—the number of protons that would collide each second—was much lower than designers had originally planned. Still, with these collisions, everything at the LHC was at long last on track. We could finally believe that our understanding of the inner nature of matter would soon improve. And if all went okay, in a couple of years the machine would shut down, gear up, and come back online at full capacity and provide the real answers we were waiting for.

One of the most important goals will be learning how fundamental particles acquire their mass. Why isn’t everything whizzing around at the speed of light, which is what matter would do if it had zero mass? The answer to this question hinges on the set of particles that are known collectively as the Higgs sector, including the Higgs boson. This chapter explains why a successful search for this particle will tell us whether our ideas about how elementary particle masses arise are correct. Searches that will take place once the LHC comes back online with higher intensity and greater energy should ultimately tell us about the particles and interactions that underlie this critical and rather remarkable phenomenon.

THE HIGGS MECHANISM

No physicist questions that the Standard Model works at the energies we have studied so far. Experiments have tested its many predictions, which agree with expectations to better than one percent precision.

However, the Standard Model relies on an ingredient that no one has yet observed. The Higgs mechanism, named after the British physicist Peter Higgs, is the only way we know to consistently give elementary particles their mass. According to the basic premises of the naive version of the Standard Model, neither the gauge bosons that communicate forces nor the elementary particles, such as quarks and leptons that are essential to the Standard Model should have nonzero masses. Yet measurements of physical phenomena clearly demonstrate that they do. Elementary particle masses are critical to understanding atomic and particle physics phenomena, such as the radius of an electron’s orbit in an atom or the extremely tiny range of the weak force, not to mention the formation of structure in the universe. Masses also determine how much energy is needed to create elementary particles—in accordance with the equation E=mc2. Yet in the Standard Model without a Higgs mechanism, elementary particles’ masses would be a mystery. They would not be allowed.

The notion that particles don’t have an inalienable right to their masses might sound needlessly autocratic. You could quite reasonably expect that particles always have the option of possessing a nonvanishing mass. Yet the subtle structure of the Standard Model and any theory of forces is just that tyrannical. It constrains the types of masses that are allowed. The explanations will seem a little different for gauge bosons than for fermions, but the underlying logic for both relates to the symmetries at the heart of any theory of forces.

The Standard Model of particle physics includes the electromagnetic, weak, and strong nuclear forces, and each force is associated with a symmetry. Without such symmetries, too many oscillation modes of the gauge bosons—the particles that communicate those forces—would be predicted to be present by the theory that quantum mechanics and special relativity tells us describes them. In the theory without symmetries, theoretical calculations would generate nonsensical predictions, such as probabilities for high-energy interactions greater than one for the spurious oscillation modes. In any accurate description of nature, such unphysical particles—particles that don’t actually exist because they oscillate in the wrong direction—clearly need to be eliminated.

In this context, symmetries act like spam filters, or quality control constraints. Quality requirements might specify keeping only those cars that are symmetrically balanced, for instance, so that the cars that make it out of the factory all behave as expected. Symmetries in any theory of forces also screen out the badly behaved elements. That’s because interactions among the undesirable, unphysical particles don’t respect the symmetries, whereas those particles that interact in a way that preserves the necessary symmetries oscillate as they should. Symmetries thereby guarantee that theoretical predictions involve only the physical particles and therefore make sense and agree with experiments.

Symmetries therefore permit an elegant formulation of a theory of forces. Rather than eliminate unphysical modes in each calculation one by one, symmetries eliminate all the unphysical particles with one fell swoop. Any theory with symmetric interactions involves only the physical oscillation modes whose behavior we want to describe.

This works perfectly in any theory of forces involving zero mass force carriers, such as electromagnetism or the strong nuclear force. In symmetric theories, predictions for their high-energy interactions all make sense and only physical modes—modes that exist in nature—get included. For massless gauge bosons, the problem with high-energy interactions is relatively straightforward to solve, since appropriate symmetry constraints remove any unphysical, badly behaved modes from the theory.

Symmetries thereby solve two problems: unphysical modes are eliminated, and the bad high-energy predictions that would accompany them are as well. However, a gauge boson with nonzero mass has an additional physical—existent in nature—mode of oscillation. The gauge bosons that communicate the weak nuclear force fall into this category. Symmetries would eliminate too many of their oscillation modes. Without some new ingredient, weak boson masses cannot respect the Standard Model symmetries. For gauge bosons with nonzero mass, we have no choice but to keep a badly behaved mode—and that means the solution to the bad high-energy behavior is not so simple. Nonetheless something is still required for the theory to generate sensible high-energy interactions.

