Unification Of The Weak And Electromagnetic Interactions

Type of physical science: Elementary particle (high-energy) physics

Field of study: Unified theories

The electroweak theory unifies the forces that govern the weak and electromagnetic interactions between elementary particles. This theory also successfully predicts the existence and properties of the particles that transmit the weak force.

Overview

The unified electroweak theory of electromagnetic and weak forces was begun by Sheldon L. Glashow in 1961 and was completed independently by Steven Weinberg in 1967 and Abdus Salam in 1968, for which all three received the 1979 Nobel Prize in Physics. Together with the more tentative theory of the strong nuclear force, the unified electroweak theory has been remarkably successful in describing elementary particles and their interactions on scales as small as one-thousandth of the size of the atomic nucleus, the smallest distance probed by particle accelerators. The electroweak theory is a quantum-field theory in which particles interact by means of a field that carries quantum (discrete) units of energy and momentum through space by the exchange of other particles called bosons. It represents the merger of quantum electrodynamics (QED) and quantum weak dynamics, in much the same way that James Clerk Maxwell's electromagnetic theory merged classical electricity and magnetism in the nineteenth century.

Like Maxwell's electromagnetic theory, the electroweak theory is a gauge theory in which the equations describing physical processes remain unchanged in form by certain symmetry transformations. The equations for interacting particles can be made gauge-invariant by adding new terms, which correspond to new particles (bosons) that mediate interactions between the original particles. In the equation describing how electric current produces magnetic fields (Ampere's law), Maxwell added a term representing a changing electric field to ensure the local conservation of charge, thus making the equations linking electric and magnetic fields gauge-symmetric. When these equations were combined, they led to the prediction of electromagnetic waves (the basis for all of optics), identified later with photons, the bosons that mediate electromagnetic forces.

By 1930, QED had been formulated by Paul Adrien Maurice Dirac (1902–84) and refined by Werner Heisenberg (1901–76) and Wolfgang Pauli (1900–1958). This theory combined classical electromagnetic theory with special relativity and quantum mechanics, yielding the first successful quantum-field theory. In it, electromagnetic interactions between charged particles are mediated by the emission and absorption of photons, the quantum unit of the field. The theory also predicted the existence of antiparticles such as the positron (positive electron), which would be produced along with an electron from radiation of sufficiently high energy (consistent with E = mc²) and would annihilate itself and the electron back into radiation if they came together again.

Because this early version of QED treated the electron as a point charge, it had infinite charge density and thus infinite interaction energy with its own radiation field, giving it infinite mass. By the late 1940s, Shin'ichiro Tomonaga, Richard P. Feynman, and Julian Schwinger had independently shown how these infinities could be avoided by incorporating corrections into Dirac's equations for charge and mass and then substituting measured values for these quantities. This "renormalization" of QED was possible because of the gauge symmetry of Dirac's equation, giving an incredible precision of about one part in a billion when accounting for phenomena such as the hyperfine splitting of hydrogen spectrum lines and magnetic moments of the hydrogen atom.

Weak interactions were first identified in 1934 by Enrico Fermi (1901–54) in his theory of radioactive β (beta) decay, or electron emission, such as the decay of neutrons into protons and electrons. When the emitted electrons were found to have a continuous distribution of energies, always less than what was needed for conservation of energy, Pauli suggested that the missing energy might be carried off by unobserved neutral particles with little or no mass. Fermi named this supposed particle the neutrino and incorporated it into a quantum-field theory of beta decay patterned after QED. He was able to account for the electron energy distribution by introducing a new force, much weaker than electromagnetism, acting on the particles at the point where the neutron decayed into a proton, electron, and neutrino.

Although Fermi's theory worked well at most energies, it failed at its high-energy limit because it assumed zero range for the weak force. In 1935, Hideki Yukawa proposed a quantum field for both strong and weak forces in which the weak force was mediated by the exchange of charged bosons (W⁺ and W^-, each with one unit of electron charge) rather than acting at a point. Neutrons would change into protons by emitting a W^-, which would then decay into an electron and a neutrino. His theory predicted a mass for bosons that was inversely proportional to the range of the forces they mediate. Thus, photons have zero mass since electromagnetic forces have infinite range, but W bosons are massive because of the short range of the weak force.

