Leptons and the Weak Interaction

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

Field of study: Systematics (particle physics)

The elementary particles that are the fundamental constituents of matter include six leptons, which interact by the weak force associated with radioactivity. There are three charged leptons (the electron, muon, and tauon), each of which has an associated neutrino.

Overview

The first subatomic particle to be discovered was the electron, which has been classified as one of six elementary particles known as leptons. The word "lepton" comes from the Greek for "light one," since the first four leptons to be discovered had less mass than the proton. The electron was discovered by Sir Joseph John Thomson in 1897 from his analysis of cathode rays emanating from the negative electrode (cathode) of a vacuum tube. By deflecting the cathode rays with electric and magnetic fields, Thomson showed that they consisted of identical particles with a negative charge and a mass whose ratio could be measured. In 1908, Robert Andrews Millikan measured the charge of electrons on oil drops suspended in an electric field and found a constant negative value now designated by e. From this value and the charge-to-mass ration (e:m), the mass of the electron was found to be 1,846 times less than the mass of the proton, with equal but opposite charge (+e).

Radioactivity was discovered in 1896 by Antoine-Henri Becquerel. This spontaneous and continuous radiation from various heavy elements was eventually related to a unique force called the weak interaction, as compared to the electromagnetic force between charged particles. In 1898, Ernest Rutherford showed that one component of radioactivity could be absorbed by a single piece of paper, while another was about one hundred times more penetrating. The short-range "alpha rays" were later identified as helium ions (nuclei). The more penetrating "beta rays" were studied by Becquerel, who showed in 1899 that their deflection in a magnetic field was consistent with the behavior of high-speed electrons with a variety of energies. By contrast, alpha particles were emitted from a given element with a single energy.

The spontaneous energy associated with radioactivity seemed to contradict the law of conservation of energy. This problem was partially resolved by Albert Einstein in 1905, who showed that radioactive energy could be accounted for by a decrease in mass multiplied by the speed of light squared (E = mc²). The energy of alpha particles was found to agree closely with this change in mass, but beta particles did not fit as well. The continuous beta-energy spectrum was found to vary over a range of values up to a maximum that did correspond to the decrease in mass. In 1931, Niels Bohr suggested that energy conservation might not apply to beta decay. In the same year, Wolfgang Pauli suggested that conservation would apply if beta-decay electrons were accompanied by a neutral particle too small to be observed, which would carry the missing energy as well as spin and recoil momentum needed for the conservation of these components of motion.

Enrico Fermi called Pauli's light neutral particle the neutrino (Italian diminutive for neutral particle) to distinguish it from the neutron, which was discovered by Sir James Chadwick in 1932 and shown to have a mass slightly greater than the proton. In 1934, Fermi developed a quantitative theory for the role of the neutrino (υ) in beta decay. He used an approach similar to one developed by Paul Adrien Maurice Dirac to explain electromagnetic forces, which had led to the concept of antimatter and the discovery of the positron (antielectron e+) in simultaneous pair-creation with an electron. Fermi postulated the pair-creation of an electron and an antineutrino (ῡ) when a neutron converts into a proton during beta decay (n → p⁺ + e^- + ῡ). He was able to account for the beta-decay half-life and the measured electron energy distribution by introducing a new "weak" force, much weaker than electromagnetism, interacting with the particles at the point where the neutron decayed into a proton, electron, and antineutrino. The upper limit of beta energies implied that the neutrino would have near-zero rest mass, permitting it to travel at or near the speed of light. In the theory, both energy and momentum were conserved if the neutrino carried both energy and a half-unit of spin, in contrast with one unit of spin for the photon associated with light and other electromagnetic waves.