Moreover, none of the elementary particles in the Standard Model without a Higgs can have a nonzero mass that respects the symmetries of the most naive theory of forces. With the symmetries associated with forces present, quarks and leptons in the Higgsless Standard Model would not have nonzero masses either. The reason appears to be unrelated to the logic about gauge bosons, but it can also be traced to symmetries.

In Chapter 14, we presented a table that included both left-and right-handed fermions—particles that get paired in the presence of nonzero masses. When quark or lepton masses are nonzero, they introduce interactions that convert left-handed fermions to right-handed fermions. But for left-handed and right-handed fermions to be interconvertible, they would both have to experience the same forces. Yet experiments demonstrate that the weak force acts differently on left-handed fermions than on the right-handed fermions that massive quarks or leptons could turn into. This violation of parity symmetry, which if preserved would treat left and right as equivalent for the laws of physics, is startling to everyone when they first learn about it. After all, the other known laws of nature don’t distinguish left and right. But this remarkable property—that the weak force does not treat left and right the same—has been demonstrated experimentally and is an essential feature of the Standard Model.

The different interactions of left- and right-handed quarks and leptons tells us that without some new ingredient, nonzero masses for quarks and leptons would be inconsistent with known physical laws. Such nonzero masses would connect particles that carry weak charge with particles that do not.

In other words, since only left-handed particles carry this charge, weak charge could be lost. Charges would apparently disappear into the vacuum—the state of the universe that doesn’t contain any particles. Generally that should not happen. Charges should be conserved. If charge could appear and disappear, the symmetries associated with the corresponding force would be broken, and the bizarre probabilistic predictions about high-energy gauge boson interactions that they are supposed to eliminate would reemerge. Charges should never magically disappear in this manner if the vacuum is truly empty and contains no particles or fields.

But charges can appear and disappear if the vacuum is not really empty—but instead contains a Higgs field that supplies weak charge to the vacuum. A Higgs field, even one that gives charge to the vacuum, isn’t composed of actual particles. It is essentially a distribution of weak charge throughout the universe that happens only when the field itself takes a nonzero value. When the Higgs field is nonvanishing, it is as if the universe has an infinite supply of weak charges. Imagine that you had an infinite supply of money. You could lend or take money at will and you would always still have an infinite amount at your disposal. In a similar spirit, the Higgs field puts infinite weak charge into the vacuum. In doing so, it breaks the symmetries associated with forces and lets charges flow into and out of the vacuum so that particle masses arise without causing any problems.

One way to think about the Higgs mechanism and the origin of masses is that it lets the vacuum behave like a viscous fluid—a Higgs field that permeates the vacuum—that carries weak charge. Particles that carry this charge, such as the weak gauge bosons and Standard Model quarks and leptons, can interact with this fluid, and these interactions slow them down. This slowing down then corresponds to the particles acquiring mass, since particles without mass will travel through the vacuum at the speed of light.

This subtle process by which elementary particles acquire their masses is known as the Higgs mechanism. It tells us not only how elementary particles acquire their masses, but also quite a bit about those masses’ properties. The mechanism explains, for instance, why some particles are heavy while others are light. It is simply that particles that interact more with the Higgs field have larger masses and those that interact less have smaller ones. The top quark, which is the heaviest, has the biggest such interaction. An electron or an up quark, which have relatively small masses, have much more feeble ones.

The Higgs mechanism also provides a deep insight into the nature of electromagnetism and the photon that communicates that force. The Higgs mechanism tells us that only those force carriers that interact with the weak charge distributed throughout the vacuum acquire mass. Because the W gauge bosons and the Z boson interact with these charges, they have nonvanishing masses. However, the Higgs field that suffuses the vacuum carries weak charge but is electrically neutral. The photon doesn’t interact with the weak charge, so its mass remains zero. The photon is thereby singled out. Without the Higgs mechanism, there would be three zero mass weak gauge bosons and one other force carrier—also with zero mass—known as the hypercharge gauge boson. No one would ever mention a photon at all. But in the presence of the Higgs field, only a unique combination of the hypercharge gauge boson and one of the three weak gauge bosons will not interact with the charge in the vacuum—and that combination is precisely the photon that communicates electromagnetism. The photon’s masslessness is critical to the important phenomena that follow from electromagnetism. It explains why radio waves can extend over enormous distances, while the weak force is screened over extremely tiny ones. The Higgs field carries weak charge—but no electric charge. So the photon has zero mass and travels at the speed of light—by definition—while the weak force carriers are heavy.

