The Moon's cosmic ray shadow, as seen in secondary muons generated by cosmic rays in the atmosphere, and detected 700 meters below ground, at the Soudan II detector. Credit: Deglr6328.

"[T]here is a window of opportunity for muon astronomy with the AMANDA, Lake Baikal, and MILAGRO detectors."[1]

## Astronomy

This is an image obtained from muon radiography of Japan's Asama volcano. Credit: H T M Tanaka.

The image shows the principle of muon radiography. Credit: Nicola Graf.

This is an image of a muon telescope. Credit: Paolo Strolin.

"Muons are produced, along with other particles, when cosmic rays (high-energy particles originating in outer space) interact with atomic nuclei in Earth’s atmosphere to produce ‘showers’ of secondary particles. The muons inherit the high energy of the parent cosmic rays, which enables them to penetrate and pass through the rock of the volcano and to be detected on the other side of the mountain. Because denser materials absorb more muons (just as dense materials such as bone absorb more X-rays), this provides a basis for producing shadow images of the volcano’s interior."[2]

"Muon radiography was first used in 1971 – not for volcanoes, but for investigating the interior of the pyramid of Chefren at Giza, Egypt. The Nobel-prize winning physicist Louis Alvarez placed a muon detector inside the pyramid to pick up changes in muon flux (rate of muon flow) that could indicate the presence of a hidden burial chamber. However, none was found."[2]

"In 2007, Hiroyuki Tanaka and collaborators from the University of Tokyo were the first to apply this technique to volcanoes. They carried out radiography of the top part of the Asama volcano in Honshu, Japan, which revealed a region with rock of low density under the bottom of the crater. The presence of low-density regions can be used in computer simulations that predict how possible eruptions could develop, indicating the most dangerous areas around the volcano. Their observations showed that muon radiography could indeed produce useful images of the internal structure of volcanoes."[2]

"The really important advantages of muon radiography of volcanoes are two-fold. First, whereas current indirect methods can provide information to a spatial resolution of some 100 m, muon radiography can be up to ten times more specific, mapping internal structures to a resolution of some 10 m. Second, muon radiography offers the possibility of continuous monitoring, thus potentially revealing the evolution of structures over time. The time resolution depends on the thickness of the rock traversed by the muons: the thicker it is, the fainter the muon flux and the longer it takes to accumulate enough muons for a picture. The time needed can thus be weeks, months or years."[2]

Vesuvius "is a special challenge, not only because it represents the highest volcanic risk in Europe, but also because of the mountain’s unusual structure. Vesuvius is in fact situated within the remnants of a much larger volcano, Mount Somma. Moreover, inside the summit of Vesuvius is a crater that is 500 m wide and 300 m deep: this means that, to look below the bottom of the crater, muons have to penetrate deep into the mountain, through almost two kilometres of rock, to reach the detector on the opposite side of the volcano. Only muons of very high energy travelling in a near-horizontal direction are able to pass through all this rock, so their flux at the detector is very low, making imaging extremely difficult."[2]

This lepton box provides information about muons. Credit: MissMJ.

This is a Feynman Diagram of the most common of Muon Decays. Credit: Richard Feynman.

"TeV muons from γ ray primaries ... are rare because they are only produced by higher energy γ rays whose flux is suppressed by the decreasing flux at the source and by absorption on interstellar light."[1]

The muon from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with unitary negative electric charge (−1) and a spin of ​12. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton. As is the case with other leptons, the muon is not believed to have any sub-structure at all (i.e., is not thought to be composed of any simpler particles).

The muon is an unstable subatomic particle with a mean lifetime of 2.2 us. This comparatively long decay lifetime (the second longest known) is due to being mediated by the weak interaction. The only longer lifetime for an unstable subatomic particle is that for the free neutron, a baryon particle composed of quarks, which also decays via the weak force. Muon decay produces three particles, an electron plus two neutrinos of different types.

Like all elementary particles, the muon has a corresponding antiparticle of opposite charge (+1) but equal mass and spin: the antimuon (also called a positive muon). Muons are denoted by μ
and antimuons by μ+
.