Although Fermi's theory worked well at most energies, it failed at the high-energy limit because it assumed zero range for the weak force. In 1935, Hideki Yukawa proposed a similar theory which applied to both the weak force of radioactivity and the strong nuclear force that binds protons and neutrons together in the nucleus of the atom. In Yukawa's theory, the strong and weak forces had a finite range and were mediated by exchange particles similar to the photon exchange postulated by Dirac in electromagnetic interactions. He calculated that the exchange particle for the strong force (the meson) would have a mass larger than 200 electron masses, and the exchange particles for the shorter range weak force (W+ and W- particles) would be even more massive. For Yukawa, the neutron would change into a proton by emitting a W-particle, which would decay into an electron and an antineutrino.

In 1937, a 207-electron-mass particle called the muon μ was discovered in cloud-chamber studies of cosmic rays from outer space. At first the muon seemed to confirm Yukawa's meson prediction, but Fermi and his associates soon showed that it easily penetrated matter, and thus interacted by the weak force rather than the strong force. The muon appeared to have all the properties of the electron (charge e and spin 1/2) except for its large mass and short lifetime, and thus was classified with the electron and the neutrino as a lepton. It was found to have a mean life of about two microseconds before decaying into one electron and at least two neutrinos for the conservation of both energy and spin (μ⁺ → e⁺ + υ + ῡ or μ^- → e^- + υ + ῡ). In 1947, a 273-electron-mass particle was discovered, which matched Yukawa's meson--zero spin, now called the pion (π)--and decayed in about three-hundredths of a microsecond into a muon plus a presumed neutrino (π⁺ → μ⁺ + υ or π^- → μ^- + ῡ)

In 1953, Clyde L. Cowan and Frederick Reines obtained the first experimental evidence for the existence of the neutrino. They used a reversal of neutron decay, in which an antineutrino would interact with a proton to produce a neutron and positron (ῡ + p → n + e⁺). Because of the weakness of neutrino interactions, they placed their target and counting apparatus near a nuclear reactor at Savannah River in South Carolina, where enough antineutrinos were produced (10 to the power of 18 per second) as a by-product of fission to get a neutron-positron event about once every twenty minutes. The positron will quickly annihilate with an atomic electron and emit two energetic photons, while the neutron would soon be slowed and absorbed by a cadmium solution causing a characteristic photon emission. Thus, the unique signal of an antineutrino-proton interaction would be two photons from electron-positron annihilation followed in a few microseconds by a cadmium photon emission. By 1956, such events were observed at the expected rate, confirming the existence of the elusive neutrino.

The existence of two distinct neutrinos was established in 1962 by Leon M. Lederman and his Columbia University associates at Brookhaven National Laboratory, where a large particle accelerator was used to produce high-energy neutrinos. The idea of two neutrino species, one associated with the electron (υ_e) and one with the muon (υ_μ), was introduced to explain why muon decay into an electron and photon was never observed, even though it seemed to be a valid electromagnetic transition. Thus, neutron decay producing an electron must be accompanied by an electron-type antineutrino (n → p + e^- + ῡ^e), pion decay into a muon involves a muon-type neutrino (π⁺→μ⁺ + υ_μ)and muon decay into an electron must include both a mu-neutrino and an electron antineutrino (μ^-; → ē^- + ῡ_e + υ_μ). Yet, muon decay into an electron and a photon would not involve the required neutrinos, so it would be forbidden. Lederman was able to produce pions in the accelerator and then absorb the resulting muons in a thick shield, leaving a pure neutrino beam. He found that these assumed mu-neutrinos would interact with neutrons to produce only muons and protons (υ_μ + n → μ^- + p) but not electrons, which would apparently have required electron neutrinos (υ_e + n → e^- + p). In twenty-five days of accelerator time, fifty-one muons and no electrons were observed in a spark-chamber detector, giving evidence of two distinct neutrino types.