Don’t be confused. Photons are elementary particles. But in a sense, the original gauge bosons were misidentified since they didn’t correspond to the physical particles that have definite masses (which might be zero) and travel through the vacuum unperturbed. Until we know the weak charges that are distributed throughout the vacuum via the Higgs mechanism, we have no way to pick out which particles have nonzero mass and which of them don’t. According to the charges assigned to the vacuum by the Higgs mechanism, the hypercharge gauge boson and the weak gauge boson would flip back and forth into each other as they travel through the vacuum and we couldn’t assign either one a definite mass. Given the vacuum’s weak charge, only the photon and the Z boson travel without changing identity as they travel through the vacuum, with the Z boson acquiring mass, whereas the photon does not. The Higgs mechanism thereby singles out the particular particle called the photon and the charge that we know as the electric charge which it communicates.

So the Higgs mechanism explains why it is the photon and not the other force carriers that has zero mass. It also explains one other property of masses. This next lesson is even a bit more subtle, but gives us deep insights into why the Higgs mechanism allows masses that are consistent with sensible high-energy predictions. If we think of the Higgs field as a fluid, we can imagine that its density is also relevant to particle masses. And if we think of this density as arising from charges with a fixed spacing, then these particles—which travel such small distances that they never hit a weak charge—will travel as if they had zero mass, whereas particles that travel over larger distances would inevitably bounce off weak charges and slow down.

This corresponds to the fact that the Higgs mechanism is associated with spontaneous breaking of the symmetry associated with the weak force—and that symmetry breaking is associated with a definite scale.

Spontaneous breaking of a symmetry occurs when the symmetry it-self is present in the laws of nature—as with any theory of forces—but is broken by the actual state of a system. As we’ve argued, symmetries must exist for reasons connected to the high-energy behavior of particles in the theory. The only solution then is that the symmetries exist—but they are spontaneously broken so that the weak gauge bosons can have mass, but not exhibit bad high-energy behavior.

The idea behind the Higgs mechanism is that the symmetry is indeed part of the theory. The laws of physics act symmetrically. But the actual state of the world doesn’t respect the symmetry. Think of a pencil that originally stood on end and then falls down and chooses one particular direction. All of the directions around the pencil were the same when it was upright, but the symmetry is broken once the pencil falls. The horizontal pencil thereby spontaneously breaks the rotational symmetry that the upright pencil preserved.

The Higgs mechanism similarly spontaneously breaks weak force symmetry. This means that the laws of physics preserve the symmetry, but it is broken by the state of the vacuum that is suffused with weak force charge. The Higgs field, which permeates the universe in a way that is not symmetric, allows elementary particles to acquire mass, since it breaks the weak force symmetry that would be present without it. The theory of forces preserves a symmetry associated with the weak force, but that symmetry is broken by the Higgs field that suffuses the vacuum.

By putting charge into the vacuum, the Higgs mechanism breaks the symmetry associated with the weak force. And it does so at a particular scale. The scale is set by the distribution of charges in the vacuum. At high energies, or equivalently—via quantum mechanics—small distances, particles won’t encounter any weak charge and therefore behave as if they have no mass. At small distances, or equivalently high energies, the symmetry therefore appears to be valid. At large distances, however, the weak charge acts in some respects like a frictional force that would slow the particles down. Only at low energies, or equivalently large distances, does the Higgs field seem to give particles mass.

And this is exactly as we need it to be. The dangerous interactions that wouldn’t make sense for massive particles apply only at high energies. At low energies particles can—and must, according to experiments—have mass. The Higgs mechanism, which spontaneously breaks the weak force symmetry, is the only way we know to accomplish this task.

Although we have not yet observed the particles responsible for the Higgs mechanism that is responsible for elementary particle masses, we do have experimental evidence that the Higgs mechanism applies in nature. It has already been seen many times in a completely different context—namely, in superconducting materials. Superconductivity occurs when electrons pair up and these pairs permeate a material. The so-called condensate in a superconductor consists of electron pairs that play the same role that the Higgs field does in our example above.

But rather than carry weak charge, the condensate in a superconductor carries electric charge. The condensate therefore gives mass to the photon that communicates electromagnetism inside the superconducting material. The mass screens the charge, which means that inside a superconductor, electric and magnetic fields do not reach very far. The force falls off very quickly over a short distance. Quantum mechanics and special relativity tell us that this screening distance inside a superconductor is the direct result of a photon mass that exists only inside the superconducting substrate. In these materials, electric fields can’t penetrate farther than the screening distance because in bouncing off the electron pairs that permeate the superconductor, the photon acquires a mass.

