The Higgs Boson: Searching for the God Particle

by Scientific American Editors

  Second, once they are detected we can observe how Higgs bosons interact with other particles. The very same terms in the Lagrangian that determine the masses of the particles also fix the properties of such interactions. So we can conduct experiments to test quantitatively the presence of interaction terms of that type. The strength of the interaction and the amount of particle mass are uniquely connected.

  Third, different sets of Higgs fields, as occur in the Standard Model or in the various SSMs, imply different sets of Higgs bosons with various properties, so tests can distinguish these alternatives, too. All that we need to carry out the tests are appropriate particle colliders—ones that have sufficient energy to produce the different Higgs bosons, suffi- cient intensity to make enough of them and very good detectors to analyze what is produced.

  A practical problem with performing such tests is that we do not yet understand the theories well enough to calculate what masses the Higgs bosons themselves should have, which makes searching for them more difficult because one must examine a range of masses. A combination of theoretical reasoning and data from experiments guides us about roughly what masses to expect.

  The Large Electron-Positron Collider (LEP) at CERN, the European laboratory for particle physics near Geneva, operated over a mass range that had a significant chance of including a Higgs boson. It did not find one—although there was tantalizing evidence for one just at the limits of the collider’s energy and intensity—before it was shut down in 2000 to make room for constructing a newer facility, CERN’s Large Hadron Collider (LHC). The Higgs must therefore be heavier than about 120 proton masses. Nevertheless, LEP did produce indirect evidence that a Higgs boson exists: experimenters at LEP made a number of precise measurements, which can be combined with similar measurements from the Tevatron and the collider at the Stanford Linear Accelerator Center. The entire set of data agrees well with theory only

  if certain interactions of particles with the lightest Higgs boson are included and only if the lightest Higgs boson is not heavier than about 200 proton masses. That provides researchers with an upper limit for the mass of the Higgs boson, which helps focus the search.

  For the next few years, the only collider that could produce direct evidence for Higgs bosons will be the Tevatron. Its energy is suffi cient to discover a Higgs boson in the range of masses implied by the indirect LEP evidence, if it can consistently achieve the beam intensity it was expected to have, which so far has not been possible. In 2007 the LHC, which is seven times more energetic and is designed to have far more intensity than the Tevatron, is scheduled to begin taking data. It will be a factory for Higgs bosons (meaning it will produce many of the particles a day). Assuming the LHC functions as planned, gathering the relevant data and learning how to interpret it should take one to two years. Carrying out the complete tests that show in detail that the interactions with Higgs fields are providing the mass will require a new electron-positron collider in addition to the LHC (which collides protons) and the Tevatron (which collides protons and antiprotons).

  Dark Matter

  What is discovered about Higgs bosons will not only test whether the Higgs mechanism is indeed providing mass, it will also point the way to how the Standard Model can be extended to solve problems such as the origin of dark matter.

  With regard to dark matter, a key particle of the SSM is the lightest superpartner (LSP). Among the superpartners of the known Standard Model particles predicted by the SSM, the LSP is the one with the lowest mass. Most superpartners decay promptly to lower-mass superpartners, a chain of decays that ends with the LSP, which is stable because it has no lighter particle that it can decay into. (When a superpartner decays, at least one of the decay products should be another superpartner; it should not decay entirely into Standard Model particles.) Superpartner particles would have been created early in the big bang but then promptly decayed into LSPs. The LSP is the leading candidate particle for dark matter.

  The Higgs bosons may also directly affect the amount of dark matter in the universe. We know that the amount of LSPs today should be less than the amount shortly after the big bang, because some would have collided and annihilated into quarks and leptons and photons, and the annihilation rate may be dominated by LSPs interacting with Higgs bosons.

  As mentioned earlier, the two basic SSM Higgs fields give mass to the Standard Model particles and some mass to the superpartners, such as the LSP. The superpartners acquire more mass via additional interactions, which may be with still further Higgs fields or with fields similar to the Higgs. We have theoretical models of how these processes can happen, but until we have data on the superpartners themselves we will not know how they work in detail. Such data are expected from the LHC or perhaps even from the Tevatron.

  Neutrino masses may also arise from interactions with additional Higgs or Higgs-like fields, in a very interesting way. Neutrinos were originally assumed to be massless, but since 1979 theorists have predicted that they have small masses, and over the past decade several impressive experiments have confirmed the predictions. The neutrino masses are less than a millionth the size of the next smallest mass, the electron mass. Because neutrinos are electrically neutral, the theoretical description of their masses is more subtle than for charged particles. Several processes contribute to the mass of each neutrino species, and for technical reasons the actual mass value emerges from solving an equation rather than just adding the terms.

  Thus, we have understood the three ways that mass arises: The main form of mass we are familiar with—that of protons and neutrons and therefore of atoms—comes from the motion of quarks bound into protons and neutrons. The proton mass would be about what it is even without the Higgs field. The masses of the quarks themselves, however, and also the mass of the electron, are entirely caused by the Higgs field. Those masses would vanish without the Higgs. Last, but certainly not least, most of the amount of superpartner masses, and therefore the mass of the dark matter particle (if it is indeed the lightest superpartner), comes from additional interactions beyond the basic Higgs one.

