Muon
20146
226183224
2008-07-17T05:40:35Z
72.1.154.41
/* Muon decays */ *All* decays of muons involve a W boson.
{{Infobox Particle
| bgcolour =
| name = Muon
| image = [[Image:Moons shodow in muons.gif|256px]]
| caption = The [[Moon]]'s cosmic ray shadow, as seen in secondary muons detected 700m below ground, at the [[Soudan II]] detector.
| num_types =
| composition = [[Elementary particle]]
| family = [[Fermion]]
| group = [[Lepton]]
| generation = Second
| interaction = [[Gravity]], [[Electromagnetic interaction|Electromagnetic]], <br>[[Weak interaction|Weak]]
| antiparticle = Antimuon
| theorized =
| discovered = [[Carl D. Anderson]], [[1936]]
| symbol = <math>\mu^-</math>
| mass = 105.658369(9) [[MeV]]/[[speed of light|c]]<sup>2</sup>{{inote|http://pdg.lbl.gov}}
| mean_lifetime = 2.19703(4)×10<sup>−6</sup>s<ref name="Yao 2006">W.-M. Yao et al. ([[Particle Data Group]]), J. Phys. G 33, 1 (2006)</ref>
| decay_particle =
| electric_charge = −1 [[Elementary charge|e]]
| color_charge = None
| spin = ½
| num_spin_states =
}}
The '''muon''' (from the letter [[mu (letter)|mu]] (μ)--used to represent it) is an [[elementary particle]] with negative [[electric charge]] and a [[spin (physics)|spin]] of 1/2. It has a [[mean lifetime]] of 2.2μs, longer than any other unstable [[lepton]], [[meson]], or [[baryon]] except for the [[neutron]]. Together with the [[electron]], the [[tau lepton|tau]], and the [[neutrino]]s, 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 μ<sup>−</sup> and antimuons by μ<sup>+</sup>.
For historical reasons, muons are sometimes referred to as '''mu mesons''', even though they are not classified as [[meson]]s by modern particle physicists (''see [[#History|History]]''). Muons have a [[mass]] of 105.7 [[MeV]]/[[speed of light|c]]<sup>2</sup>, 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 (physics)|flavor]] as the muon. Muon-neutrinos are denoted by ν<sub>μ</sub>.
== 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.
{{Quote|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 Wolvertron, science writer|''Scientific American'' magazine, September 2007, page 26 "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 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 [http://www.bnl.gov/bnlweb/pubaf/pr/2002/bnlpr073002.htm 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==
[[Image:Muon-Electron-Decay.svg|right|frame|The most common decay of the muon]]
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:
:<math>\mu^-\to e^- + \bar\nu_e + \nu_\mu,~~~\mu^+\to e^+ + \nu_e + \bar\nu_\mu</math>.
The tree level muon decay width is
:<math>\Gamma=\frac{G_F^2 m_\mu^5}{192\pi^3}I\left(\frac{m_e^2}{m_\mu^2}\right),</math> where <math>I(x)=1-8x+12x^2ln\left(\frac{1}{x}\right)+8x^3-x^4</math>.
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 2.197019±0.000021 μs[http://arxiv.org/abs/0704.1981v1]. The equality of the muon and anti-muon lifetimes has been established to better than one part in 10<sup>4</sup>.
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 physics]]—no 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
: <math>\mu^-\to e^- + \gamma</math> and <math>\mu^-\to e^- + e^+ + e^-</math>.
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 10<sup>−11</sup> to 10<sup>−12</sup>.
== Muonic atoms ==
The muon was the first [[elementary particle]] discovered that does not appear in ordinary [[atom]]s. 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|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 [http://www.g-2.bnl.gov/ 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 [http://pdg.lbl.gov/2007/reviews/g-2_s004219.pdf (from the July 2007 review by Particle Data Group)]
:<math>a = \frac{g-2}{2} = 0.0011659208(5.4)(3.3)</math>
where the first errors are statistical and the second systematic.
The difference between the [[g-factor]]s 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 interaction]]s and from contributions involving [[hadron]]s 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 ([http://arxiv.org/abs/hep-ph/0611102 Phys.Lett. B649, 173 (2007)]).
==History==
{{antimatter}}
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 [[proton]]s, 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 ''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''.
==See also==
*[[Muonium]]
*[[Muon spin spectroscopy]]
*[[Muon-catalyzed fusion]]
*[[List of particles]]
==External links==
* [http://antwrp.gsfc.nasa.gov/apod/ap050828.html Muon anomalous magnetic moment and supersymmetry]
* [http://www.g-2.bnl.gov/ g-2 (muon anomalous magnetic moment) experiment]
* [http://www.npl.uiuc.edu/exp/mulan/ muLan (Measurement of the Positive Muon Lifetime) experiment]
* [http://pdg.lbl.gov/ The Review of Particle Physics]
* [http://twist.triumf.ca/ The TRIUMF Weak Interaction Symmetry Test]
==References==
{{reflist}}
{{refbegin}}
*S.H. Neddermeyer and C.D. Anderson, "Note on the Nature of Cosmic-Ray Particles", Phys. Rev. 51, 884–886 (1937). Full text available in [http://prola.aps.org/pdf/PR/v51/i10/p884_1''PDF''].
*J.C. Street and E.C. Stevenson, "New Evidence for the Existence of a Particle of Mass Intermediate Between the Proton and Electron", Phys. Rev. 52, 1003-1004 (1937). Full text available in [http://prola.aps.org/pdf/PR/v52/i9/p1003_1''PDF''].
*Serway & Faughn, ''College Physics, Fourth Edition'' (Fort Worth TX: Saunders, 1995) page 841
*Emanuel Derman, ''My Life As A Quant'' (Hoboken, NJ: Wiley, 2004) pp. 58-62.
* Marc Knecht ; ''The Anomalous Magnetic Moments of the Electron and the Muon'', Poincaré Seminar (Paris, Oct. 12, 2002), published in : Duplantier, Bertrand; Rivasseau, Vincent (Eds.) ; ''Poincaré Seminar 2002'', Progress in Mathematical Physics 30, Birkhäuser (2003) [ISBN 3-7643-0579-7]. Full text available in [http://parthe.lpthe.jussieu.fr/poincare/textes/octobre2002/Knecht.ps ''PostScript''].
{{refend}}
{{Particles}}
[[Category:Leptons]]
[[bs:Mion]]
[[ca:Muó]]
[[cs:Mion]]
[[de:Myon]]
[[es:Muón]]
[[eo:Muono]]
[[fa:میون]]
[[fr:Muon]]
[[ko:뮤온]]
[[hr:Mion]]
[[id:Muon]]
[[it:Muone]]
[[he:מיואון]]
[[la:Myon]]
[[lv:Mions]]
[[lt:Miuonas]]
[[hu:Müon]]
[[nl:Muon]]
[[ja:ミュー粒子]]
[[no:Myon]]
[[pl:Mion]]
[[pt:Muão]]
[[ru:Мюон]]
[[simple:Muon]]
[[sk:Mión]]
[[sl:Mion]]
[[sr:Мион]]
[[fi:Myoni]]
[[sv:Myon]]
[[uk:Мюон]]
[[zh:Μ子]]