The Higgs mechanism works in a similar fashion. But rather than electron pairs (carrying electric charge) permeating the substance, we predict there is a Higgs field (that carries weak charge) that permeates the vacuum. And instead of a photon acquiring mass that screens electric charge, we find the weak gauge bosons acquire mass that screens weak charge. Because weak gauge bosons have nonzero mass, the weak force is effective only over very short distances of subnuclear size.

Since this is the only consistent way to give gauge bosons masses, physicists are fairly confident that the Higgs mechanism applies in nature. And we expect that it is responsible not just for the gauge boson masses, but for the masses of all elementary particles. We know of no other consistent theory that permits the Standard Model weakly charged particles to have mass.

This was a difficult section with several abstract concepts. The notions of a Higgs mechanism and a Higgs field are intrinsically linked to quantum field theory and particle physics and are remote from phenomena we can readily visualize. So let me briefly summarize some of the salient points. Without the Higgs mechanism, we would have to forfeit sensible high-energy predictions or particle masses. Yet both of these are essential to the correct theory. The solution is that symmetry exists in the laws of nature, but can be spontaneously broken by the nonzero value of a Higgs field. The broken symmetry of the vacuum allows Standard Model particles to have nonzero masses. However, because spontaneous symmetry breaking is associated with an energy (and length) scale, its effects are relevant only at low energies—the energy scale of elementary particle masses and smaller (and the weak length scale and bigger). For these energies and masses, the influence of gravity is negligible and the Standard Model (with masses taken into account) correctly describes particle physics measurements. Yet because symmetry is still present in the laws of nature, it allows for sensible high-energy predictions. Plus, as a bonus, the Higgs mechanism explains the photon’s zero mass as a result of its not interacting with the Higgs field spread throughout the universe.

However, successful as they are theoretically, we have yet to find experimental evidence that confirms these ideas. Even Peter Higgs has acknowledged the importance of such tests. In 2007, he said that he finds the mathematical structure very satisfying but “if it’s not verified experimentally, well, it’s just a game. It has to be put to the test.”60 Since we expect that Peter Higgs’ proposal is indeed correct, we anticipate an exciting discovery within the next few years. The evidence should appear at the LHC in the form of a particle or particles, and, in the simplest implementation of the idea, the evidence would be the particle known as the Higgs boson.

THE SEARCH FOR EXPERIMENTAL EVIDENCE

“Higgs” refers to a person and to a mechanism, but to a putative particle as well. The Higgs boson is the key missing ingredient of the Standard Model.61 It is the anticipated vestige of the Higgs mechanism that we expect that LHC experiments will find. Its discovery would confirm theoretical considerations and tell us that a Higgs field indeed permeates the vacuum. We have good reasons to believe the Higgs mechanism is at work in the universe, since no one knows how to construct a sensible theory with fundamental particle masses without it. We also believe that some evidence for it should soon appear at the energy scales the LHC is about to probe, and that evidence is likely to be the Higgs boson.

The relationship between the Higgs field, which is part of the Higgs mechanism, and the Higgs boson, which is an actual particle, is subtle—but is very similar to the relationship between an electromagnetic field and a photon. You can feel the effects of a classical magnetic field when you hold a magnet close to your refrigerator, even though no actual physical photons are being produced. A classical Higgs field—a field that exists even in the absence of quantum effects—spreads throughout space and can take a nonzero value that influences particle masses. But that nonzero value for the field can also exist even when space contains no actual particles.

However, if something were to “tickle” the field—that is, add a little energy—that energy could create fluctuations in the field that lead to particle production. In the case of an electromagnetic field, the particle that would be produced is the photon. In the case of the Higgs field, the particle is the Higgs boson. The Higgs field permeates space and is responsible for electroweak symmetry breaking. The Higgs particle, on the other hand, is created from a Higgs field where there is energy—such as at the LHC. The evidence that the Higgs field exists is simply that elementary particles have mass. The discovery of a Higgs boson at the LHC (or anywhere else it could be produced) would confirm our conviction that the Higgs mechanism is the origin of those masses.

Sometimes the press calls the Higgs boson the “God particle,” as do many others who seem to find the name intriguing. Reporters like the term because people pay attention, which is why the physicist Leon Lederman was encouraged to use it in the first place. But the term is just a name. The Higgs boson would be a remarkable discovery, but not one whose moniker should be taken in vain.

