Muon

The muon (from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with a negative electric charge and a spin of 1⁄2. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton. It is an unstable subatomic particle with the second longest mean lifetime (2.2 µs), exceeded only by that of the free neutron (~15 min). Like all elementary particles, the muon has a corresponding antiparticle of opposite charge but equal mass and spin: the antimuon (also called a positive muon). Muons are denoted by μ⁻ and antimuons by μ⁺. Muons were sometimes referred to as mu mesons in the past, even though they are not classified as mesons by modern particle physicists (see History).

Muons have a mass of 105.7 MeV/c², which is about 200 times the mass of the electrons. Since the muon's interactions are very similar to those of the electron, a muon can be thought of in most ways as simply a much heavier version of the electron. Due to their greater mass, muons aren't as sharply accelerated when they encounter electromagnetic fields, and do not emit as much bremsstrahlung radiation. For this reason, muons of a given energy penetrate matter far more deeply than electrons, since slowing of these particles in matter to capture velocities is primarily due to energy loss by this mechanism.

Secondary muons generated by cosmic rays impacting the atmosphere are capable of penetrating to the Earth's surface and farther, into deep mines.

As with the case of the other charged leptons, the muon has an associated muon neutrino. Muon neutrinos are denoted by νμ.

History

Muons were discovered by Carl D. Anderson in 1936 while he studied cosmic radiation. He had noticed particles that curved in a manner distinct from that of electrons and other known particles, when passed through a magnetic field. In particular, these new particles were negatively charged but curved to a smaller degree than electrons, but more sharply than protons, for particles of the same velocity. It was assumed that the magnitude of their negative electric charge was equal to that of the electron, and so to account for the difference in curvature, it was supposed that these particles were of intermediate mass (lying somewhere between that of an electron and that of a proton). The discovery of the muon seemed so incongruous and surprising at the time that Nobel laureate I. I. Rabi famously quipped, "Who ordered that?"

For this reason, Anderson initially called the new particle a mesotron, adopting the prefix meso- from the Greek word for "mid-". Shortly thereafter, additional particles of intermediate mass were discovered, and the more general term meson was adopted to refer to any such particle. Faced with the need to differentiate between different types of mesons, the mesotron was in 1947 renamed the mu meson (with the Greek letter μ (mu) used to approximate the sound of the Latin letter m).

However, it was soon found that the mu meson significantly differed from other mesons; for example, its decay products included a neutrino and an antineutrino, rather than just one or the other, as was observed in other mesons. Other mesons were eventually understood to be hadrons—that is, particles made of quarks—and thus subject to the residual strong force. In the quark model, a meson is composed of exactly two quarks (a quark and antiquark), unlike baryons, which are composed of three quarks. Mu mesons, however, were found to be fundamental particles (leptons) like electrons, with no quark structure. Thus, mu mesons were not mesons at all (in the new sense and use of the term meson), and so the term mu meson was abandoned, and replaced with the modern term muon.

In a 1941 experiment on Mount Washington, muons were used to observe the time dilation predicted by special relativity for the first time.[2]

Muon sources

Since the production of muons requires an available center of momentum frame energy of 105.7 MeV, neither ordinary radioactive decay events nor nuclear fission and fusion events (such as those occurring in nuclear reactors and nuclear weapons) are energetic enough to produce muons. Only nuclear fission produces single-nuclear-event energies in this range, but due to conservation constraints, muons are not produced.

On Earth, most naturally occurring muons are created by cosmic rays, which consist mostly of protons, many arriving from deep space at very high energy. A small number are created from nuclear cowes on the Earth's surface[3]

About 10,000 muons reach every square meter of the earth's surface a minute; these charged particles form as by-products of cosmic rays colliding with molecules in the upper atmosphere. Traveling at relativistic speeds, muons can penetrate tens of meters into rocks and other matter before attenuating as a result of absorption or deflection by other atoms.
— Mark Wolverton (September 2007). "Muons for Peace: New Way to Spot Hidden Nukes Gets Ready to Debut". Scientific American 297 (3): 26–28. http://www.sciam.com/article.cfm?id=muons-for-peace.

When a cosmic ray proton impacts atomic nuclei of air atoms in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (the pion's preferred decay product), and neutrinos. The muons from these high energy cosmic rays, generally continuing essentially in the same direction as the original proton, do so at very high velocities. Although their lifetime without relativistic effects would allow a half-survival distance of only about 0.66 km (660 meters) at most, the time dilation effect of special relativity allows cosmic ray secondary muons to survive the flight to the Earth's surface. Indeed, since muons are unusually penetrative of ordinary matter, like neutrinos, they are also detectable deep underground (700 meters in the illustration above) and underwater, where they form a major part of the natural background ionizing radiation. Like cosmic rays, as noted, this secondary muon radiation is also directional.

