Muon
The muon (from the letter mu ()--used to represent it) is an elementary particle with negative electric charge and a spin of 1/2.  It has a mean lifetime of 2.2s,  longer than any other unstable lepton, meson, or baryon except for the neutron. Together with the electron, the tau, and the neutrinos, it is classified as a lepton.  Like all fundamental particles, the muon has an antimatter partner of opposite charge but equal mass and spin: the antimuon, also called a positive muon.  Muons are denoted by  and antimuons by +.
For historical reasons, muons are sometimes referred to as mu mesons, 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 206.7 times the electron mass.  Since their interactions are very similar to those of the electron, a muon can be thought of as a much heavier version of the electron. Due to their greater mass, muons do not emit as much bremsstrahlung radiation; consequently, they are highly penetrating, much more so than electrons.
As with the case of the other charged leptons, there is a muon-neutrino which has the same flavor as the muon.  Muon-neutrinos are denoted by .

# Muon sources
Since the production of muons requires an available center of momentum frame energy of over 105 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, all naturally occurring muons are apparently created by cosmic rays, which consist mostly of protons, many arriving from deep space at very high energy.
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.
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 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 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. See the illustration above of the moon's cosmic ray shadow, detected when 700 m of soil and rock filters secondary radiation, but allows enough muons to form a crude image of the moon, in a directional detector.
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 gyromagnetic ratio experiment (see link below). 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 decays
Muons are unstable elementary particles and are heavier than the electron and neutrinos but lighter than all other matter particles.  They decay via the weak interaction to an electron, two neutrinos and possibly other particles with a net charge of zero.  Nearly all of the time, they decay into an electron, an electron-antineutrino, and a muon-neutrino.  Antimuons decay to a positron, an electron-neutrino, and a muon-antineutrino:
The tree level muon decay width is
A photon or electron-positron pair is also present in the decay products about 1.4% of the time.
The mean lifetime of the muon is 2.1970190.000021 s.  The equality of the muon and anti-muon lifetimes has been established to better than one part in 104.
The decay distributions of the electron in muon decays have been parametrized using the so-called Michel parameters.  The values of these five parameters can be predicted unambiguously in the Standard Model of particle physicsno deviation with respect to these predictions has yet been found.
Certain neutrino-less decay modes are kinematically allowed but forbidden in the Standard Model.  Examples are
Observation of such decay modes would constitute clear evidence for physics beyond the Standard Model (BSM).
Upper limits for the branching fractions of such decay modes are in the range 1011 to 1012.

# Muonic atoms
The muon was the first elementary particle discovered that does not appear in ordinary atoms. Negative muons can, however, form muonic atoms by replacing an electron in ordinary atoms. Muonic atoms are much smaller than typical atoms because the larger mass of the muon gives it a smaller ground-state wavefunction than the electron.
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.

# 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)).

# 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).
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  (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 hadronsthat is, particles made of quarksand 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.