After the discovery of the neutrino in 1953 and the violation of parity (the weak force behaves differently from its mirror image) in 1956, weak-interaction theory was generalized by Feynman, Schwinger, and Murray Gell-Mann in 1958. It was then applied to more complicated processes, such as neutron-neutrino scattering, in which boson pairs are exchanged, leading to infinities that could not be renormalized. The problem was compounded by the fact that, unlike the massless photon, massive bosons break the gauge invariance of the field equations for the weak force, which is the symmetry needed for renormalization. Thus, the quantum-field theory for massive vector bosons gave a good first approximation for weak interactions in processes such as beta decay, but it broke down when it was applied to more complicated processes requiring higher approximations.

The first attempt to unify electromagnetic and weak interactions was made by Glashow in 1961. He set up an electroweak gauge theory by combining the QED gauge symmetry (the unitary U group) with a rotation-type symmetry (the special unitary SU group) for the weak force to obtain a natural unification of weak and electromagnetic interactions based on the combined symmetry (the SU(2) x U(1) group). This led to the requirement of four bosons: the photon, the charged vector bosons W⁺ and W^-, and an unanticipated neutral vector boson, Z⁰. The symmetry of W⁺ and W^- is related to similar symmetries between the electron and its associated neutrino and between the proton and the neutron (or their up and down quarks, u and d), allowing W emission or absorption in transitions between these particles. Unfortunately, this form of the electroweak theory required massless bosons for gauge symmetry and thus did not allow for the masses required by the short range of the weak force.

The problem of vector-boson masses was first solved in 1967 by Weinberg, who was then able to complete the formulation of a successful electroweak theory. He applied an idea suggested by Peter Higgs in 1964 called spontaneous symmetry breaking. Higgs showed that the lowest energy solution (ground state) of a gauge theory may have less symmetry than the equations of motion and that this asymmetry can be compensated for by a new field. Weinberg introduced this Higgs field to restore the symmetry of the weak interactions, and he found that the W and Z bosons can acquire mass by coupling to this field. The success of this Higgs mechanism suggested the existence of a fifth force in nature and its exchange particle, called the Higgs boson. In the resulting unified electroweak theory, the W and Z boson masses can be calculated in the terms of the measured strengths of the weak and electromagnetic interactions and a mixing angle relating them (M_W = M_Zcosθ_W). This Weinberg angle can be measured in many different experiments and is an important test of the theory.

The unified electroweak theory attracted more attention after 1972, when Gerard 't Hooft and Martinus Veltman proved that the theory was renormalizable, even with the spontaneous symmetry breaking that gave large masses to the W and Z bosons. It was found that the various multiparticle exchanges of photons, bosons, and other particles add up so as to cancel unresolved infinities. The unanticipated Z⁰ particle also suggested the possibility of previously unknown neutral-current processes in which weak interactions between particles might be mediated by the Z⁰ without any change in charge of the particles. The observation of neutral-current interactions with accelerators at the European Organization for Nuclear Research (CERN) in Geneva and at Fermilab near Chicago in 1973 provided direct evidence to support the theory.

One remaining problem was the possible interaction of Z⁰ with the three quarks known at the time—u, d, and s (strange)—which would permit the neutral-current transition of a strange quark into a down quark, both with a charge of -1/3e, in violation of experimental evidence. A solution to this problem was the 1970 proposal of a fourth quark, c (charm), linked to the strange quark, which would cancel any transitions from strange to down quarks. Discovery of the charm quark in 1974 was a further success for the electroweak theory. Another triumph was the 1983 discovery of the W and Z particles with their predicted masses.

The existence of the Higgs boson, and thus the associated Higgs field, remained entirely theoretical until 2012, when researchers at CERN announced the experimental discovery of a previously unknown boson they believed to be the Higgs boson. Its identity was tentatively confirmed in March 2013, thus proving, or at least supporting, the existence of a Higgs field throughout space that lends the W and Z particles their mass.

Applications

The existence of neutral currents and the discovery of the W and Z particles gave substance to the electroweak theory. Subsequent quantitative tests of the theory and experimental discoveries have established its basic validity and the underlying unity of the electromagnetic and weak interactions.

