Asymptotic freedom: From paradox to paradigm
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Fig. 1.A photograph from the L3 collaboration, showing three jets emerging from electron–positron annihilation at high energy. These jets are the materialization of a quark, antiquark, and gluon. (Reprinted with permission of the L3 Collaboration.)
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Fig. 2.These Feynman graphs are schematic representations of the fundamental processes in electron–positron annihilation, as they take place in space and time. They show the origin of two-jet and three-jet events.
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Fig. 3.Many quite different experiments, performed at different energies, have been successfully analyzed by using QCD. Each fits a large quantity of data to a single parameter, the strong coupling αs. By comparing the values they report, we obtain direct confirmation that the coupling evolves as predicted. (Figure courtesy S. Bethke, ref. 8.)
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Fig. 4.Comparison of observed hadron masses to the energy spectrum predicted by QCD, upon direct numerical integration of the equations, exploiting immense computer power. The small remaining discrepancies are consistent with what is expected given the approximations that were necessary to make the calculation practical. (Figure reprinted with permission from the Center for Computational Physics, University of Tsukuba, Tsukuba, Japan.)
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Fig. 5.A snapshot of spontaneous quantum fluctuations in the gluon fields. For experts: what is shown is the topological charge density in a typical contribution to the functional integral, with high-frequency modes filtered out. (Image courtesy of Derek B. Leinweber, CSSM, University of Adelaide, Adelaide, Australia; www.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/Nobel.)
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Fig. 6.The calculated net distribution of field energy caused by injecting and removing a quark–antiquark pair. By calculating the energy in these fields and the energy in analogous fields produced by other disturbances, we predict the masses of hadrons. In a profound sense, these fields are the hadrons. (Figure courtesy of G. Kilcup.)
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Fig. 7.A picture of particle tracks emerging from the collision of two gold ions at high energy. The resulting fireball and its subsequent expansion recreate, on a small scale and briefly, physical conditions that last occurred during the Big Bang. (Figure courtesy of Brookhaven National Laboratory–Star Collaboration.)
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Fig. 8.A schematic representation of the symmetry structure of the standard model. There are three independent symmetry transformations, under which the known fermions fall into five independent units (or fifteen, after threefold family repetition). The color gauge group SU(3) of QCD acts horizontally, the weak interaction gauge group SU(2) acts vertically, and the hypercharge U(1) acts with the relative strengths indicated by the subscripts. Right-handed neutrinos do not participate in any of these symmetries.
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Fig. 9.The hypothetical enlarged symmetry SO(10) [unification based on SO(10) symmetry was first outlined in ref. 7] accommodates all of the symmetries of the standard model, and more, into a unified mathematical structure. The fermions, including a right-handed neutrino that plays an important role in understanding observed neutrino phenomena, now form an irreducible unit (neglecting family repetition). The allowed color charges, both strong and weak, form a perfect match to what is observed. The phenomenologically required hypercharges, which appear so peculiar in the standard model, are now theoretically determined by the color and weak charges, according to the formula displayed.
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Fig. 10.We can test the hypothesis that the disparate coupling strengths of the different gauge interactions derive a common value at short distances by doing calculations to take into account the effect of virtual particle clouds (9). These are the same sort of calculations that go into Fig. 3, but extrapolated to much higher energies, or equivalently shorter distances. (Upper) Extrapolated by using known virtual particles. (Lower) Including also the virtual particles required by low-energy supersymmetry (10).
