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The Higgs Boson
Searching for the God Particle
By Scientific American
Scientific American Inc.Copyright © 2012 Scientific American, a division of Nature America, Inc.
All rights reserved.
The Standard Model
Elementary Particles and Forces
By Chris Quigg
The notion that a fundamental simplicity lies below the observed diversity of the universe has carried physics far. Historically the list of particles and forces considered to be elementary has changed continually as closer scrutiny of matter and its interactions revealed microcosms within microcosms: atoms within molecules, nuclei and electrons within atoms, and successively deeper levels of structure within the nucleus. Over the past decade, however, experimental results and the convergence of theoretical ideas have brought new coherence to the subject of particle physics, raising hopes that an enduring understanding of the laws of nature is within reach.
Higher accelerator energies have made it possible to collide particles with greater violence, revealing the subatomic realm in correspondingly finer detail; the limit of experimental resolution now stands at about 10 centimeter, about a thousandth the diameter of a proton. A decade ago physics recognized hundreds of apparently elementary particles; at today's resolution that diversity has been shown to represent combinations of a much smaller number of fundamental entities. Meanwhile the forces through which these constituents interact have begun to display underlying similarities. A deep connection between two of the forces, electromagnetism and the weak force that is familiar in nuclear decay, has been established, and prospects are good for a description of fundamental forces that also encompasses the strong force that binds atomic nuclei.
Of the particles that now appear to be structureless and indivisible, and therefore fundamental, those that are not affected by the strong force are known as leptons. Six distinct types, fancifully called flavors, of lepton have been identified. Three of the leptons, the electron, the muon and the tau, carry an identical electric charge of –1 ; they differ, however, in mass. The electron is the lightest and the tau the heaviest of the three. The other three, the neutrinos, are, as their name suggests, electrically neutral. Two of them, the electron neutrino and the muon neutrino, have been shown to be nearly massless. In spite of their varied masses all six leptons carry precisely the same amount of spin angular momentum. They are designated spin –1/2 because each particle can spin in one of two directions. A lepton is said to be right-handed if the curled fingers of a right hand indicate its rotation when the thumb points in its direction of travel and left-handed when the fingers and thumb of the left hand indicate its spin and direction.
For each lepton there is a corresponding antilepton, a variety of antiparticle. Antiparticles have the same mass and spin as their respective particles but carry opposite values for other properties, such as electric charge. The antileptons, for example, include the antielectron, or positron, the antimuon and the antitau, all of which are positively charged, and three electrically neutral antineutrinos.
In their interactions the leptons seem to observe boundaries that define three families, each composed of a charged lepton and its neutrino. The families are distinguished mathematically by lepton numbers; for example, the electron and the electron neutrino are assigned electron number 1, muon number 0 and tau number 0. Antileptons are assigned lepton numbers of the opposite sign. Although some of the leptons decay into other leptons, the total lepton number of the decay products is equal to that of the original particle; consequently the family lines are preserved.
The muon, for example, is unstable. It decays after a mean lifetime of 2.2 microseconds into an electron, an electron antineutrino and a muon neutrino through a process mediated by the weak force. Total lepton number is unaltered in the transformation. The muon number of the muon neutrino is 1, the electron number of the electron is 1 and that of the electron antineutrino is –1. The electron numbers cancel, leaving the initial muon number of 1 unchanged. Lepton number is also conserved in the decay of the tau, which endures for a mean lifetime of 3 X 10-13 second.
The electron, however, is absolutely stable. Electric charge must be conserved in all interactions, and there is no less massive charged particle into which an electron could decay. The decay of neutrinos has not been observed. Because neutrinos are the less massive members of their respective families, their decay would necessarily cross family lines.
Where are leptons observed? The electron is familiar as the carrier of electric charge in metals and semiconductors. Electron antineutrinos are emitted in the beta decay of neutrons into protons. Nuclear reactors, which produce large numbers of unstable free neutrons, are abundant sources of antineutrinos. The remaining species of lepton are produced mainly in high-energy collisions of subnuclear particles, which occur naturally as cosmic rays interact with the atmosphere and under controlled conditions in particle accelerators. Only the tau neutrino has not been observed directly, but the indirect evidence for its existence is convincing.
