The Higgs Boson: Searching for the God Particle

by Scientific American Editors

  From this point of view, every effective theory is open-ended and equally fundamental—that is, not truly fundamental at all. Will the ladder of effective theories continue? The MSSM solves a number of problems the Standard Model does not solve, but it is also an effective theory because it has inputs as well. Its inputs might be calculable in string theory.

  Even from the perspective of effective theories, particle physics may have special status. Particle physics might increase our understanding of nature to the point where the theory can be formulated with no inputs. String theory or one of its cousins might allow the calculation of all inputs—not only the electron mass and such quantities but also the existence of spacetime and the rules of quantum theory. But we are still an effective theory or two away from achieving that goal.

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  Sidebar: The Standard Model

  THE PARTICLES

  Although the standard model needs to be extended, its particles suffice to describe the everyday world (except for gravity) and almost all data collected by particle physicists.

  Matter Particles (Fermions)

  In the Standard Model, the fundamental particles of ordinary matter are the electron, the up quark (u) and the down quark (d). Triplets of quarks bind together to form protons (uud) and neutrons (udd), which in turn make up atomic nuclei (above). The electron and the up and the down quarks, together with the electron-neutrino, form the first of three groups of particles called generations. Each generation is identical in every respect except for the masses of the particles (see grid, scroll below). The values of the neutrino masses in the chart are speculative but chosen to be consistent with observations.

  Force Carriers: Bosons

  The Standard Model describes three of the four known forces: electromagnetism, the weak force (which is involved in the formation of the chemical elements) and the strong force (which holds protons, neutrons and nuclei together). The forces are mediated by force particles: photons for electromagnetism, the W and Z bosons for the weak force, and gluons for the strong force. For gravity, gravitons are postulated, but the Standard Model does not include gravity. The Standard Model partially unifies the electromagnetic and weak forces—they are facets of one “electroweak” force at high energies or, equivalently, at distances smaller than the diameter of protons.

  One of the greatest successes of the Standard Model is that the forms of the forces—the detailed structure of the equations describing them—are largely determined by general principles embodied in the theory rather than being chosen in an ad hoc fashion to match a collection of empirical data. For electromagnetism, for example, the validity of relativistic quantum field theory (on which the Standard Model is based) and the existence of the electron imply that the photon must also exist and interact in the way that it does—we finally understand light. Similar arguments predicted the existence and properties, later confirmed, of gluons and the W and Z particles.

  The Source of Mass

  In addition to the particles described above, the Standard Model predicts the existence of the Higgs boson, which has not yet been directly detected by experiment. The Higgs interacts with the other particles in a special manner that gives them mass.

  Deeper Levels

  Might the Standard Model be superseded by a theory in which quarks and electrons are made up of more fundamental particles? Almost certainly not. Experiments have probed much more deeply than ever before without finding a hint of additional structure. More important, the Standard Model is a consistent theory that makes sense if electrons and quarks are fundamental. There are no loose ends hinting at a deeper underlying structure. Further, all the forces become similar at high energies, particularly if supersymmetry is true. If electrons and quarks are composite, this unification fails: the forces do not become equal. Relativistic quantum field theory views electrons and quarks as being pointlike—they are structureless. In the future, they might be thought of as tiny strings or membranes (as in string theory), but they will still be electrons and quarks, with all the known Standard Model properties of these objects at low energies.

  THE RULES OF THE GAME

  The standard model describes the fundamental particles and how they interact. For a full understanding of nature, we also need to know what rules to use to calculate the results of the interactions. An example that helps to elucidate this point is Newton’s law, F = ma. F is any force, m is the mass of any particle, and a is the acceleration of the particle induced by the force. Even if you know the particles and the forces acting on them, you cannot calculate how the particles behave unless you also know the rule F = ma. The modern version of the rules is relativistic quantum field theory, which was invented in the first half of the 20th century. In the second half of the 20th century the development of the Standard Model taught researchers about the nature of the particles and forces that were playing by the rules of quantum field theory. The classical concept of a force is also extended by the Standard Model: in addition to pushing and pulling on one another, when particles interact they can change their identity and be created or destroyed.

  Feynman diagrams (a–g, below), first devised by physicist Richard P. Feynman, serve as useful shorthand to describe interactions in quantum field theory. The straight lines represent the trajectories of matter particles; the wavy lines represent those of force particles. Electromagnetism is produced by the emission or absorption of photons by any charged particle, such as an electron or a quark. In a, the incoming electron emits a photon and travels off in a new direction. The strong force involves gluons emitted (b) or absorbed by quarks. The weak force involves W and Z particles (c, d), which are emitted or absorbed by both quarks and leptons (electrons, muons, taus and neutrinos). Notice how the W causes the electron to change identity. Gluons (e) and Ws and Zs (f) also self-interact, but photons do not.