During the 1970s, continuing neutral-current (Z⁰ exchange) research concentrated on measuring the Weinberg angle in neutrino-scattering experiments, which produced remarkably consistent results. Inelastic (multiparticle) scattering from target nuclei of energetic neutrinos produced by the decay of muons (heavy electrons) in high-energy accelerator reactions usually results in charged-current events producing charged muons. The neutral-current signature is the absence of muons in such inelastic neutrino-scattering experiments. The ratio of neutral-current to charged-current events gave the first values for the Weinberg angle. Elastic neutrino-electron scattering, which produces no new particles, allows a much cleaner test of the electroweak theory, since it requires no corrections for the strong nuclear force. The ratio of neutrino-electron scattering angles to antineutrino-electron scattering angles gave the same value for the Weinberg angle within the limits of experimental error.

The neutral-current measurements of the Weinberg angle, confirmed by several other types of experiments, led to predictions for the masses of the W and Z particles in the range of eighty-five to one hundred times the mass of the proton. The equivalent energy to produce these particles was far beyond the range of particle accelerators in the early 1980s. In 1982, Carlo Rubbia, Simon van der Meer, and their CERN colleagues recognized that the fixed-target Super Proton Synchrotron (SPS) could be converted to a colliding-beam storage ring with more than a twentyfold increase in the collision energy. This produced more than enough energy to create the predicted heavy bosons from proton-antiproton collisions. In 1983, the researchers found all three of the vector bosons predicted by the electroweak theory, for which Rubbia and van der Meer received the 1984 Nobel Prize in Physics.

The measured masses of the W and Z particles are eighty-five proton masses and ninety-seven proton masses respectively, giving a value for the Weinberg angle that agrees with neutral-current and other measurements. This gives a range for the weak force of about one-thousandth of the size of the atomic nucleus. The W and Z bosons decay rapidly into all possible lepton-antilepton and quark-antiquark pairs. They were detected in the SPS collider at CERN from the W-decay into electrons and neutrinos and the Z-decay into electrons and positrons.

Precise measurements of the Z⁰ mass and its coupling to leptons and quarks are important not only to test the electroweak theory itself but also to check higher-order corrections of the theory induced by other heavy particles. Because it is a gauge theory, these corrections are not infinite and can be calculated. One such correction made prior to 1995 showed that boson masses depend on the mass of the then-undiscovered top quark, which is required to complete the heaviest of the three quark families. The electroweak theory links the up and down quarks to the electron and its neutrino, the strange and charm quarks to the muon and its neutrino, and the bottom and top quarks to the τ (tau) lepton, which is heavier than the muon, and its neutrino. Neutral-current and boson-mass data predicted an upper limit of about 200 proton masses for the mass of the top quark, while experiments set a lower limit of about 85 proton masses. When the top quark was finally discovered in 1995, its mass was revealed to be approximately 180 proton masses.

Context

The success of the electroweak theory is the first step toward a theoretical unification of the fundamental forces of nature and their associated elementary particles. The theory has already contributed to the organization of these particles into family groups, linking the three lepton doublets with the three quark doublets by group symmetry and shedding new light on the charm and top quarks. The theory may also account for the small differences in mass of strongly interacting particles in family groups, such as the proton and neutron, which lead to infinities from electromagnetic corrections to calculations of the strong nuclear force. Because the intrinsic strengths of electromagnetic and weak forces are similar, they may provide additional corrections that cancel these infinities.

The next major step would be a grand unification of the strong and electroweak forces in a unified gauge-symmetric field theory. Experiments at CERN and at the Deutsches Elektronen-Synchrotron (DESY) in Germany in the 1990s confirmed the 1973 proposal by David Gross, David Politzer, and Frank Wilczek that the strong force exhibits asymptotic freedom, meaning that the strength of the interaction between quarks decreases at high energies and short distances. As a result, quarks cannot exist singly but must group together to form ordinary particles—a phenomenon called color confinement, because the quarks are permanently confined within the particles they constitute. Taking this into account, grand unification theories (GUTs) suggest that the intrinsic strength of strong interactions is comparable with that of electroweak interactions, only appearing stronger because of the relatively low energies and large distances at which the strong force must be observed. At a high enough energy level, known as the grand unification energy, the strong, electromagnetic, and weak forces would converge to a single unified force. The ultimate goal would be to include the force of gravity in this type of unification, which would change it from a GUT to a "theory of everything" (TOE), but this would appear to require a quantum theory of general relativity that has yet to be achieved.