  Finally, we consider an issue known as the family problem. Over the past half a century physicists have shown that the world we see, from people to flowers to stars, is constructed from just six particles: three matter particles (up quarks, down quarks and electrons), two force quanta (photons and gluons), and Higgs bosons—a remarkable and surprisingly simple description. Yet there are four more quarks, two more particles similar to the electron, and three neutrinos. All are very short-lived or barely interact with the other six particles. They can be classifi ed into three families: up, down, electron neutrino, electron; charm, strange, muon neutrino, muon; and top, bottom, tau neutrino, tau. The particles in each family have interactions identical to those of the particles in other families. They differ only in that those in the second family are heavier than those in the first, and those in the third family are heavier still. Because these masses arise from interactions with the Higgs field, the particles must have different interactions with the Higgs field.

  Hence, the family problem has two parts: Why are there three families when it seems only one is needed to describe the world we see? Why do the families differ in mass and have the masses they do? Perhaps it is not obvious why physicists are astonished that nature contains three almost identical families even if one would do. It is because we want to fully understand the laws of nature and the basic particles and forces. We expect that every aspect of the basic laws is a necessary one. The goal is to have a theory in which all the particles and their mass ratios emerge inevitably, without making ad hoc assumptions about the values of the masses and without adjusting parameters. If having three families is essential, then it is a clue whose signifi cance is currently not understood.

  Tying It All Together

  The standard model and the SSM can accommodate the observed family structure, but they cannot explain it. This is a strong statement. It is not that the SSM has not yet explained the family struc
ture but that it cannot. For me, the most exciting aspect of string theory is not only that it may provide us with a quantum theory of all the forces but also that it may tell us what the elementary particles are and why there are three families. String theory seems able to address the question of why the interactions with the Higgs fi eld differ among the families. In string theory, repeated families can occur, and they are not identical. Their differences are described by properties that do not affect the strong, weak, electromagnetic or gravitational forces but that do affect the interactions with Higgs fields, which fits with our having three families with different masses. Although string theorists have not yet fully solved the problem of having three families, the theory seems to have the right structure to provide a solution. String theory allows many different family structures, and so far no one knows why nature picks the one we observe rather than some other. Data on the quark and lepton masses and on their superpartner masses may provide major clues to teach us about string theory.

  One can now understand why it took so long historically to begin to understand mass. Without the Standard Model of particle physics and the development of quantum fi eld theory to describe particles and their interactions, physicists could not even formulate the right questions. Whereas the origins and values of mass are not yet fully understood, it is likely that the framework needed to understand them is in place. Mass could not have been comprehended before theories such as the Standard Model and its supersymmetric extension and string theory existed. Whether they indeed provide the complete answer is not yet clear, but mass is now a routine research topic in particle physics.

  -Originally published: Scientific American 293(1), 40-48 (July 2005)

  Is Nature Supersymmetric?

  by Howard E. Haber and Gordon L. Kane

  About 25 centuries ago the Ionian Greeks argued that the apparent complexity of the universe could be understood in terms of a few simple underlying laws. Remarkable progress has been made toward realizing that goal. It appears that the basic constituents of matter have been identified. A few forces can account for the behavior of any form of matter, ranging from subatomic particles to galaxies. To complete the description of the laws of nature, however, further insight is still needed. For the past decade a large number of theoretical physicists have extensively explored an approach called supersymmetry. A supersymmetric theory incorporates and extends the successful discoveries of past years in an attempt to construct a new and more comprehensive theory. It also makes testable predictions.

  Perhaps the most convenient point of entry into the concept of supersymmetry is the standard picture of the fundamental constituents of matter. All matter consists of molecules, which in turn consist of atoms. An atom consists of a number of protons and neutrons bound together in a nucleus, which is surrounded by a "cloud" of electrons. Individual elements are distinguished by their number of protons.

  Until recently protons and neutrons were thought to be fundamental particles. Experiments carried out with high-energy particle accelerators during the past two decades have revealed that they are not; protons and neutrons appear to be composed of elementary particles known as quarks. Quarks are observed to carry a fraction (+2/3 or -1/3) of the electric charge of the proton. There are six "flavors," or types, of quarks. They are called up, down, charm, strange, top and bottom.

  An individual quark is not expected to be isolated, or observed alone; quarks are always part of composite particles known as hadrons. Hundreds of hadrons have been identified and catalogued. They include the proton and neutron as well as the more exotic pion and kaon. A proton, for instance, is composed of two up quarks and one down quark, and a neutron is composed of one up quark and two down quarks. For an appropriate analogy one can liken quarks to the ends of a string and hadrons to the entire string, including the quarks. Suppose one tries to isolate a quark by colliding two hadrons. If a quark tries to get out after the collision, it stretches the string, which breaks. The result is more strings, that is, more hadrons (mainly pions, since they are the lightest hadrons).