  Diagrams a through f are called interaction vertices. Forces are produced by combining two or more vertices. For example, the electromagnetic force between an electron and a quark is largely generated by the transfer of a photon (g). Everything that happens in our world, except for gravity, is the result of combinations of these vertices. —G.K.

  Illustrations by Bryan Christie Design

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  -Originally published: Scientific American 288(6), 68-75 (June 2003)

  The Mysteries of Mass

  by Gordon Kane

  Most people think they know what mass is, but they understand only part of the story. For instance, an elephant is clearly bulkier and weighs more than an ant. Even in the absence of gravity, the elephant would have greater mass— it would be harder to push and set in motion. Obviously the elephant is more massive because it is made of many more atoms than the ant is, but what determines the masses of the individual atoms? What about the elementary particles that make up the atoms— what determines their masses? Indeed, why do they even have mass?

  We see that the problem of mass has two independent aspects. First, we need to learn how mass arises at all. It turns out mass results from at least three different mechanisms, which I will describe below. A key player in physicists’ tentative theories about mass is a new kind of field that permeates all of reality, called the Higgs field. Elementary particle masses are thought to come about from the interaction with the Higgs field. If the Higgs field exists, theory demands that it have an associated particle, the Higgs boson. Using particle accelerators, scientists are now hunting for the Higgs.

  The second aspect is that scientists want to know why different species of elementary particles have their specific quantities of mass. Their intrinsic masses span at least 11 orders of magnitude, but we do not yet know why that should be so. For comparison, an elephant and the smallest of ants differ by about 11 orders of magnitude of mass.

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  MASSES OF THE PARTICLES of the Standard Model differ by at least 11 orders of magnitude and are believed to be generated by interactions with the Higgs fi eld. At least fi ve Higgs particles are likely to exist.
Their masses are not known; possible Higgs masses are indicated.

  Illustration by Bryan Christie Design

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  What Is Mass?

  Isaac Newton presented the earliest scientific definition of mass in 1687 in his landmark Principia: “The quantity of matter is the measure of the same, arising from its density and bulk conjointly.” That very basic definition was good enough for Newton and other scientists for more than 200 years. They understood that science should proceed first by describing how things work and later by understanding why. In recent years, however, the why of mass has become a research topic in physics. Understanding the meaning and origins of mass will complete and extend the Standard Model of particle physics, the well-established theory that describes the known elementary particles and their interactions. It will also resolve mysteries such as dark matter, which makes up about 25 percent of the universe.

  The foundation of our modern understanding of mass is far more intricate than Newton’s definition and is based on the Standard Model. At the heart of the Standard Model is a mathematical function called a Lagrangian, which represents how the various particles interact. From that function, by following rules known as relativistic quantum theory, physicists can calculate the behavior of the elementary particles, including how they come together to form compound particles, such as protons. For both the elementary particles and the compound ones, we can then calculate how they will respond to forces, and for a force F, we can write Newton’s equation F = ma, which relates the force, the mass and the resulting acceleration. The Lagrangian tells us what to use for m here, and that is what is meant by the mass of the particle.

  But mass, as we ordinarily understand it, shows up in more than just F = ma. For example, Einstein’s special relativity theory predicts that massless particles in a vacuum travel at the speed of light and that particles with mass travel more slowly, in a way that can be calculated if we know their mass. The laws of gravity predict that gravity acts on mass and energy as well, in a precise manner. The quantity m deduced from the Lagrangian for each particle behaves correctly in all those ways, just as we expect for a given mass.

  Fundamental particles have an intrinsic mass known as their rest mass (those with zero rest mass are called massless). For a compound particle, the constituents’ rest mass and also their kinetic energy of motion and potential energy of interactions contribute to the particle’s total mass. Energy and mass are related, as described by Einstein’s famous equation, E = mc2 (energy equals mass times the speed of light squared).

  An example of energy contributing to mass occurs in the most familiar kind of matter in the universe—the protons and neutrons that make up atomic nuclei in stars, planets, people and all that we see. These particles amount to 4 to 5 percent of the mass-energy of the universe. The Standard Model tells us that protons and neutrons are composed of elementary particles called quarks that are bound together by massless particles called gluons. Although the constituents are whirling around inside each proton, from outside we see a proton as a coherent object with an intrinsic mass, which is given by adding up the masses and energies of its constituents.

  The Standard Model lets us calculate that nearly all the mass of protons and neutrons is from the kinetic energy of their constituent quarks and gluons (the remainder is from the quarks’ rest mass). Thus, about 4 to 5 percent of the entire universe—almost all the familiar matter around us—comes from the energy of motion of quarks and gluons in protons and neutrons.