## Planetary sciences

"The nuclear processes that produce cosmogenic 36Cl in rocks are spallation, neutron capture, and muon capture. The first two processes dominate production on the land surface; muon production in Ca and K becomes more important with increasing depth (Rama and Honda, 1961)."[3]

"The decay of radioactive U and Th also give rise to the production of 36Cl, via neutron capture (Bentley et al., 1986)."[3]

"The production rate of cosmogenic 36Cl in bedrock and regolith exposed at Earth's surface is dependent on its calcium, potassium, and chloride content and can be expressed by the equation

${\displaystyle P=\psi _{Ca}(C_{Ca})+\psi _{K}(C_{K})+\psi _{n}(\sigma _{35}N_{35}/\Sigma \sigma _{i}N_{i}),}$

where ${\displaystyle \psi _{K}}$  and ${\displaystyle \psi _{Ca}}$  are the total production rates (including production due to slow negative muons) of 36Cl due to potassium and calcium, respectively; ${\displaystyle C_{K}}$  and ${\displaystyle C_{Ca}}$  are the elemental concentrations of potassium and calcium, respectively; and ${\displaystyle \psi _{n}}$  is the thermal neutron capture rate, which is dependent on the fraction of neutrons stopped by 35Cl ${\displaystyle (\sigma _{35}N_{35}/\Sigma \sigma _{i}N_{i}),}$  as determined by the effective cross sections of 35Cl${\displaystyle (\sigma _{35})}$  and all other absorbing elements ${\displaystyle (\Sigma \sigma )}$  and their respective abundances ${\displaystyle (N_{35}}$  and ${\displaystyle N_{i})}$ ."[3]

## Colors

Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo[4] whereby a neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates. Neutrino oscillation is of theoretical and experimental interest since observation of the phenomenon implies that the neutrino has a non-zero mass.

## Minerals

This is a diagram of muon target minerals. Credit: Derek Fabel.

"The Earth is continually being bombarded by high-energy cosmic rays that originate predominantly from super nova explosions within our galaxy. Interactions between these high energy cosmic rays and the Earth's atmosphere creates secondary and tertiary cosmic rays, including neutrons and muons."[5]

"When reaching the Earth's surface these high energy particles can penetrate meters into rock and sediment."[5]

"Nuclear interactions between neutrons and muons and minerals [as in the diagram at the right] such as quartz, calcite, K-feldspar, and olivine, produce long-lived radionuclides such as Be-10, Al-26 and Cl-36."[5]

"The production rates of these "in-situ produced terrestrial cosmogenic nuclides" are almost unimaginably small - a few atoms per gram of rock per year, however using accelerator mass spectrometry (AMS) we can detect and count cosmogenic nuclides down to levels of a few thousand atoms per gram (parts per million of parts per billion!)."[5]

"The build-up of cosmogenic nuclides through time provides us with a way to measure exposure ages for rock surfaces such as fault scarps, lava flows and glacial pavements.Where surfaces are gradually evolving, cosmogenic nuclide measurements allow us to calculate erosion or soil accumulation rates.Where previously exposed rock or sediment is re-buried the relative decay between different cosmogenic nuclides can be used to date the burial time."[5]

## Theoretical muon astronomy

Def. an "unstable [elementary particle in the lepton family,][6] having similar properties to the electron but with a mass [207][7] times greater"[8] is called a muon.

Def. the "antiparticle corresponding to a muon"[9] is called an antimuon.

Here's a theoretical definition:

Def. radiation astronomy of and using muons is called muon radiation astronomy, or muon astronomy.

### Electromagnetic loops

"The particle known as the muon has the same negative charge as the electron and the same spin (intrinsic angular momentum) but is considerably heavier than the electron. It may well be that the muon is a single wavelength photon twisted into a tight 4-loop helix. The pattern of magnetic and electric vectors would still be the same as for the electron. This argument may also be extended to the tauon — a super heavy version of the electron."[10]

"There is also a way to model the property of spin. Every elementary particle must possess, in addition to a characteristic mass, a certain spin (its intrinsic angular momentum). The looping and twisting motion of the confined photon is ideal for establishing a correspondence with a particle’s spin property."[10]

"According to the new paradigm, all particles consist of electromagnetic loops (or loops of loops) — all particles are essentially confined photons. When these loops are complete, resonant, and harmonic they represent independent particles, such as the electron, muon, and tauon (and their antiparticle versions)."[10]

### Leptogenesis

"In realistic unified models involving so-called SO(10)-inspired patterns of Dirac and heavy right-handed (RH) neutrino masses, the lightest right-handed neutrino N1 is too light to yield successful thermal leptogenesis, barring highly fine tuned solutions, while the second heaviest right-handed neutrino N2 is typically in the correct mass range."[11]

Flavour "coupling effects in the Boltzmann equations may be crucial to the success of such N2 dominated leptogenesis, by helping to ensure that the flavour asymmetries produced at the N2 scale survive N1 washout."[11]

The "only relevant asymmetry is that one produced at the N2 scale in the tauon flavour".[11]

"This implies that, at least at lower order, the observed asymmetry can only be produced in the tauon flavour".[11]

The "asymmetry is mainly produced by the next-to-lightest RH neutrinos in the tauon flavour but this asymmetry is fully washed-out by the lightest RH neutrinos since the condition K ≲􏰗 1 is not compatible with the measured values of the mixing parameters."[11]

One "has also to consider that part of the asymmetry in the tauon flavour is transferred to the electron and muon flavours by flavour coupling effects due primarily to the fact that N2-decays produce in addition to an asymmetry in the tauon lepton doublets also an (hyper charge) asymmetry in the Higgs bosons. This Higgs asymmetry unavoidably induces, through the inverse decays, also an asymmetry in the lepton doublets that at the production are a coherent admixture of electron and muon components. Therefore, in this case, inverse decays actually produce an asymmetry instead of wash it out as in a traditional picture."[11]

"It should be noticed how the source of the electron and muon asymmetries is in any case the tauon asymmetry, but part of this induces a muon and an electron asymmetry thanks to flavour coupling."[11]

"The A to Z model can not only provide a satisfactory fit to all parameters in the leptonic mixing matrix but can also reproduce the correct value of the matter-antimatter asymmetry with N2-dominated leptogenesis. In this respect it is crucial to account for flavour coupling effects due to the redistribution of the asymmetry in particles that do not participate directly to the generation of the asymmetry, in primis the Higgs asymmetry. In particular a “flavour swap” scenario is realised whereby the asymmetry generated in the tauon flavour emerges as a surviving asymmetry dominantly in the muon flavour. The solution works even in the simplest case where the neutrino Dirac mass matrix is equal to the up quark mass matrix."[11]

"The muon and the tauon are unstable and after a while they decay into electrons."[12]

### Muonic hydrogen

This image is of the proton accelerator at the Paul Scherrer Institute, which was used to create the muons used to make muonic hydrogen. Credit: Paul Scherrer Institute, Switzerland.

"How big is a proton? Unlike an electron or neutrino, which are fundamental particles that behave like points, a proton is a messy collection of quarks, gluons, and virtual particles that occupies what should be a measurable amount of space. And just how much space can be rather significant; as the authors of a new paper on the proton's size put it, "The proton structure is important because an electron in an S [ground] state has a nonzero probability to be inside the proton.""[13]

"Within experimental error, various measurements of the proton's size have all put it about 0.88 femtometers (an fm is 10-15 meters). But a team of researchers, working at a particle accelerator in Switzerland, has found a different way of measuring the proton's size: put a muon—a heavy, unstable, relative of the electron—in orbit around a proton. The resulting atom, called muonic hydrogen, can be measured during the brief time it exists before the muon decays. Those measurements have produced a new, very high-precision value for the proton's radius. Just one small problem: it differs from the other measurements by nearly seven standard deviations."[13]

"The fact that hydrogen only emits or absorbs specific frequencies as its electrons hop between orbitals was critical to the development of quantum mechanics. Better precision measurements revealed that many of these absorption or emissions lines were actually two closely spaced frequencies; that provided experimental validation of the Dirac equation. Small deviations from this equation eventually helped trigger the development of quantum electrodynamics."[13]

"Because the physics of a hydrogen atom is so well defined, it's possible to use these precise measures of how it absorbs and emits light to generate measures of the atom's components. These include things like the size, magnetic radius, and charge radius of the proton at the center of it all. These have produced values generally in the area of 0.88fm, which is great, because that agrees with measures of the proton's radius obtained by scattering electrons off it. Everything looked good."[13]

