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 ½. 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 minutes). 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 previously called
mu mesons, but 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 an electron. Since the muon's 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 are not as sharply accelerated when they encounter electromagnetic fields, and do not emit as much
bremsstrahlung radiation. Thus muons of a given energy penetrate matter far more deeply than electrons, since the deceleration of electrons and muons is primarily due to energy loss by this mechanism. So-called "secondary muons", generated by
cosmic rays hitting the atmosphere, can penetrate to the Earth's surface and 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 and
Seth Neddermeyer at Caltech in 1936, while studying
cosmic radiation. Anderson had 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
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 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-". Shortly thereafter, additional particles of intermediate mass were discovered, and the more general term
meson was adopted to refer to any such particle. To differentiate between different types of mesons, the mesotron was in 1947 renamed the
mu meson (the Greek letter
μ (
mu) corresponds to
m).
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 with 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.
Another particle (the
pion, with which the muon was initially confused) had been predicted by theorist
Hideki Yukawa:
[2]
"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 mission of light particles. The transition is sometimes taken up by another heavy particle."
The existence of the muon was confirmed in 1937 by J. C. Street and E. C. Stevenson's cloud chamber experiment.
[3] The discovery of the muon seemed so incongruous and surprising at the time that Nobel laureate
I. I. Rabi famously quipped, "Who ordered that?"
In a 1941 experiment on
Mount Washington in
New Hampshire, muons were used to observe the
time dilation predicted by
special relativity for the first time.
[4]
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 do not produce muons as the production of a single muon would violate the conservation of quantum numbers (see under "muon decay" below).
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
[5]
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. Travelling 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 continue in about the same direction as the original proton, at a very high velocity. Although their lifetime
without relativistic effects would allow a half-survival distance of only about 0.66 km (660 meters) at most (as seen from Earth) the
time dilation effect of
special relativity (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 due to their velocity. From the viewpoint (
inertial frame) of the muon, on the other hand, it is the
length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the distance through the atmosphere and earth appears far shorter than these distances in the Earth rest-frame. Both 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 II 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.
[6]
Muon decay
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. Because
lepton numbers must be conserved, 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 a net charge and spin of zero (i.e. 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 2.197 019 ± 0.000 021 μs
[7]. The equality of the muon and anti-muon lifetimes has been established to better than one part in 10
4.
The
tree-level muon
decay width is
where
I(x) = 1 − 8x − 12x2lnx + 8x3 − x4;
is the
Fermi coupling constant.
The decay distributions of the electron in muon decays have been parameterised 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 a good test of 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[clarification needed], 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 a twelve 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
[8]. The
Lamb shift in muonic hydrogen was measured by driving the muon from the from its 2s state up to an excited 2p state using a
laser. The frequency of the photon required to induce this transition was revealed to be 50 terahertz which, according to present theories of
quantum electrodynamics, yields a value of 0.84184 ± 0.00067 femtometres for the charge radius of the proton.
[9]
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)).
See also
References
- ^ K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010), URL: http://pdg.lbl.gov
- ^ Yukaya Hideka, On the Interaction of Elementary Particles 1, Proceedings of the Physico-Mathematical Society of Japan (3) 17, 48, pp 139-148 (1935). (Read 17 November 1934)
- ^ New Evidence for the Existence of a Particle Intermediate Between the Proton and Electron", Phys. Rev. 52, 1003 (1937).
- ^ David H. Frisch and James A. Smith, "Measurement of the Relativistic Time Dilation Using Muons", American Journal of Physics, 31, 342, 1963, cited by Michael Fowler, "Special Relativity: What Time is it?"
- ^ S. Carroll (2004). Spacetime and Geometry: An Introduction to General Relativity. Addison Wesly. p. 204
- ^ Brookhaven National Laboratory (30 July 2002). "Physicists Announce Latest Muon g-2 Measurement". Press release. http://www.bnl.gov/bnlweb/pubaf/pr/2002/bnlpr073002.htm. Retrieved 2009-11-14.
- ^ [1]
- ^ TRIUMF Muonic Hydrogen collaboration. "A brief description of Muonic Hydrogen research". Retrieved 2010-11-7
- ^ Pohl, Randolf et al. "The Size of the Proton" Nature 466, 213-216 (8 July 2010)
External links
***
Comment on Backreaction made to Steven
Hi Steven
Would we not be correct to say that unification with the small would be most apropos indeed with the large?
Pushing through that veil.
My interest with the QGP is well documented, as it presented itself "with an interesting location" with which to look at during the collision process.
Natural Microscopic blackhole creations? Are such conditions possible in the natural way of things? Although quickly dissipative, they leave their mark as Cerenkov effects.
As one looks toward the cosmos this reductionist process is how one might look at the cosmos at large, as to some of it's "motivations displayed" in the cosmos?
What conditions allow such reductionism at play to consider the end result of geometrical propensity as a message across the vast distance of space, so as to "count these effects" here on earth?
Let's say cosmos particle collisions and LHC are hand in hand "as to decay of the original particles in space" as they leave their imprint noticeably in the measures of SNO or Icecube, but help us discern further effects of that decay chain as to the constitutions of LHC energy progressions of particles in examination?
Emulating the conditions in LHC progression, adaptability seen then from such progressions, working to produce future understandings. Muon detections through the earth?
So "modeled experiments" in which "distillation of thought" are helped to be reduced too, in kind, lead to matter forming ideas with which to progress? Measure. Self evident.
You see the view has to be on two levels, maybe as a poet using words to describe, or as a artist, trying to explain the natural world. The natural consequence, of understanding of our humanity and it's continuations expressed as abstract thought of our interactions with the world at large, unseen, and miscomprehended?
Do you think Superstringy has anything to do with what I just told you here?:)
Best,
Hi Steven,
Maybe the following will help, and then I will lead up to a modern version for consideration, so you understand the relation.
Keep Gran Sasso in your mind as you look at what I am giving you.
The underground laboratory, which opened in 1989, with its low background radiation is used for experiments in particle and nuclear physics,including the study of neutrinos, high-energy cosmic rays, dark matter, nuclear decay, as well as geology, and biology-wiki
Neutrinos, get set, go!
This summer, CERN gave the starting signal for the long-distance neutrino race to Italy. The CNGS facility (CERN Neutrinos to Gran Sasso), embedded in the laboratory's accelerator complex, produced its first neutrino beam. For the first time, billions of neutrinos were sent through the Earth's crust to the Gran Sasso laboratory, 732 kilometres away in Italy, a journey at almost the speed of light which they completed in less than 2.5 milliseconds. The OPERA experiment at the Gran Sasso laboratory was then commissioned, recording the first neutrino tracks.
Because I am a layman, does not reduce the understanding that I can have, that a scientist may have.
Now for the esoteric :)
Secrets of the Pyramids In a boon for archaeology, particle physicists plan to probe ancient structures for tombs and other hidden chambers. The key to the technology is the muon, a cousin of the electron that rains harmlessly from the sky.
What kind of result would they get from using the muon. What will it tell them?:)
Best,