A new lepton, named the tauon, was discovered in 1975 from the study of electron-positron collisions at the Stanford Linear Accelerator Center (SLAC) by Martin Perl and a team of thirty-five collaborators. At high energies corresponding to twice the muon mass, such collisions can produce muon-antimuon pairs (e⁺ + e^- → μ^τ + μ^-) from mutual annihilation and pair-creation processes. At much higher energies, Perl and his associates observed anomalous muon-electron production from electron-positron collisions. Some sixty-four of these events were seen, contrary to conventional pair-creation processes. Perl's suggestion was that the muon and electron might result from the production of a new pair of heavy leptons, the tauon and antitauon (e⁺ + e^- → τ⁺ + τ^-), followed by the decay of the tauon into an electron (τ^- → e^- + ῡ_e + υ_τ) and the antitauon into a muon (τ⁺ → μ⁺ + υ_μ + ῡ_τ), or vice versa. After excluding a number of background events, this interpretation was confirmed at a threshold energy that gave a mass of about 3,500 electron masses. The energy spectrum for the electrons and muons was consistent with the existence of associated tau-neutrinos. The lifetime of the tauon was measured at less than one-millionth of a microsecond (5 x 10^-13 seconds).

Applications

The discovery and subsequent study of leptons and their weak interactions have led to new understanding of the behavior and organizing principles of particles and forces. Elementary particles can be classified by their interactions and by various conservation laws. All charged particles interact by the electromagnetic force in a way that conserves electric charge. The six leptons interact by the weak force, but none is affected by the strong nuclear force and the three neutrinos are unaffected by the electromagnetic force.

In 1953, a lepton conservation was suggested to account for observed and forbidden decay processes. By assigning a lepton number of +1 to the negatively charged leptons and their neutrinos, a lepton number of -1 to their antiparticles (positively charged leptons and antineutrinos), and a lepton number of zero to all other particles, the sum of lepton numbers in any observed reaction is unchanged. Thus, the beta decay of the neutron (n → p + e^- + ῡ_e) begins with lepton number zero and ends with 0 + 1 - 1 = 0, while muon decay (μ^- → e^- + ῡ_e + ν_μ) begins with lepton number +1 and ends with +1 - 1 + 1 = +1. Furthermore, each type of lepton must be conserved separately. Thus, in muon decay, both muon number (1 = 0 + 0 + 1) and electron number (0 = 1 -1 + 0) are conserved.

The physical significance of lepton conservation is evident from the absence of reactions that otherwise seem feasible. For example, antineutrino-proton interactions do produce positrons and neutrons (ῡ_e + p → e⁺ + n) in which the lepton number is conserved (-1 + 0 = -1 + 0). Yet, antineutrino-neutron interactions, which might seem likely to produce electrons and protons (ῡ_e + p → e^- + p?), do not conserve the lepton number (-1 + 0 is not equal to +1 + 0) and are not observed. Lepton conservation also implies a connection between charged leptons and their neutrinos, adding support for the existence of the tau-neutrino.

In 1956, Tsung-Dao Lee and Chen Ning Yang predicted that weak interactions would not conserve the usual reflection symmetry called parity. This means that, unlike other processes, weak interactions would behave differently from their mirror images. This idea was confirmed in 1956 by Chien-Shiung Wu in a cobalt beta-decay experiment, in which the emitted electrons had a preferential spin orientation relative to the nuclear spin, consistent with the prediction of Lee and Yang. An experiment in 1958 confirmed the nonconservation of parity by showing that all neutrinos have a left-handed helicity in which their spin is that of a left-handed screw in relation to their motion, and all antineutrinos have a right-handed helicity.

One of the most important applications of leptons is the use of their pointlike structure and lack of strong interactions to probe the internal structure of protons, neutrons, and other heavy particles (baryons). Electron and neutrino scattering experiments since 1967 have confirmed the composite nature of these particles, which was first proposed in the quark theory of Murray Gell-Mann in 1964. He was able to account for the properties of elementary particles by a bound combination of three quarks in baryons or a quark-antiquark pair in mesons (the exchange particles that transmit the strong force in the nucleus). The quarks are pointlike particles with -1/3 or +2/3 of the electron charge e. At first, only three types of quarks were required and were named "up" (u), "down" (d), and "strange" (s).