  The Higgs Mechanism

  Unlike protons and neutrons, truly elementary particles—such as quarks and electrons—are not made up of smaller pieces. The explanation of how they acquire their rest masses gets to the very heart of the problem of the origin of mass. As I noted above, the account proposed by contemporary theoretical physics is that fundamental particle masses arise from interactions with the Higgs field. But why is the Higgs field present throughout the universe? Why isn’t its strength essentially zero on cosmic scales, like the electromagnetic field? What is the Higgs field?

  The Higgs field is a quantum field. That may sound mysterious, but the fact is that all elementary particles arise as quanta of a corresponding quantum field. The electromagnetic field is also a quantum field (its corresponding elementary particle is the photon). So in this respect, the Higgs field is no more enigmatic than electrons and light. The Higgs field does, however, differ from all other quantum fields in three crucial ways.

  The first difference is somewhat technical. All fields have a property called spin, an intrinsic quantity of angular momentum that is carried by each of their particles. Particles such as electrons have spin ½ and most particles associated with a force, such as the photon, have spin 1. The Higgs boson (the particle of the Higgs field) has spin 0. Having 0 spin enables the Higgs field to appear in the Lagrangian in different ways than the other particles do, which in turn allows—and leads to—its other two distinguishing features.

  The second unique property of the Higgs field explains how and why it has nonzero strength throughout the universe. Any system, including a universe, will tumble into its lowest energy state, like a ball bouncing down to the bottom of a valley. For the familiar fields, such as the electromagnetic fields that give us radio broadcasts, the lowest energy state is the one in which the fields have zero value (that is, the fields vanish)—if any nonzero field is introduced, the energy stored in the fields increases the net energy of the system. But for the Higgs field, the energy of the universe is lower if the field is not zero but instead has a constant nonzero value. In terms of the valley metaphor, for ordinary fields the valley floor is at the location of zero field; for the Higgs, the valley has a hillock at its center (at zero field) and the lowest point of the valley forms a circle around the hillock. The universe, like a ball, comes to rest somewhere on this circular trench, which corresponds to a nonzero value of the field. That is, in its natural, lowest energy state, the universe is permeated throughout by a nonzero Higgs field.

  The final distinguishing characteristic of the Higgs field is the form of its interactions with the other particles. Particles that interact with the Higgs field behave as if they have mass, proportional to the strength of the field times the strength of the interaction. The masses arise from the terms in the Lagrangian that have the particles interacting with the Higgs field.

  Our understanding of all this is not yet complete, however, and we are not sure how many kinds of Higgs fields there are. Although the Standard Model requires only one Higgs field to generate all the elementary particle masses, physicists know that the Standard Model must be superseded by a more complete theory. Leading contenders are extensions of the Standard Model known as Supersymmetric Standard Models (SSMs). In these models, each Standard Model particle has a so-called superpartner (as yet undetected) with closely related properties. With the Supersymmetric Standard Model, at least two different kinds of Higgs fields are needed. Interactions with those two fields give mass to the Standard Model particles. They also give some (but not all) mass to the superpartners. The two Higgs fields give rise to five species of Higgs boson: three that are electrically neutral and two that are charged. The masses of particles called neutrinos, which are tiny compared with other particle masses, could arise rather indirectly from these interactions or from yet a third kind of Higgs field.

  Theorists have several reasons for expecting the SSM picture of the Higgs interaction to be correct. First, without the Higgs mechanism, the W and Z bosons that mediate the weak force would be massless, just like the photon (which they are related to), and the weak interaction would be as strong as the electromagnetic one. Theory holds that the Higgs mechanism confers mass to the W and Z in a very special manner. Predictions of that approach (such as the ratio of the W and Z masses) have been confi rmed experimentally.

  Second, essentially all other aspects of the Standard Model have been well tested, and with such a detailed, interlocking theory it is difficult to change one part (s
uch as the Higgs) without affecting the rest. For example, the analysis of precision measurements of W and Z boson properties led to the accurate prediction of the top quark mass before the top quark had been directly produced. Changing the Higgs mechanism would spoil that and other successful predictions.

  Third, the Standard Model Higgs mechanism works very well for giving mass to all the Standard Model particles, W and Z bosons, as well as quarks and leptons; the alternative proposals usually do not. Next, unlike the other theories, the SSM provides a framework to unify our understanding of the forces of nature. Finally, the SSM can explain why the energy “valley” for the universe has the shape needed by the Higgs mechanism. In the basic Standard Model the shape of the valley has to be put in as a postulate, but in the SSM that shape can be derived mathematically.

  Testing the Theory

  Naturally, physicists want to carry out direct tests of the idea that mass arises from the interactions with the different Higgs fields. We can test three key features. First, we can look for the signature particles called Higgs bosons. These quanta must exist, or else the explanation is not right. Physicists are currently looking for Higgs bosons at the Tevatron Collider at Fermi National Accelerator Laboratory in Batavia, Ill.