Unified-force theories contribute to an understanding of astrophysics and cosmology. Supernova explosions of giant stars begin with an implosion (collapse), which then reverses and becomes an explosion. Neutrino pressure can account for this reversal, but only because of the electroweak neutral currents that produce coherent neutrino interactions with entire nuclei rather than with individual neutrons and protons. Such theories also cast light on what took place during the earliest fractions of a second after the creation of the universe, as described by the big bang theory, which postulates that the universe began as an expanding fireball from an initial point of infinite energy density. As the temperature fell in the expansion, first gravitation and then the strong force separated from an original single unified force. This was followed by the inflationary epoch, which ended with the creation of a quark-gluon plasma. Next, the electroweak force separated into the electromagnetic and weak forces, and a large number of exotic particles were created, including massive bosons. As the universe expanded and energy decreased, these bosons quickly decayed. When energy levels decreased enough for color confinement to become a factor, the quarks in the quark-gluon plasma began to combine to form particles, including protons and neutrons. Expansion continued until energies were low enough for electromagnetic forces to bind electrons to protons and for gravity to form stars and galaxies. Radiation and elementary particles left over from the big bang may provide the evidence needed to develop a completely unified theory of forces.

Principal terms

ANTIPARTICLE: an elementary particle with the same mass and spin as another particle but with opposite charge and magnetic moment; a particle and its antiparticle annihilate into radiation when they come together

BOSONS: elementary particles that have integral spin values and mediate forces between other particles; vector bosons have a spin value of 1

GAUGE THEORIES: theories for the fundamental forces whose equations remain unchanged in form by certain symmetry transformations at any point in space and time

LEPTONS: elementary particles that have half-integral spin values and are not affected by the strong nuclear force; includes electrons, muons, and neutrinos and their antiparticles

NEUTRAL CURRENT PROCESS: a weak interaction mediated by the neutral vector boson (Z⁰) that leaves the charge of the interacting particles unchanged

PHOTONS: quantum units of light and other radiation that mediate electromagnetic forces between charged particles

QUARKS: component particles with one-third or two-thirds of the electron charge that join in groups of two or three to form mesons and baryons

STRONG FORCE: the strongest of the fundamental forces in nature, responsible for binding the atomic nucleus together through the mediation of mesons

WEAK FORCE: the shortest-range fundamental interaction between elementary particles, mediated by charged W⁺ and W^- bosons and neutral Z⁰ bosons; responsible for radioactivity

Bibliography

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Eisberg, Robert M., and Robert Resnick. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. 2nd ed. New York: Wiley, 1985. Print. This intermediate-level college physics textbook has good sections on beta decay, Enrico Fermi's theory of weak interactions, quantum electrodynamics (QED), and the electroweak theory. Theoretical results are discussed with equations, graphs, and diagrams, but without lengthy mathematical derivations.

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Langacker, Paul, and Alfred K. Mann. "The Unification of Electromagnetism with the Weak Force." Physics Today Dec. 1989: 22–31. Print. This discussion of the history of the electroweak theory has a particular emphasis on the successful experimental tests of the theory. References to original articles are also given.

Quigg, Chris. Gauge Theories of the Strong, Weak, and Electromagnetic Interactions. 2nd ed. Princeton: Princeton UP, 2013. Print.

Trefil, James S. From Atoms to Quarks. New York: Scribner's, 1980. Print. This very readable introduction to elementary particle physics has several chapters on quarks and two chapters on weak interactions and unified force theories. Many diagrams and a glossary are included, but no index.

Weinberg, Steven. "Unified Theories of Elementary-Particle Interaction." Scientific American July 1974: 50–51. Print. An excellent and readable discussion of the electroweak theory, including its background and applications. The article was written by one of the formulaters of the theory who shared the 1979 Nobel Prize in Physics for its development.

Grand Unification Theories and Supersymmetry

Group Theory and Elementary Particles

Leptons and the Weak Interaction

Quantum Elecrodynamics

Quarks and the Strong Interaction