A muon ( ; from the
Greek letter
mu (μ) used to represent it) is an
elementary particle
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, ...
similar to the
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
, with an
electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons res ...
of −1 ''
e'' and a
spin of , but with a much greater mass. It is classified as a
lepton. As with other leptons, the muon is not thought to be composed of any simpler particles; that is, it is a
fundamental particle.
The muon is an unstable
subatomic particle
In physical sciences, a subatomic particle is a particle that composes an atom. According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a p ...
with a
mean lifetime
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and ( lambda) is a positive rate ...
of , much longer than many other subatomic particles. As with the decay of the non-elementary
neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...
(with a lifetime around 15 minutes), muon decay is slow (by subatomic standards) because the decay is mediated only by the
weak interaction (rather than the more powerful
strong interaction
The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called th ...
or
electromagnetic interaction), and because the mass difference between the muon and the set of its decay products is small, providing few kinetic
degrees of freedom for decay. Muon decay almost always produces at least three particles, which must include an electron of the same charge as the muon and two types of
neutrinos.
Like all elementary particles, the muon has a corresponding
antiparticle of opposite charge (+1 ''e'') but equal
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
and spin: the antimuon (also called a ''positive muon''). Muons are denoted by and antimuons by . Formerly, muons were called ''mu mesons'', but are not classified as
mesons by modern particle physicists (see '), and that name is no longer used by the physics community.
Muons have a
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
of , which is approximately 207 times that of the electron, ''m''. More precisely, it is There is also a third lepton, the
tau, approximately 17 times heavier than the muon.
Due to their greater mass, muons accelerate more slowly than electrons in electromagnetic fields, and emit less
bremsstrahlung
''Bremsstrahlung'' (), from "to brake" and "radiation"; i.e., "braking radiation" or "deceleration radiation", is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typical ...
(deceleration radiation). This allows muons of a given energy to
penetrate far deeper into matter because the deceleration of electrons and muons is primarily due to energy loss by the bremsstrahlung mechanism. For example, so-called ''secondary muons'', created by
cosmic rays
Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our ...
hitting the atmosphere, can penetrate the atmosphere and reach Earth's land surface and even into deep mines.
Because muons have a greater mass and energy than the
decay energy of radioactivity, they are not produced by
radioactive decay. However they are produced in great amounts in high-energy interactions in normal matter, in certain
particle accelerator experiments with
hadron
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ...
s, and in cosmic ray interactions with matter. These interactions usually produce
pi meson
In particle physics, a pion (or a pi meson, denoted with the Greek letter pi: ) is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more ge ...
s initially, which almost always decay to muons.
As with the other charged leptons, the muon has an associated
muon neutrino, denoted by , which differs from the
electron neutrino and participates in different nuclear reactions.
History
Muons were discovered by
Carl D. Anderson
Carl David Anderson (September 3, 1905 – January 11, 1991) was an American physicist. He is best known for his discovery of the positron in 1932, an achievement for which he received the 1936 Nobel Prize in Physics, and of the muon in 1936.
...
and
Seth Neddermeyer
Seth Henry Neddermeyer (September 16, 1907 – January 29, 1988) was an American physicist who co-discovered the muon, and later championed the Implosion-type nuclear weapon while working on the Manhattan Project at the Los Alamos Labor ...
at
Caltech
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
in 1936, while studying
cosmic radiation
Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our ow ...
. Anderson noticed particles that curved differently from electrons and other known particles when passed through a
magnetic field. They were negatively charged but curved less sharply than electrons, but more sharply than
proton
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
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 their mass was greater than an electron but smaller than a proton. Thus Anderson initially called the new particle a ''mesotron'', adopting the prefix ''meso-'' from the Greek word for "mid-". The existence of the muon was confirmed in 1937 by
J. C. Street and E. C. Stevenson's
cloud chamber experiment.
A particle with a mass in the meson range had been predicted before the discovery of any mesons, by theorist
Hideki Yukawa:
It seems natural to modify the theory of Heisenberg and Fermi in the following way. The transition of a heavy particle from neutron state to proton state is not always accompanied by the emission of light particles. The transition is sometimes taken up by another heavy particle.
Because of its mass, the mu meson was initially thought to be Yukawa's particle and some scientists, including
Niels Bohr, originally named it the yukon. Yukawa's predicted particle, the
pi meson
In particle physics, a pion (or a pi meson, denoted with the Greek letter pi: ) is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more ge ...
, was finally identified in 1947 (again from cosmic ray interactions), and was shown to differ from the mu meson by having the properties of a particle that mediated the
nuclear force.
With two particles now known with the intermediate mass, the more general term ''
meson'' was adopted to refer to any such particle within the correct mass range between electrons and nucleons. Further, in order to differentiate between the two different types of mesons after the second meson was discovered, the initial mesotron particle was renamed the ''mu meson'' (the Greek letter ''μ''
'mu''corresponds to ''m''), and the new 1947 meson (Yukawa's particle) was named the
pi meson
In particle physics, a pion (or a pi meson, denoted with the Greek letter pi: ) is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more ge ...
.
As more types of mesons were discovered in accelerator experiments later, it was eventually found that the mu meson significantly differed not only from the pi meson (of about the same mass), but also from all other types of mesons. The difference, in part, was that mu mesons did not interact with the
nuclear force, as pi mesons did (and were required to do, in Yukawa's theory). Newer mesons also showed evidence of behaving like the pi meson in nuclear interactions, but not like the mu meson. Also, the mu meson's decay products included both a
neutrino and an
antineutrino, rather than just one or the other, as was observed in the decay of other charged mesons.