The same nuclear reaction described above (i.e., hadron-hadron impacts to produce pion beams, which then quickly decay to muon beams over short distances) is used by particle physicists to produce muon beams, such as the beam used for the muon g − 2 experiment.[4] In naturally produced muons, the very high-energy protons to begin the process are thought to originate from acceleration by electromagnetic fields over long distances between stars or galaxies, in a manner somewhat analogous to the mechanism of proton acceleration used in laboratory particle accelerators.

Muon decay
See also: Michel parameters

The most common decay of the muon

Muons are unstable elementary particles and are heavier than electrons and neutrinos but lighter than all other matter particles. They decay via the weak interaction to an electron, two neutrinos, and sometimes other particles that have a net charge of zero (i.e. a photon or a electron-positron pair). Because lepton numbers must be conserved, one of the product neutrinos must be a muon-type (anti)neutrino and the other an electron-type (anti)neutrino.

The dominant muon decay mode (sometimes called the Michel decay after Louis Michel) is the simplest possible: the muon decays to an electron, an electron-antineutrino, and a muon-neutrino. Antimuons, in mirror fashion, most often decay to the corresponding antiparticles: a positron, an electron-neutrino, and a muon-antineutrino. In formulaic terms, these two decays are:

The mean lifetime of the (positive) muon is 2.197 019 ± 0.000 021 μs[5]. The equality of the muon and anti-muon lifetimes has been established to better than one part in 104.

The tree-level muon decay width is

whereI(x) = 1 − 8x − 12x²lnx + 8x³ − x⁴; is the Fermi coupling constant.

The decay distributions of the electron in muon decays have been parametrized using the so-called Michel parameters. The values of these four parameters are predicted unambiguously in the Standard Model of particle physics, thus muon decays represent an excellent laboratory to test the space-time structure of the weak interaction. No deviation from the Standard Model predictions has yet been found.

Certain neutrino-less decay modes are kinematically allowed but forbidden in the Standard Model. Examples forbidden by lepton flavour conservation are

and .

Observation of such decay modes would constitute clear evidence for physics beyond the Standard Model (BSM). Current experimental upper limits for the branching fractions of such decay modes are in the range 10⁻¹¹ to 10⁻¹².

Muonic atoms

The muon was the first elementary particle discovered that does not appear in ordinary atoms. Negative muons can, however, form muonic atoms (also called mu-mesic atoms), by replacing an electron in ordinary atoms. Muonic hydrogen atoms are much smaller than typical hydrogen atoms because the much larger mass of the muon gives it a much smaller ground-state wavefunction than is observed for the electron. In multi-electron atoms, when only one of the electrons is replaced by a muon, the size of the atom continues to be determined by the other electrons, and the atomic size is nearly unchanged. However, in such cases the orbital of the muon continues to be smaller and far closer to the nucleus than the atomic orbitals of the electrons.

A positive muon, when stopped in ordinary matter, can also bind an electron and form an exotic atom known as muonium (Mu) atom, in which the muon acts as the nucleus. The positive muon, in this context, can be considered a pseudo-isotope of hydrogen with one ninth of the mass of the proton. Because the reduced mass of muonium, and hence its Bohr radius, is very close to that of hydrogen, this short-lived "atom" behaves chemically — to a first approximation — like hydrogen, deuterium and tritium.

Use in measurement of the proton charge radius

The recent culmination of an eight year experiment investigating the proton's charge radius involved the use of muonic hydrogen. This form of hydrogen is composed of a muon orbiting a proton[6]. The orbiting muon was induced to undergo a Lamb shift from its 2p state up to an excited 2s state. The frequency of the photon required to induce this shift was revealed to be 50 terahertz which, according to present theories of quantum electrodynamics, yields a value of 0.841 femtometres for the charge radius of the proton.[7]

Anomalous magnetic dipole moment

The anomalous magnetic dipole moment is the difference between the experimentally observed value of the magnetic dipole moment and the theoretical value predicted by the Dirac equation. The measurement and prediction of this value is very important in the precision tests of QED (quantum electrodynamics). The E821 experiment at Brookhaven National Laboratory (BNL) studied the precession of muon and anti-muon in a constant external magnetic field as they circulated in a confining storage ring. The E821 Experiment reported the following average value (from the July 2007 review by Particle Data Group)

where the first errors are statistical and the second systematic.

The difference between the g-factors of the muon and the electron is due to their difference in mass. Because of the muon's larger mass, contributions to the theoretical calculation of its anomalous magnetic dipole moment from Standard Model weak interactions and from contributions involving hadrons are important at the current level of precision, whereas these effects are not important for the electron. The muon's anomalous magnetic dipole moment is also sensitive to contributions from new physics beyond the Standard Model, such as supersymmetry. For this reason, the muon's anomalous magnetic moment is normally used as a probe for new physics beyond the Standard Model rather than as a test of QED (Phys.Lett. B649, 173 (2007)).