Subnuclear particles that experience the strong force make up the second great class of particles studied in the laboratory. These are the hadrons; among them are the protons, the neutrons and the mesons. A host of other less familiar hadrons exist only ephemerally as the products of high-energy collisions, from which extremely massive and very unstable particles can materialize. Hundreds of species of hadron have been catalogued, varying in mass, spin, charge and other properties.
Hadrons are not elementary particles, however, since they have internal structure. In 1964 Murray Gell-Mann of the California Institute of Technology and George Zweig, then working at CERN, the European laboratory for particle physics in Geneva, independently attempted to account for the bewildering variety of hadrons by suggesting they are composite particles, each a different combination of a small number of fundamental constituents. Gell-Mann called them quarks. Studies at the Stanford Linear Accelerator Center (SLAC) in the late 1960's in which high-energy electrons were fired at protons and neutrons bolstered the hypothesis. The distribution in energy and angle of the scattered electrons indicated that some were colliding with pointlike, electrically charged objects within the protons and neutrons.
Particle physics now attributes all known hadron species to combinations of these fundamental entities. Five kinds, also termed flavors, of quark have been identified-the up (u), down (d), charm (c), strange (s) and bottom (b) quarks-and a sixth flavor, the top (t) quark, is believed to exist. Like the leptons, quarks have half a unit of spin and can therefore exist in left-hand right-handed states. They also carry electric charge equal to a precise fraction of an electron's charge: the d, s and b quarks have a charge of –1/3, and the u, c and the conjectured t quark have a charge of +2/3. The corresponding antiquarks have electric charges of the same magnitude but opposite sign.
Such fractional charges are never observed in hadrons, because quarks form combinations in which the sum of their charges is integral. Mesons, for example, consist of a quark and an antiquark, whose charges add up to –1, 0 or + 1. Protons and neutrons consist respectively of two u quarks and a d quark, for a total charge of + 1 , and of a u quark and two d quarks, for a total charge of 0.
Like leptons, the quarks experience weak interactions that change one species, or flavor, into another. For example, in the beta decay of a neutron into a proton one of the neutron's d quarks metamorphoses into a u quark, emitting an electron and an antineutrino in the process. Similar transformations of c quarks into s quarks have been observed. The pattern of decays suggests two family groupings, one of them thought to contain the u and the d quarks and the second the c and the s quarks. In apparent contrast to the behavior of leptons, some quark decays do cross family lines, however; transformations of u quarks into s quarks and of c quarks into d quarks have been observed. It is the similarity of the two known quark families to the families of leptons that first suggested the existence of a t quark, to serve as the partner of the b quark in a third family.
In contrast to the leptons, free quarks have never been observed. Yet circumstantial evidence for their existence has mounted steadily. One indication of the soundness of the quark model is its success in predicting the outcome of high-energy collisions of an electron and a positron. Because they represent matter and antimatter, the two particles annihilate each other, releasing energy in the form of a photon. The quark model predicts that the energy of the photon can materialize into a quark and an antiquark. Because the colliding electron-positron pair had a net momentum of 0, the quark-antiquark pair must diverge in opposite directions at equal velocities so that their net momentum is also 0. The quarks themselves go unobserved because their energy is converted into additional quarks and antiquarks, which materialize and combine with the original pair, giving rise to two jets of hadrons (most of them pions, a species of meson). Such jets are indeed observed, and their focused nature confirms that the hadrons did not arise directly from the collision but from single, indivisible particles whose trajectories the jets preserve.
The case for the reality of quarks is also supported by the variety of energy levels, or masses, at which certain species of hadron, notably the psi and the upsilon particles, can be observed in accelerator experiments. Such energy spectra appear analogous to atomic spectra: they seem to represent the quantum states of a bound system of two smaller components. Each of its quantum states would represent a different degree of excitation and a different combination of the components' spins and orbital motion. To most physicists the conclusion that such particles are made up of quarks is irresistible. The psi particle is held to consist of a c quark and its antiquark, and the upsilon particle is believed to comprise a b quark and its antiquark.