  Unlike protons and neutrons, electrons do seem to be fundamental particles. In fact, they are part of another family of so-called elementary particles known as leptons. There are six flavors of leptons too: the electron, the muon, the tau particle, the electron neutrino, the muon neutrino and the tau neutrino.

  All interactions between leptons and quarks can be accounted for by four kinds of force: gravitation, electromagnetism, the strong force and the weak force. The electromagnetic force binds electrons and nuclei to make atoms. The atoms, although they are electrically neutral, interact through a residual electromagnetic force to form molecules. The strong force binds quarks to make protons, neutrons and all other hadrons, and the resid ual strong force between protons and neutrons is the so-called nuclear force that binds them into nuclei. The weak force is responsible for such phenomena as some nuclear decays and aspects of the fusion process that releases energy from the sun. In reality there are only three fundamental forces: a great accomplishment of the past two decades has been the demonstration that the electromagnetic and weak forces are manifestations of the same force, known as the electroweak force. The strengths of the forces vary widely. The strength of the electromagnetic force between two protons, for instance, is roughly 1036 times greater than the strength of the corresponding gravitational force.

  The forces are transmitted by the exchange of a number of particles. The photon, the quantum of electromagnetic radiation, is the carrier of the electromagnetic force. Eight particles known as gluons mediate the strong force. The photon and the giuons can be interpreted as particles having zeromass. The weak force is mediated by three particles: the positively charged W+ , the negatively charged W- and the neutral Z0 Unlike the photon and the gluons, these particles are heavy: they have masses nearly 100 times the mass of the proton. All these carriers have been experimentally observed. The mediating agent of the gravitational force, as yet only conjectured, is the graviton.

  The theory that describes the quarks and the leptons and their interactions has come to be called the standard model. For the standard model to be mathematically consistent a so-called Higgs particle must exist. (The simplest version of the model contains an electrically neutral Higgs particle; more general models allow for electrically charged Higgs particles as well.) It is thought the masses of the W+ , wand Z0 particles and of the quarks and the leptons are generated through interactions with the Higgs particle. The standard model predicts how the Higgs particle should interact with the other particles, but the mass of the Higgs particle itself is not predicted. The expected properties are such that so far no experiment could have found a Higgs particle, and since the mass is not known it is hard to plan experiments to search for it.

  How have physicists made sense of the panoply of particles described in the standard model? First, the particles can be divided into two fundamental classes: fermions and bosons. Leptons and quarks, the basic constituents of matter, are fermions. The basic particles that mediate the four forces are bosons. Fermions behave as though they carry an intrinsic angular momentum, called spin, equal to half-integer units (1/2, 3/2 and so on) of Planck's constant, which is itself the fundamental unit of angular momentum in quantum theory. Bosons have spins that are integer units (0, 1, 2 and so on) of Planck's constant. The effects of the half-integer spin difference between fermions and bosons are profound. Fermions are "antisocial" and tend to occupy different energy states; bosons are "gregarious" and tend to clump together in the same energy states. All leptons and quarks are spin-1/2 fermions. The photon, the W+ , W- and Z0 particles and the eight gluons are spin-1 bosons. The graviton is expected to be a spin-2 boson and the Higgs particle is expected to be a spin-0, or spinless, boson.

  An important unifying element of the standard model is the concept of symmetry. The interactions among the various particles are symmetric (that is, invariant, or unchanged) in the face of a number of subtle interchanges. Suppose, for example, se
veral protons are arranged in close proximity to one another (as in a nucleus), so that the strong force among them is much greater than the repulsive electromagnetic force. Imagine that the strong forces acting among the protons are then measured. If one now replaces each proton with a neutron, the forces remain unchanged. In fact, mathematically one can imagine replacing each proton with a "mixture" of the proton and the neutron, and again the forces remain unchanged. This is an example of a symmetry where the same interchange is made at all points in space.

  More generalized symmetries are those in which interchanges vary from point to point in space and time. Such symmetries are important elements of gauge theories. All interactions described by the standard model can be successfully accounted for by exploiting such generalized symmetries.

  The stage is now set for supersymmetry. It is apparent that in spite of the success of the standard model, physicists must look beyond it if they hope to understand completely the properties of matter; some aspects of the standard model are mysterious and suggest that more discoveries will come. First, no one can explain why the standard model takes the form it does. The mathematical structure of the theory is elegant and surprisingly simple, and the observed interactions show many symmetries. Yet a number of other forms (different choices of symmetries) would theoretically have been equally plausible and elegant. Second, there is no understanding of the physical origin of the masses of the fundamental particles and the strength of the forces acting between them. Why do they have the values they do? Most particle physicists hope that eventually such parameters can be calculatedrather than just measured. Although there are no direct clues at present as to how to extend the standard model, supersymmetry seems to many physicists to be a likely direction in which to look. In the past few years efforts have been under way to search for evidence of supersymmetry in nature.