"Muons come from the same family of particles as electrons. They carry an identical charge but are 207 times heavier than their more familiar cousins. They also typically decay in about 2 x 10-6 seconds. Still, if everything is timed perfectly, it's possible to put one into orbit around a proton, creating an atom of muonic hydrogen (also called µp)."[13]

"In this case, the research team had some lasers poised to go off, waiting on a trigger provided by a muon detector. As soon as the muonic hydrogen was likely to be present, the lasers fired, allowing spectroscopic measurements of this atom. Because of the muon's (relatively) large mass, these measurements provided very precise values for some of the basic properties of the protons they were orbiting. The researchers also measured two different energy level transitions, allowing them to get a second set of independent values."[13]

"Both of them placed the proton's radius at 0.84fm. That may not seem like a huge difference, but the high precision meant that there was very little statistical error. So little, in fact, that the value they calculate is about seven standard deviations (or seven sigma) out from the value obtained by the other methods. [...] muons interact with protons in a fundamentally different way than electrons."[13]

## Entities

"By virtue of it large volume, AMANDA can search for relativistic magnetic monopoles with unprecedented sensitivity. Our technique relies on fact that the equivalent charge of a magnetic monopole is 68.5, and since the amount of Cherenkov light depends on the square of the charge, the light produced by monopoles is prodigious. By constraining the search to monopoles that pass through the earth, we simplify the analysis. The downside of this restriction is that the mass of the monopole must be large to possess enough kinetic energy to pass through the earth."[14]

## Sources

The plot shows 90% CL upper limits (averaged over right ascension) for a source with an assumed differential spectrum of E-2. Credit: Amanda Collaboration.

Experimental limits on muon fluxes from high energy neutrinos, and projected sensitivity for AMANDA-II. Credit: Amanda Collaboration.

The figure shows the neutrino sky as seen by AMANDA-II. Credit: Amanda Collaboration.

Statistically significant excesses, if found, are shown in the contour plot. Credit: Amanda Collaboration.

The differential flux limit for two different assumptions of the spectral index, alpha is shown. Credit: Amanda Collaboration.

The table provides upper limits for a selection of candidate sources. Credit: Amanda Collaboration.

"The point source analysis optimizes the selection criteria on hard spectra (differential energy spectra proportionally to E-2), although it has reasonable sensitivity to softer spectra. The critical features of the point source analysis: demonstrate good angular resolution and absolute pointing and maintain good effective size for as much of the sky as possible. For the point source analysis, the AMANDA-II detector achieves:"[14]

1. ~25,000 m2 if the muon energy at the detector is greater than 10 TeV.
2. space angle resolution of 2 deg (median),
3. Neutrino flux sensitivity of ~0.22 x10-7 cm-2 s-1.

"Sensitivity achieved by the AMANDA-II point source analysis. The plot [at right] shows 90% CL upper limits (averaged over right ascension) for a source with an assumed differential spectrum of E^-2. The neutrino signal is then integrated for energies above 10 GeV to determine the limit on the neutrino flux. The units for the vertical scale are 10-7 cm-2 s-1."[14]

"Experimental limits on muon fluxes from high energy neutrinos, and projected sensitivity [second figure at the right] for AMANDA-II assuming data is analyzed from several years of operation."[14]

"The [third figure at the right] shows the neutrino sky as seen by AMANDA-II using data from just the first year of operation (Feb -Oct of 2000). The point source analysis was developed by randomizing the true azimuthal (or right ascension, RA) distribution of events to insure that human expectation does not bias the analysis. Nearly all events in the northern sky are compatible with atmospheric neutrinos (plus a small admixture poorly reconstructed atmospheric muons). While the angular distribution of this data reveals NO evidence for extraterrestrial neutrino sources, it provides important constraints on theoretical models."[14]

"A total of 1555 events are shown in the [third figure at the right] (in equatorial coordinates). Compared to the previous sky map from AMANDA-B10, the coverage near the horizon (declination = 0 degrees) is markedly improved. The angular resolution of AMANDA-II is much improved so the angular dimensions of a search bin are likely to be reduced to 6x6 square degrees. The downgoing atmospheric muon background is responsible for the thick band of events below the horizon. Less than 3% of the events above a declination of 5 degrees are due to atmospheric muon contamination."[14]