What rules govern the combinations of quarks that form hadrons? Mesons are composed of a quark and an antiquark. Because each quark has a spin of 1/2, the net spin of a meson is 0 if its constituents spin in opposite directions and 1 if they spin in the same direction, although in their excited states mesons may have larger values of spin owing to the quarks' orbital motion. The other class of hadrons, the baryons, consist of three quarks each. Summing the constituent quarks' possible spins and directions yields two possible values for the spin of the least energetic baryons: 1/2 and 3/2 . No other combinations of quarks have been observed; hadrons that consist of two or four quarks seem to be ruled out.
The reason is linked with the answer another puzzle. According to the exclusion principle of Wolfgang Pauli, no two particles occupying a minute region of space and possessing half-integral spins can have the same quantum number–the same values of momentum, charge and spin. The Pauli exclusion principle accounts elegantly for the configurations of electrons that determine an element's place in the periodic table. We should expect it to be a reliable guide to the panoply of hadrons as well. The principle would seem to suggest, however, that exotic hadrons such as the delta plus plus and the omega minus particles, which materialize briefly following high-energy collisions, cannot exist. They consist respectively of three u and three s quarks and possess a spin of 3/2; all three quarks in each of the hadrons must be identical in spin as well as in other properties and hence must occupy the same quantum state
To explain such observed combinations it is necessary to suppose the three otherwise identical quarks are distinguished by another trait: a new kind of charge, whimsically termed color, on which the strong force acts. Each flavor of quark can carry one of three kinds of color charge: red, green or blue. To a red quark there corresponds an antiquark with a color charge of antired (which may be thought of as cyan); other antiquarks bear charges of antigreen (magenta) and antiblue (yellow).
The analogy between this new kind of charge and color makes it possible to specify the rules under which quarks combine. Hadrons do not exhibit a color charge; the sum of the component quarks' colors must be white, or color-neutral. Therefore the only allowable combinations are those of a quark and its antiquark, giving rise to mesons, and of a red, a green and a blue quark, yielding the baryons.
Colored states are never seen in isolation. This concealment is consistent with the fact that free quarks, bearing a single color charge, have never been observed. The activity of the strong force between colored quarks must be extraordinarily powerful, perhaps powerful enough to confine quarks permanently within colorless, or color-neutral, hadrons. The description of violent electron-positron collisions according to the quark model, however, assumes the quarks that give rise to the observed jets of hadrons diverge freely during the first instant following the collision. The apparent independence of quarks at very short distances is known as asymptotic freedom; it was described in 1973 by David J. Gross and Frank Wilczek of Princeton University and by H. David Politzer, then at Harvard University.
Analogy yields an operational understanding of this paradoxical state of affairs, in which quarks interact only weakly when they are close together and yet cannot be separated. We may think of a hadron as a bubble within which quarks are imprisoned. Within the bubble the quarks move freely, but they cannot escape from it. The bubbles, of course, are only a metaphor for the dynamical behavior of the force between quarks, and a fuller explanation for what is known as quark confinement can come only from an examination of the forces through which particles interact.
The Fundamental Interactions
Nature contrives enormous complexity of structure and dynamics from the six leptons and six quarks now thought to be the fundamental constituents of matter. Four forces govern their relations: electromagnetism, gravity and the strong and weak forces. In the larger world we experience directly, a force can be defined as an agent that alters the velocity of a body by changing its speed or direction. In the realm of elementary particles, where quantum mechanics and relativity replace the Newtonian mechanics of the larger world, a more comprehensive notion of force is in order, and with it a more general term, interaction. An interaction can cause changes of energy, momentum or kind to occur among several colliding particles; an interaction can also affect a particle in isolation, in a spontaneous decay process.
Only gravity has not been studied at the scale on which elementary particles exist; its effects on such minute masses are so small that they can safely be ignored. Physicists have attempted with considerable success to predict the behavior of the other three interactions through mathematical descriptions known as gauge theories.
The notion of symmetry is central to gauge theories;. A symmetry, in the mathematical sense, arises when the solutions to a set of equations remain the same even though a characteristic of the system they describe is altered. If a mathematical theory remains valid when a characteristic of the system is changed by an identical amount at every point in space, it can be said that the equations display a global symmetry with respect to that characteristic. If the characteristic can be altered independently at every point in space and the theory is still valid, its equations display local symmetry with respect to the characteristic.
Excerpted from The Higgs Boson by Scientific American. Copyright © 2012 Scientific American, a division of Nature America, Inc.. Excerpted by permission of Scientific American Inc..
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