Efforts to develop a unified theory of electromagnetic and weak interactions were begun in 1961 by Sheldon L. Glashow, leading to a successful electroweak theory by Steven Weinberg in 1967 and by Abdus Salam in 1968. This generalization of the earlier theories of Dirac, Fermi, and Yukawa predicted the masses of the W+ and W- exchange particles for weak interactions, plus the existence and mass of an unanticipated neutral exchange particle designated as Z to the power of 0. The symmetry of the W+ and W- particles in the theory is related to similar symmetries between the electron and its neutrino, and between the up and down quarks, allowing W emission or absorption in interactions between these particles. The possible interactions of the Z to the power of 0 particle with the three original quarks, however, would permit the transition of an s-quark into a d-quark in violation of experimental evidence to the contrary. A solution to this problem was the 1970 proposal of a fourth quark named "charm" (c) linked by symmetry theory to the s-quark, which would cancel any transitions from s-quark to d-quark. Discovery of the c-quark in 1974 was a success for the electroweak theory, which also links the s- and c-quarks to the muon and its neutrino in the same way that u- and d-quarks are linked to the electron and its neutrino.

Discovery of the c-quark stimulated the search for further new quarks, especially since the analogy between the two quark doublets (u,d and s,c) and the two lepton doubles ((e, ν_e, and μ, ῡ[sub μ)) suggested a third quark doublet in analogy to the third lepton doublet (tau, nu sub tau). The first member of the third quark generation was discovered from proton-collision experiments at the Fermilab accelerator in 1977, and was designated the b-quark ("bottom" or "beauty"). The W+, W-, and Z to the power of 0 particles were discovered in 1983, with their predicted masses of about 85 and 97 proton masses. They decay rapidly into all possible lepton-antilepton and quark-antiquark pairs. Further study of Z to the power of 0 particle interactions (neutral current processes) has led to a predicted mass for the remaining member of the third quark doublet, called the t-quark ("top" or "truth"), of up to 200 proton masses. The b- and t-quarks complete the third-generation symmetry with the tauon and the tau-neutrino leptons.

Context

The study of leptons and their interactions has helped to establish the fundamental ingredients of matter and contributes to an understanding of the large-scale structure of the universe. Ordinary matter consists of two leptons (electron and electron neutrino) that can exist alone, two quarks (up and down) that can exist only in bound states of two or three, and the exchange particles that mediate the forces between these particles. A second, heavier family of leptons (muon and mu-neutrino) and of quarks (charmed and strange), plus a third and heaviest family of leptons (tauon and tau-neutrino) and of quarks (top and bottom), make up the more exotic forms of matter that are found in high-energy collisions and existed in the early moments after the big bang (the origin of the universe).

Leptons interact by weak and electromagnetic forces that have been unified in the electroweak theory. This theory explains these interactions by exchange particles such as the W+, W-, Z to the power of 0, and photon. Studies at Stanford University in 1989 of the precise range of electron-positron collision energies that create Z₀ particles led to the conclusion that the three generations of particles identified thus far are very likely the only families that can exist in nature. Some physicists have calculated odds of about twenty-five to one against their being additional families. Thus, matter seems to be limited to only three generations consisting of six leptons, six quarks, several types of exchange particles, and their corresponding antiparticles. Theoretical efforts to unify the strong and electroweak forces seek to produce a grand unified theory (GUT). Theory suggests that, at the high temperatures immediately after the big bang, these distinct forces existed as a single unified force that separated as the universe expanded and cooled.