In the eventual
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
of particle physics codified in the 1970s, all mesons other than the mu meson were understood to be
hadrons – that is, particles made of
quarks
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All common ...
– and thus subject to the
nuclear force. In the quark model, a ''meson'' was no longer defined by mass (for some had been discovered that were very massive – more than
nucleons), but instead were particles composed of exactly two quarks (a quark and antiquark), unlike the
baryon
In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classifie ...
s, which are defined as particles composed of three quarks (protons and neutrons were the lightest baryons). Mu mesons, however, had shown themselves 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'' used with the quark model of particle structure.
With this change in definition, the term ''mu meson'' was abandoned, and replaced whenever possible with the modern term ''muon'', making the term "mu meson" only a historical footnote. In the new quark model, other types of mesons sometimes continued to be referred to in shorter terminology (e.g., ''pion'' for pi meson), but in the case of the muon, it retained the shorter name and was never again properly referred to by older "mu meson" terminology.
The eventual recognition of the muon as a simple "heavy electron", with no role at all in the nuclear interaction, seemed so incongruous and surprising at the time, that Nobel laureate
I. I. Rabi famously quipped, "Who ordered that?"
In the
Rossi–Hall experiment (1941), muons were used to observe the
time dilation (or, alternatively,
length contraction
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGera ...
) predicted by
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The law ...
, for the first time.
Muon sources
Muons arriving on the Earth's surface are created indirectly as decay products of collisions of cosmic rays with particles of the Earth's atmosphere.
When a cosmic ray proton impacts atomic nuclei in the upper atmosphere,
pions
In particle physics, a pion (or a pi meson, denoted with the Greek letter pi: ) is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more gene ...
are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and
muon neutrinos. The muons from these high-energy cosmic rays generally continue in about the same direction as the original proton, at a velocity near the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
. Although their lifetime ''without'' relativistic effects would allow a half-survival distance of only about 456 meters at most (as seen from Earth) the
time dilation effect of
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The law ...
(from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame the muons have a longer
half-life
Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ...
due to their velocity. From the viewpoint (
inertial frame
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration ...
) of the muon, on the other hand, it is the
length contraction
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGera ...
effect of special relativity which allows this penetration, since in the muon frame its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. Both effects are equally valid ways of explaining the fast muon's unusual survival over distances.
Since muons are unusually penetrative of ordinary matter, like neutrinos, they are also detectable deep underground (700 meters at the
Soudan 2 detector) 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.
Muon decay
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. Because
leptonic family numbers are conserved in the absence of an extremely unlikely immediate
neutrino oscillation, one of the product neutrinos of muon decay must be a muon-type neutrino and the other an electron-type antineutrino (antimuon decay produces the corresponding antiparticles, as detailed below).
Because charge must be conserved, one of the products of muon decay is always an electron of the same charge as the muon (a positron if it is a positive muon). Thus all muons decay to at least an electron, and two neutrinos. Sometimes, besides these necessary products, additional other particles that have no net charge and spin of zero (e.g., a pair of photons, or an electron-positron pair), are produced.
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 .
The equality of the muon and antimuon lifetimes has been established to better than one part in 10
4.
Prohibited decays
Certain neutrino-less decay modes are kinematically allowed but are, for all practical purposes, forbidden in the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
, even given that neutrinos have mass and oscillate. Examples forbidden by lepton flavour conservation are:
: → +
and
: → + + .
To be precise: in the Standard Model with neutrino mass, a decay like → + is technically possible, for example by
neutrino oscillation of a virtual muon neutrino into an electron neutrino, but such a decay is astronomically unlikely and therefore should be experimentally unobservable: Less than one in 10
50 muon decays should produce such a decay.
Observation of such decay modes would constitute clear evidence for theories
beyond the Standard Model. Upper limits for the branching fractions of such decay modes were measured in many experiments starting more than years ago. The current upper limit for the → + branching fraction was measured 2009–2013 in the
MEG
Meg is a feminine given name, often a short form of Megatron, Megan, Megumi (Japanese), etc. It may refer to:
People
* Meg (singer), a Japanese singer
*Meg Cabot (born 1967), American author of romantic and paranormal fiction
* Meg Burton Cahill ...
experiment and is .
Theoretical decay rate
The muon
decay width which follows from
Fermi's golden rule has dimension of energy, and must be proportional to the square of the amplitude, and thus the square of
Fermi's coupling constant (
), with over-all dimension of inverse fourth power of energy. By dimensional analysis, this leads to
Sargent's rule of fifth-power dependence on ,
:
where
,
[ and:
: is the fraction of the maximum energy transmitted to the electron.
The decay distributions of the electron in muon decays have been parameterised using the so-called ]Michel parameters
The Michel parameters, usually denoted by \rho, \eta, \xi and \delta, are four parameters used in describing the phase space distribution of leptonic decays of charged leptons, l_^-\rightarrow l_^\nu_\bar. They are named after the physicist Louis ...
. The values of these four parameters are predicted unambiguously in the Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
of particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, thus muon decays represent a good test of the spacetime structure of the weak interaction. No deviation from the Standard Model predictions has yet been found.
For the decay of the muon, the expected decay distribution for the Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
values of Michel parameters is
: