The Higgs Boson: Searching for the God Particle
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The search for experimental evidence of supersymmetry centers on the discovery of new particles. The reason is that the theory requires that for every ordinary particle there exist a "superpartner" with identical properties- except its spin differs by half a unit. In other words, supersymmetry differs from all previous theories in that it relates the two fundamental classes of particles, fermions and bosons, to each other. In addition the strengths of the interaction forcesamong the proposed superpartners are identical with the strengths of the interaction forces among the various normal particles.
The spin-0 superpartners of the fermions are named by adding the prefix s- to the normal particle name; for example, the spin-1/2 electron and the quark have the spin-0 partners selectron and squark respectively. The spin-1/2 superpartners of the bosons are named by adding the suffix -ina to the root of the normal particle name; for example, the partner of the spin-1 photon is the spin-1/2 photino and the partner of the spin-1 gluon is the spin-1/2 gluino. (For the Higgs particle there is a minor technical complication. The supersymmetric theory requires both electrically charged and neutral Higgs particles; a positively charged H+, a negatively charged H and three neutrals, collectively denoted as H0, are needed.)
What advantages are gained by multiplying the number of elementary particles by 2? First, supersymmetry can solve a fundamental problem: it provides a mechanism by which a single theory can account for two important energies, or masses, that differ by many orders of magnitude. (As expressed by Einstein's famous equation E=mc2, mass and energy are eq uivalent and can be referred to interchangeably.) Those energies are the masses of the W+, W- and Z0 particles, roughly 1011 electron-volt units of energy, and the so-called Planck mass, about 1028 electron volts. The Planck mass is an important quantity to include in any theory that tries to account for gravity in a unification of the four fundamental forces; if elementary particles with a mass of 1028 electron volts existed, the strength of the gravitational force among them would be greater than the strength of each of the other fundamental forces.
Ordinarily one would expect that if the masses of the W and Z0 particles were computable in a fundamental theory that contained the Planck mass, they would turn out to be roughly the same order of magnitude as the Planck mass, rather than 1017 times smaller. In the supersymmetric theory, however, delicate cancellations occur that allow the W and Z0 masses to be many orders of magnitude smaller than the Planck mass, just as they are observed to be. These delicate cancellations are not contrived but are guaranteed by the mathematical structure of the supersymmetric theory.
We should point out, however, that not all widely separated energies are problematical. For example, existing theories can easily account for the energy levels observed in both hadrons (such as protons and neutrons) and atoms, even though the energy levels of the hadrons are roughly 109 electron volts and those of the atoms are roughly 10 electron volts. The reason is found in the hierarchy of structure: atoms are made up of nuclei and electrons, nuclei are made up of protons and neutrons, and protons and neutrons are made up of quarks: If, however, one wants to develop a theory of fundamental particles and interactions, one no longer has recourse to such a hierarchy.
A second feature of supersymmetry is its close relation to Einstein's theory of gravity. Ever since Einstein introduced general relativity physicists have attempted, without much success, to unify gravity and quantum mechanics. It is now widely believed by theorists that a quantum-mechanical theory of gravity will be a supersymmetric one.
Although many physicists have contributed to the development of supersymmetry, a mathematically consistent formulation of the theory was first made in the early 1970's by a number of different groups working independently: Andre Neveu and John H. Schwarz, then at Princeton University; Pierre M. Ramond of the University of Florida; Yu. A. Gol'fond and E. P. Likhtman of the Physics Institute of the U.S.S.R. Academy of Sciences; V. P. Akulov and D. V. Volkov of the Ukrainian Physical-Technical Institute, and Julius Wess of the University of Karlsruhe in West Germany and Bruno Zumino of the University of California at Berkeley.
If indeed nature is supersymmetric, the super symmetry must be a "broken symmetry," that is, a symmetry that holds true approximately, or for parts of the theory only. Imagine what would happen if nature were exactly supersymmetric. Selectrons would have the same mass as electrons and would bind to protons by the electromagnetic force. The properties of atoms formed in such a way would be very different from those of normal atoms. As fermions, electrons must occupy different energy levels in atoms; as bosons, selectrons would occupy the same energy levels. If atoms contained selectrons instead of electrons, the structure of the periodic table of elements would be completely altered. Since such atoms have not been observed, the mass of the selectron (if the selectron exists) must be larger than the mass of the electron, and so the symmetry is broken.
The appeal to a broken symmetry may at first seem to be an ad hoc solution. In reality, however, the concept of broken symmetry is a familiar and powerful tool of physics. One of its great triumphs is seen in the theory of electroweak interactions. In that theory a symmetry naively implying that the photon, W+ , W- and Z0 particles are all massless is broken. As a result the W+ , W- and Z0 particles are expected to have mass. Moreover, their masses are correctly predicted by the theory. It is easy to construct a theory that maintains all the desirable aspects of a perfect supersymmetry but in which the supersymmetry is broken in such a way that the masses of the superpartners are much larger than the masses of the corresponding standardmodel particles.