Although it might sound overly theoretical, the logic for the existence of a new particle playing the role of the Higgs boson is very sound. In addition to the theoretical justification mentioned above, consistency of the theory with massive Standard Model particles requires it. Suppose only particles with mass were part of the underlying theory, but there was no Higgs mechanism to explain the mass. In that case, as the earlier part of the chapter explained, predictions for the interactions of high-energy particles would be nonsensical—and even suggest probabilities that are greater than one. Of course we don’t believe that prediction. The Standard Model with no additional structures has to be incomplete. The introduction of additional particles and interactions is the only way out.

A theory with a Higgs boson elegantly avoids high-energy problems. Interactions with the Higgs boson not only change the prediction for high-energy interactions, they exactly cancel the bad high-energy behavior. It’s not a coincidence, of course. It’s precisely what the Higgs mechanism guarantees. We don’t yet know for sure that we have correctly predicted the true implementation of the Higgs mechanism in nature, but physicists are fairly confident that some new particle or particles should appear at the weak scale.

Based on these considerations, we know that whatever saves the theory, be it new particles or interactions, cannot be overly heavy or happen at too high an energy. In the absence of additional particles, flawed predictions would already emerge at energies of about 1 TeV. So not only should the Higgs boson (or something that plays the same role) exist, but it should be light enough for the LHC to find. More precisely, it turns out that unless the Higgs boson is less than about 800 GeV, the Standard Model would make impossible predictions for high-energy interactions.

In reality, we expect the Higgs boson to be a good deal lighter than that. Current theories favor a relatively light Higgs boson—most theoretical clues point to a mass just barely in excess of the current mass bound from the LEP experiments of the 1990s, which is 114 GeV. That was the highest-mass Higgs boson LEP could possibly produce and detect, and many people thought they were on the verge of finding it. Most physicists today expect the Higgs boson mass to be very close to that value, and probably no heavier than about 140 GeV.

The strongest argument for this expectation of a light Higgs boson is based on experimental data—not simply searches for the Higgs boson itself, but measurements of other Standard Model quantities. Standard Model predictions accord with measurements spectacularly well, and even small deviations could affect this agreement. The Higgs boson contributes to Standard Model predictions through quantum effects. If it’s overly heavy, those effects would be too large to get agreement between theoretical predictions and data.

Recall that quantum mechanics tells us that virtual particles contribute to any interaction. They briefly appear and disappear from whatever state you started with and contribute to the net interaction. So even though many Standard Model processes don’t involve the Higgs boson at all, Higgs particle exchange influences all the Standard Model predictions, such as the rate of decay of a Z gauge boson to quarks and leptons and the ratio between the Wand Z masses. The size of the Higgs’s virtual effects on these precision electroweak tests depends on its mass. And it turns out the predictions work well only if the Higgs mass is not too big.

The second (and more speculative) reason to favor a light Higgs boson has to do with a theory called supersymmetry that we’ll turn to shortly. Many physicists believe that supersymmetry exists in nature, and according to supersymmetry, the Higgs boson mass should be close to that of the measured Z gauge boson’s and hence relatively light.

So given the expectation that the Higgs boson is not very heavy, you can reasonably ask why we have seen all the Standard Model particles but we have not yet seen the Higgs boson. The answer lies in the Higgs boson’s properties. Even if a particle is light, we won’t see it unless colliders can make it and detect it. The ability to do so depends on its properties. After all, a particle that didn’t interact at all would never be seen, no matter how light it was.

We know a lot about what the Higgs boson’s interactions should be because the Higgs boson and Higgs field, though different entities, interact similarly with other elementary particles. So we know about the Higgs field’s interactions with elementary particles from the size of their masses. Because the Higgs mechanism is responsible for elementary particle masses, we know the Higgs field interacts most strongly with the heaviest particles. Because the Higgs boson is created from the Higgs field, we know its interactions too. The Higgs boson—like the Higgs field—interacts more strongly with the Standard Model particles that have the biggest mass.

This greater interaction between a Higgs boson and heavier particles implies that the Higgs boson would be more readily produced if you could start off with heavy particles and collide them to produce a Higgs boson. Unfortunately for Higgs boson production, we don’t start off with heavy particles at colliders. Think about how the LHC might make Higgs bosons—or any particles for that matter. LHC collisions involve light particles. Their small mass tells us that the interaction with the Higgs particle is so minuscule that if there were no other particles involved in Higgs production, the rate would be far too low to detect anything for any collider we have built so far.

Fortunately, quantum mechanics provides alternatives. Higgs production proceeds in a subtle manner at particle colliders that involves virtual heavy particles. When light quarks collide together, they can make heavy particles that subsequently emit a Higgs boson. For example, light quarks can collide to produce a virtual W, the first picture in gauge boson. This virtual particle can then emit a Higgs boson. (See the first picture in Figure 51 for this production mode.) Because the W boson is so much heavier than either the up or down quarks inside the proton, its interaction with the Higgs boson is significantly greater. With enough proton collisions, the Higgs boson should be produced in this manner.

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FIGURE 51 ] Three modes of Higgs production: in order (top to bottom), Higgs-strahlung, W Z fusion, and gg fusion.

Another mode for Higgs production occurs when quarks emit two virtual weak gauge bosons, which then collide to produce a single Higgs, as seen in the second picture of Figure 51. In this case, the Higgs is produced along with two jets associated with the quarks that scatter off when the gauge bosons are emitted. Both this and the previous production mechanism produce a Higgs but also other particles. In the first case, the Higgs is produced in conjunction with a gauge boson. In the second case, which will be more important at the LHC, the Higgs boson is produced along with jets.

But Higgs bosons can also be made all by themselves. This happens when gluons collide together to make a top quark and an antitop quark that annihilate to produce a Higgs boson, as seen in the third picture. Really, the top quark and antiquark are virtual quarks that don’t last a long time, but quantum mechanics tells us this process occurs reasonably often since the top quark interacts so strongly with the Higgs. This production mechanism, unlike the two we just discussed, leaves no trace aside from the Higgs particle, which then decays.

So even though the Higgs itself is not necessarily very heavy—again, it is likely to have mass comparable to the weak gauge bosons and less than that of the top quark—heavy particles such as gauge bosons or top quarks are likely to be involved in its production. Higher-energy collisions, such as those at the LHC, therefore help facilitate Higgs boson production, as does the enormous rate of particle collisions.

But even with a big production rate, another challenge to observing the Higgs boson persists—the manner in which it decays. The Higgs boson, like many other heavier particles, is not stable. Note that it is a Higgs particle, and not the Higgs field, that decays. The Higgs field spreads throughout the vacuum to give mass to elementary particles and doesn’t disappear. The Higgs boson is an actual particle. It is the detectable experimental consequence of the Higgs mechanism. Like other particles, it can be produced in colliders. And like other unstable particles, it doesn’t last forever. Because the decay happens essentially immediately, the only way to find a Higgs boson is to find its decay products. The Higgs boson decays into the particles with which it interacts—namely, all the particles that acquire mass through the Higgs mechanism and that are sufficiently light to be produced. When a particle and its antiparticle emerge from Higgs boson decay, those particles must each weigh less than half its mass in order to conserve energy. The Higgs particle will decay primarily into the heaviest particles it can produce, given this requirement. The problem is that this means that relatively light Higgs boson only rarely decays into the particles that are easiest to identify and observe.

If the Higgs boson defies expectations and is not light, but turns out to be heavier than twice the W boson mass (but less than twice the top quark mass), the Higgs search will be relatively simple. The Higgs with a big enough mass would decay to the W bosons or Z bosons practically all the time. (See Figure 52 for decay into Ws.) Experimenters know how to identify the Ws and Zs that would remain, so Higgs discovery wouldn’t be very hard.

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FIGURE 52 ] A heavy Higgs boson can decay to W gauge bosons.

The next most likely decay mode in this relatively heavy Higgs scenario would involve a bottom quark and its antiparticle. However, the rate for the decay into a bottom quark and its antiparticles would be much smaller because the bottom quark has much smaller mass—and hence much smaller interaction with the Higgs boson—than the W gauge boson. A Higgs heavy enough to decay into Ws will turn into bottom quarks less than one percent of the time. Decays to lighter particles would happen less frequently still. So if the Higgs boson is relatively heavy—heavier than we expect—it will decay to weak gauge bosons. And those decays would be relatively easy to see.

However, as suggested earlier, theory coupled with experimental data about the Standard Model tell us the Higgs boson is likely to be so light that it won’t decay into weak gauge bosons. The most frequent decay in this case would be into a bottom quark in conjunction with its antiparticle—the bottom antiquark (see Figure 53)—and this decay is challenging to observe. One problem is that when protons collide, lots of strongly interacting quarks and gluons are produced. And these can easily be confused with the small number of bottom quarks that will emerge from a hypothetical Higgs boson decay. On top of that, so many top quarks will be produced at the LHC that their decays to bottom quarks will also mask the Higgs signal. Theorists and experimenters are hard at work trying to see if there is any way to harness the bottom-antibottom final state of Higgs decay. Even so, despite the bigger rate, this mode probably isn’t the most promising way to discover the Higgs at the LHC—though theorists and experimenters are likely to find ways to capitalize on it.