The large-scale structure of the universe is affected by leptons in several ways that are still not completely understood. Electron-neutrino scattering processes account for energy transfer from the interiors of stars to their outer layers. The gravitational collapse of a massive red giant star into a neutron star produces a supernova explosion that can be brighter than an entire galaxy. Theory shows, however, that most of its energy is released in the form of neutrinos, as first confirmed by observations in 1987. Theoretical calculations of neutrinos produced by nuclear reactions in the sun exceed the rate measured by detectors on the earth by a factor of about two. One suggested solution to this solar neutrino problem is the idea that some electron neutrinos might be converted into muon neutrinos by interactions with electrons in the sun. Since detectors are usually designed for electron neutrinos, they would fail to detect any muon neutrinos resulting from such neutrino oscillations.

Neutrino oscillations from one type to another would require that they have a small but nonzero mass. The huge number of neutrinos in the universe, including a fossil-neutrino background spread throughout space by the big bang creation of the universe, might constitute enough unobserved mass eventually to slow down its expansion and cause a gravitational collapse of the entire universe. Thus, the elusive neutrinos that seem to have such slight effects on matter might decide the final state of the universe.

Principal terms:

ANTIPARTICLE: a particle with the same mass and spin (intrinsic rotation in quantum units) as an elementary particle, but with opposite charge and magnetic moment

ELECTRON: a stable elementary particle (lepton), which is the negatively charged constituent of ordinary matter and the antiparticle of the positron

LEPTON: a class of six elementary particles with half-units of spin, which have pointlike behavior and are not affected by the strong nuclear force

NEUTRINO: a stable uncharged lepton that has a zero or near-zero rest mass, interacts by the weak force, and has a left-handed spin relative to its motion at or near the speed of light

MUON: a charged lepton with a mass about 207 times the electron mass, which decays into an electron and two neutrinos

QUARK: a class of six component elementary particles with -1/3 or +2/3 of the electron charge, which make up protons, neutrons, and other strongly interacting particles in groups of two or three

TAUON: a charged lepton with a mass about thirty-five hundred times the electron mass, which decays into a tau-neutrino plus either a muon and mu-neutrino or an electron and electron neutrino

WEAK FORCE: of the four fundamental forces, the one with the shortest range; it is responsible for radioactivity and is weaker than electromagnetic or nuclear forces but stronger than the gravitational force

Bibliography

Carrigan, Richard A., and W. Peter Trower, eds. PARTICLES AND FORCES: AT THE HEART OF MATTER. New York: W. H. Freeman, 1990. This set of twelve articles from SCIENTIFIC AMERICAN was published between 1975 and 1986. The authors include the leading investigators in the field of elementary particle physics, who discuss some of the most important theories and discoveries in nontechnical language.

Dodd, J. E. THE IDEAS OF PARTICLE PHYSICS: AN INTRODUCTION FOR SCIENTISTS. New York: Cambridge University Press, 1984. This book gives basic equations, but much can be understood by the general reader. Contains several short chapters on weak interactions and lepton physics. Good diagrams, graphs, and a glossary add to its value.

Feinberg, Gerald. WHAT IS THE WORLD MADE OF? Garden City, N.Y.: Anchor Press, 1978. A popularized account of elementary particle physics. It is both readable and authoritative, with good chapters on particles, weak interactions, and symmetry principles. Some diagrams, a glossary, and an index are included.

Hughes, I. S. ELEMENTARY PARTICLES. 2d ed. New York: Cambridge University Press, 1985. This undergraduate college text discusses particle physics developments from 1950 to 1985. Mathematical equations are used, but no lengthy derivations. About five chapters discuss conservation laws, leptons, and weak interactions with diagrams.

Trefil, James S. FROM ATOMS TO QUARKS. New York: Charles Scribner's Sons, 1980. A very readable introduction to particle physics with several chapters on particle discoveries and interactions. Many diagrams and a glossary are included, but no index.

Grand Unified Theories and Supersymmetry

Group Theory and Elementary Particles

Nuclear Synthesis in Stars

Quarks and the Strong Interaction

The Unification of the Weak and Electromagnetic Interaction