Can the masses of the superpartners be predicted? A possible answer is suggested by the arguments regarding the wide difference in mass between the W and Z0 bosons and the Planck mass. The delicate cancellations required to explain the disparity remain operative in a slightly broken supersymmetric theory, but only if the superpartnermasses are not much larger than the W and Z0 boson masses.
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FUNDAMENTAL PARTICLES can be categorized by such quantities as baryon number (B), lepton number (L), spin (S), and R number (R). (The R number is given by the formula R = 3B + L + 2S.) Lepton number, baryon number and spin vary among the different particle types, but the R number is even for all ordinary particles (left side of chart) and odd for all predicted superpartners (right side). The pattern has important consequences. Specifically, one property of most supersymmetric theories is that the R number cannot change from even to odd (or from odd to even) during reactions among particles. If, for instance, protons are collided, supersymmetric particles must be produced in pairs or the R number would change from even to odd. Assuming that a supersymmetric particle is indeed produced, its decay products must contain an odd number of supersymmetric particles. As a consequence the least massive of all the supersymmetric particles must be stable, since there are no lighter supersymmetric particles into which it can decay.
Illustration by Gabor Kiss
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As work on the mathematical structure and properties of supersymmetric theories has progressed, physicists have increasingly wondered how experimental evidence for supersymmetry might be detected. If nature is supersymmetric, how would investigators recognize it? In 1979 Pierre Fayet, now at the Ecole Normale Superieure in Paris, first studied these questions, partly in collaboration with Glennys R. Farrar, now at Rutgers University. By the early 1980's the mathematical motivations for the study of supersymmetry had become clearer and a better understanding of how to build realistic models incorporating supersymmetry was developed. At that point we and others began to study in detail the question of how to recognize evidence for supersymmetry.
Today that question is essentially answered. Physicists know how to calculate the predictions of supersymmetric theories and how to decide whether a particular experimental signal, or class of events, does or does not substantiate a supersymmetric theory. Furthermore, it is known how to set quantitative limits on a supersymmetric theory if no signal is observed in a given set
of experiments.
Suppose two normal particles, such as two electrons or two protons, are accelerated to high energies and supersymmetric particles are produced in any collisions that ensue. What predictions does supersymmetry make about such particles?
A conservation law of supersymmetry leads to two results. First, supersymmetric particles cannot be produced alone; they must be produced in pairs. Second, if a supersymmetric particle is produced, its decay products must contain an odd number of supersymmetric particles. As a consequence the least massive of all the supersymmetric particles must be stable, since there are no lighter supersymmetric particles into which it can decay. There are several candidates for the least massive supersymmetric particle. For now we shall assume it is the photino.
The existence of a least massive supersymmetric particle has important consequences for the detection of supersymmetry in the laboratory. (In addition the least massive supersymmetric particle could have cosmological consequences: it might account for the so-called dark matter, or missing mass, of the universe.) All supersymmetric particles except the least massive one decay into particles that must include the least massive one at the end of their decay chain. The decays occur so fast that the decaying particle does not have time to travel a detectable distance. If a supersymmetric particle were produced, only its stable decay products, which would be standardmodel particles and the least massive supersymmetric particle, would be observed in the laboratory. To detect supersymmetric particles, therefore, the least massive supersymmetric particle must be detected.
Unfortunately the probability that the least massive supersymmetric particle could be directly detected is so low as to be negligible: it interacts very weakly with ordinary matter and would escape any detector. As a result the total energy, including the rest mass, of the detected product particles would be less than the total energy of the colliding particles. In other words, the signature of supersymmetry is missing energy: the energy is carried away by the least massive supersymmetric particle.
Can a particle be discovered indirectly by observing that a substantial amount of energy is missing? The answer is yes. That is how the existence of the neutrino was deduced about 50 years ago. Much more recently (in 1983) the existence of the W boson was confirmed by a similar method. In experiments done at CERN, the European laboratory for particle physics in Geneva, W bosons were produced by the collision of protons and antiprotons. (An antiproton is identical in mass with a proton, but its charge is negative.) Some of the W bosons subsequently decayed into an electron and a neutrino. The neutrino escaped the detector, leaving a high-energy electron. By measuring the energy of the electron and determining what the energy of the neutrino must have been for energy conservation to hold, the existence of the W boson was inferred and its mass was determined.
Similar experiments for detecting supersymmetric particles are now being done with electron-positron colliders and proton-antiproton colliders. (A positron is identical in mass with an electron, but its charge is positive.) Collisions between pairs of electrons and positrons could produce pairs of positively and negatively charged selectrons. The positively charged selectron would rapidly decay into a positron and a photino and the negatively charged selectron would decay into an electron and a photino. Both photinos would escape, so that an event of this type, if it occurred, would be characterized by the fact that on the average half of the energy would be missing.
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SUPERSYMMETRIC PARTICLES might be produced by particle accelerators called electron-positron colliders. (A positron is identical in mass with an electron, but its charge is positive). Collisions between electrons and positrons could yield positively and negatively charged selectrons, as is shown in the Feynman diagram at the top and in the drawing at the bottom depicting the collision and its products. The positively charged selectron would decay into a positron and a photino and the negatively charged selectron into an electron and a photino. Both photinos would escape detection, so that an event of this type, if it occurred, would be characterized by the fact that on the average half of the energy would be missing. Such an event would also exhibit missing momentum; the direction would be given by the "vector sum" of the photinos' momentum. No candidats have been found to date.
Illustration by Gabor Kiss
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Since the outgoing positron and electron arise from different decays, their directions would be uncorrelated: they would not point in opposite directions, as would be expected in a normal collision. Moreover, if a plane were defined by the incoming particle beams and the outgoing positron, the outgoing electron would not in general lie in that plane, again contrary to the result of a normal collision. Searches for events with these characteristics have been made at electron-positron colliders such as the CESR at Cornell University, PEP at Stanford University and PETRA in Hamburg. So far no candidates have been found.
The negative results do not rule out supersymmetry. They only mean that selectrons lighter than the highest energy available at electron-positron colliders do not exist; the mass of a selectron must be at least 23 times greater than the mass of a proton (roughly a billion electron volts), or about 28 percent of the mass of a W boson. (Certain indirect methods allow somewhat larger masses to be ruled out.) Such quantitative limits can be obtained because super symmetry is a well-defined theory in which one can calculate whether a detectable number of events due to supersymmetric particles of a given mass would be expected in a given experimental situation. Without such calculations a positive result could still be interpreted as evidence for supersymmetry, but a negative result would simply imply that too few superpartners were produced, with no information on the possible allowed masses. Because it is reasonable to expect the masses of supersymmetric particles to be as large as a few Wboson masses, colliders able to explore regions of higher energy are needed.
The available energies at protonantiproton colliders are somewhat higher, but there the comparison between theory and experiment is subtler. It is subtler because of the composite nature of the proton: calculations must take into account the fact that a proton consists of three quarks and a number of gluons that bind the quarks together. As might be expected, in a moving proton about half of the momentum is carried by the gluons and the other half by the quarks. Then each of the three quarks must carry about a sixth of the total momentum. Existing machines, limited essentially by economic considerations, have produced 23-billion-electron-volt (BeV) collisions between electrons and posi-trons and 315-BeV collisions between protons and antiprotons. As a result the quarks and gluons in a proton, even though they carry only a fraction of the proton's momentum, can still be exploited to probe mass scales higher than those accessible to present-day electron-positron colliders.
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PROTON-ANTIPROTON collisions might also produce supersymmetric particles if, for instance, a quark from one proton or antiproton collides with a gluon from another one.
Illustration by Gabor Kiss
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A number of different collisions can take place at proton-proton or protonantiproton colliders. Suppose a quark from one proton strikes a gluon from an antiproton and produces a squark and a gluino. The squark would rapidly decay into a quark and a photino, and the gluino would decay into a quark, an antiquark and a photino. An isolated quark or antiquark cannot emerge from the collision; instead it must somehow turn itself into hadrons. Because the emitted particle is energetic in this case, it turns itself into a group of hadrons all moving in roughly the same direction as the original quark. In the parlance of physics such a group of hadrons is commonly referred to as a "jet" of hadrons.
In the example, three jets of hadrons (one for each of the two quarks and one for the antiquark) and two photinos would emerge into the region around the interaction. When the gluino decays, its energy is shared among the quark, the antiquark and the photino. The energy need not be shared equally, however; sometimes one or another of the three decay products gets most of the a
vailable energy. Although the energy imbalance and other related effects make comparison of theory and experiment more difficult at proton colliders than at electron colliders, the comparison can be made.
As an example, in 1982 Jacques P. Leveille, then at the University of Michigan, and one of us (Kane) proposed that evidence for supersymmetry would be obtained if certain observations (such as one or more jets ofparticles in the presence of a large amount of missing momentum) were seen at a high-energy hadron collider. Much excitement was generated the following year when events of this type were reportedly seen at the UA1 (for Underground Area 1) and UA2 detectors at CERN. A number of groups of theorists have examined the possibility that supersymmetric particles were being produced. We have done detailed analyses in collaboration with R. Michael Barnett of the Lawrence Berkeley Laboratory. Other analyses have been made by John Ellis of CERN and Henry Kowalski of DESY (the electron accelerator in Hamburg), by Yernon D. Barger of the University of Wisconsin at Madison and his collaborators, and by Ewald Reya of the University of Dortmund in West Germany and D. P. Roy of the Tata Institute of Fundamental Research in India.
The number of missing energy events observed in the original, albeit small, data sample initially suggested the possibility of new particles. Events predicted by the standard model, however, can appear in a configuration similar to the configurations observed at CERN. Statistical analyses are therefore needed to prove that inherently new phenomena are being seen. Now that more data have been accumulated the situation remains unclear, although the possibility that the discovery of supersymmetric particles has occurred is less likely than it seemed initially. More data will be collected at the CERN collider this year and may make it clearer whether any of the few candidate events corresponds to the production of supersymmetric particles.