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FIGURE 53 ] A light Higgs boson will decay primarily to bottom quarks.

So experimenters have to investigate alternative final states from Higgs decays, even though they will occur less frequently. The most promising candidates are tau-antitau or a pair of photons. Recall that taus are the heaviest of the three types of charged leptons and are the heaviest particles aside from bottom quarks that a Higgs boson can decay into. The rate to photons is much smaller—Higgs bosons decay into photons only through quantum virtual effects—but photons are relatively easy to detect. Although the mode is challenging, experiments will be able to measure photon properties so well once enough Higgs bosons decay that they will indeed be able to identify the Higgs boson that decays into them.

In fact, because of the criticality of Higgs discovery, CMS and ATLAS put elaborate and careful search strategies in place to find photons and taus, and the detectors in both experiments were constructed with a view to detecting the Higgs boson in mind. The electromagnetic calorimeters described in Chapter 13 were designed to carefully measure photons while the muon detectors help register decays of the even heavier taus. Together these modes are expected to establish the Higgs boson’s existence, and once enough Higgs bosons are detected, we’ll learn about its properties.

Both production and decay pose challenges for Higgs boson discovery. But theorists and experimenters and the LHC itself should all be up to the challenge. Physicists hope that within a few years, we will be able to celebrate the discovery of the Higgs boson and learn more about its properties.

HIGGS SECTORS

So we expect to soon find the Higgs boson. In principle, it could be produced in the initial LHC run at half the intended energy, since that is more than sufficient to create the particle. However, we have seen that the Higgs boson will be produced from proton collisions only a small fraction of the time. This means that Higgs particles will be created only when there are many proton collisions—which means high luminosity. The original number of collisions that were scheduled before the LHC would shut down for a year and a half to prepare for its target energy was most likely too small to make enough Higgs bosons to see, but the plan for the LHC to run through 2012 before a year-long shutdown might permit access to the elusive Higgs boson. Certainly, when the LHC runs at full capacity, the luminosity will be high enough and the Higgs boson search will be one of its principal goals.

The search might seem superfluous if we are so confident that the Higgs boson exists (and if the pursuit is so difficult). But it’s worth the effort for several reasons. Perhaps most significant, theoretical predictions take us only so far. Most people rightfully trust and believe only in scientific results that have been verified through observations. The Higgs boson is a very different particle from anything anyone has ever discovered. It would be the only fundamental scalar ever observed. Unlike particles such as quarks and gauge bosons, scalars—which are particles with zero spin—remain the same when you rotate or boost your system. The only spin-0 particles that have been observed so far are bound states of particles such as quarks that do have nonzero spin. We won’t know for certain that a Higgs scalar exists until it emerges and leaves visible evidence in a detector.

Second, even if and when we find the Higgs boson and know for certain of its existence, we will want to know its properties. The mass is the most significant unknown. But learning about its decays is also important. We know what we expect, but we need to measure whether data agree with predictions. This will tell us whether our simple theory of a Higgs field is correct or whether it is part of a more complicated theory. By measuring the Higgs boson’s properties, we will gain insights into what else might lie beyond the Standard Model.

For example, if there were two Higgs fields responsible for electroweak symmetry breaking rather than one, it could significantly alter the Higgs boson interactions that would be observed. In alternative models, the rate for Higgs boson production could be different than anticipated. And if other particles charged under Standard Model forces exist, they could influence the relative decay rates of the Higgs boson into the possible final states.

This brings us to the third reason to study the Higgs boson—we don’t yet know what really implements the Higgs mechanism. The simplest model—the one this chapter has focused on so far—tells us that the experimental signal will be a single Higgs boson. However, even though we believe the Higgs mechanism is responsible for elementary particle masses, we aren’t yet confident about the precise set of particles involved in implementing it. Most people still think we are likely to find a light Higgs boson. If we do, it will be an important confirmation of an important idea.

But alternative models involve more complicated Higgs sectors with an even richer set of predictions. For example, supersymmetric models—to be further considered in the following chapter—predict more particles in the Higgs sector. We would still expect to find the Higgs boson, but its interactions would differ from a model with only a single Higgs particle. On top of that, the other particles in the Higgs sector could give interesting signatures of their own if they are light enough to be produced.

Some models even suggest that a fundamental Higgs scalar does not exist but that the Higgs mechanism is implemented by a more complicated particle that is not fundamental but is rather a bound state of more elementary particles—akin to the paired electrons that give mass to the photon in a superconducting material. If this is the case, the bound state Higgs particle should be surprisingly heavy and have other interaction properties that distinguish it from a fundamental Higgs boson. These models are currently disfavored, since they are hard to match to all experimental observations. Nonetheless, LHC experimenters will search to make sure.

THE HIERARCHY PROBLEM OF PARTICLE PHYSICS

And the Higgs boson is only the tip of the iceberg for what the LHC might find. As interesting as a Higgs boson discovery will be, it is not the only target of LHC experimental searches. Perhaps the chief reason to study the weak scale is that no one thinks the Higgs boson is all that remains to be found. Physicists anticipate that the Higgs boson is but one element of a much richer model that could teach us more about the nature of matter and perhaps even space itself.

This is because the Higgs boson and nothing else leads to another enormous enigma known as the hierarchy problem. The hierarchy problem concerns the question of why particle masses—and the Higgs mass in particular—take the values that they do. The weak mass scale that determines elementary particle masses is ten thousand trillion times smaller than another mass scale—the Planck mass that determines the strength of gravitational interactions. (See Figure 54.)

The enormity of the Planck mass relative to the weak mass corresponds to the feebleness of gravity. Gravitational interactions depend on the inverse of the Planck mass. If it is as big as we know to be the case, gravity must be extremely weak.

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FIGURE 54 ] The hierarchy problem of particle physics: The weak energy scale is 16 orders of magnitude smaller than the Planck scale associated with gravity. The Planck length scale is correspondingly shorter than the distances probed by the LHC.

The fact is that fundamentally, gravity is by far the weakest known force. Gravity might not seem feeble, but that’s because the entire mass of the Earth is pulling on you. If you were instead to consider the gravitational force between two electrons, you would find the force of electromagnetism is 43 orders of magnitude larger. That is, electromagnetism wins out by 10 million trillion trillion trillion. Gravity acting on elementary particles is completely negligible. The hierarchy problem in this way of thinking is: Why is gravity so much more feeble than the other elementary forces we know?

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FIGURE 55 ] Quantum contribution to the Higgs boson mass from a heavy particle—for example with GUT-scale masses—and its antiparticle (left) and from a virtual top quark and its antiparticle (right).

Particle physicists don’t like unexplained large numbers, such as the size of the Planck mass relative to the weak mass. But the problem is even worse than an aesthetic objection to mysterious large numbers. According to quantum field theory, which incorporates quantum mechanics and special relativity, there should be barely any discrepancy at all. The urgency of the hierarchy problem, at least for theorists, is best understood in these terms. Quantum field theory indicates that the weak mass and the Planck mass constant should be about the same.

In quantum field theory, the Planck mass is significant not only because it is the scale at which gravity is strong. It is also the mass at which both gravity and quantum mechanics are essential and physics rules as we know them must break down. However, at lower energies, we do know how to do particle physics calculations using quantum field theory, which underlies many successful predictions that convince physicists that it is correct. In fact, the best measured numbers in all of science agree with predictions based on quantum field theory. Such agreement is no accident.

But the result when we apply similar principles to incorporate quantum mechanical contributions to the Higgs mass due to virtual particles is extraordinarily perplexing. The virtual contributions from just about any particle in the theory seem to give a Higgs particle a mass almost as big as the Planck mass. The intermediate particles could be heavy objects, such as particles with enormous GUT-scale masses (see left-hand-side of Figure 55) or the particles could be ordinary Standard Model particles, such as top quarks (see right-hand-side). Either way, the virtual corrections would make the Higgs mass much too large. The problem is that the allowed energies for the virtual particles being exchanged can be as big as the Planck energy. When this is true, the Higgs mass contribution too can be almost this large. In that case, the mass scale at which the symmetry associated with the weak interactions is spontaneously broken would also be the Planck energy, and that is 16 orders of magnitude—ten thousand trillion times—too high.

The hierarchy problem is a critically important issue for the Standard Model with only a Higgs boson. Technically, a loophole does exist. The Higgs mass, in the absence of virtual contributions, could be enormous and have exactly the value that would cancel the virtual contributions to just the level of precision we need. The problem is that—although possible in principle—this would mean 16 decimal places would have to be canceled. That would be quite a coincidence.

No physicist believes this fudge—or fine-tuning as we call it. We all think the hierarchy problem, as this discrepancy between masses is known, is an indication of something bigger and better in the underlying theory. No simple model seems to address the problem completely. The only promising answers we have involve extensions of the Standard Model with some remarkable features. Along with whatever implements the Higgs mechanism, the solution to the hierarchy problem is the chief search target for the LHC—and the subject of the following chapter.