"The angular distribution of events in the [third figure at the right] skyplot was examined for statistically significant excesses. None were found, leading to preliminary limits shown in the contour plot [fourth figure at the right.] The units of the color legend are 10-7 cm-2 s-1.The horizontal units are hours of right ascension and vertical units are degrees of declination."[14]

"In the [fifth figure at the right is shown] the differential flux limit for two different assumptions of the spectral index, alpha. We compare this result to AMANDA-B10 and to the average gamma ray flux from Mrk 501 as observed in 1997, a period of high activity. Also shown is the intrinsic source flux after correction of [infrared] IR absorption (de Jager and Stecker)."[14]

"Although Mrk 501 was not very active in 2000, the figure suggests that AMANDA-II has achieved the requisite sensitivity to observe neutrinos during the active period if the neutrino to photon ratio is one."[14]

"The [table] provides upper limits for a selection of candidate sources, and compares the results to limits previously published for AMANDA-B10. The units for columns 3 and 4 are 10-8 cm-2s-1."[14]

## Objects

"The extremely low ambient photon flux in deep ice provides the opportunity to monitor the galaxy for supernova explosions. Supernova events are expected to generate neutrinos at low energies (< 20 MeV), nominally too low of an energy to trigger AMANDA electronics. However, a nearby supernova blast would generate so many neutrinos that enough of them would interact within 10m of each AMANDA OM and produce Cherenkov light. The extra photons could contribute the average "noise" rate from each OM. By summing the signals from each OM, a statistically significant signature of a supernova can be obtained. We have installed special electronics to read out and sum the "noise" rates from each OM."[14]

"AMANDA-B10 can monitor about 68% of the stars in our galaxy, and AMANDA-II can reach 95% of the stars in our galaxy."[14]

## Electromagnetics

"Charged-current charged pion production (CC þ) is a process in which a neutrino interacts with an atomic nucleus and produces a muon, a charged pion, and recoiling nuclear fragments."[15]

## Absorptions

The figure shows the absorption length as a function of depth. Credit: P. Buford Price and the Amanda Collaboration.

The figure shows the average scattering coefficent (1/scattering length) as a function of depth. Credit: P. Buford Price and the Amanda Collaboration.

"The right figure shows the absorption length as a function of depth. The bulk of the scientifically-useful optical sensors in AMANDA are embedded between 1500 and 1900 m beneath the surface."[14]

"The optical properties of in situ ice beneath the south pole are measured by a combination of in situ N2 lasers, DC lamps, and YAG laser pulses from the surface. The properties vary with depth due to climatological variation such as ice ages. [...] The two properties that most strongly affect the reconstruction capabilities of AMANDA-II are absorption and scattering."[14]

"The absorption strongly depends on wavelength. Notice [in the figure at right] that the absorption also depends on depth at wavelengths where the absorption coefficient is relatively small. For short wavelengths, the absorption coefficient is small and dust contributes significantly, which is responsible for the depth dependence. At 532nm, the absorption coefficient is large, and the value is largely determined by intrinsic properties of ice (i.e, the roll of dust is less obvious)."[14]

"The [second figure at right] shows the average scattering coefficent (1/scattering_length) as a function of depth. Note that the effective scattering length, L_eff, is (approximately) the average length to isotropize the direction of all but 1/e of the photons. This important parameter for diffusion calculations is related to the geometric scattering length by L_eff=L_geo/(1-<cos(angle)>). The solid curve shows the coefficient of the scattering length for 400 nm light. Other colors behave differently due to the slight dependence of the scattering length on wavelength."[14]

"At depths below 1400m, dust is responsible for light scattering in ice. The rapid rise in scattering at shallow depths (relative to the surface) is due to onset of air bubbles trapped in the ice. The dashed blue line shows the intrinsic scattering from dust in the region dominated by air bubbles."[14]

The "maximum absorption length is slightly more than 100m at AMANDA-II depths, but the scattering length is only 20m for wavelengths that correspond to the longest absorption lengths."[14]

## Backgrounds

"To reduce the background of ordinary cosmic ray showers, several large air shower experiments emphasize measurement of the muon content of the shower. Ironically, early indications are that the signal seems to have the same muon content as the background."[16]

"The main background to the upgoing muon flux is atmospheric neutrinos generated by cosmic ray collisions. At high energy energies, direct production by charm decay becomes important, although the predicted fluxes have large uncertainty. As the neutrino energies increase beyond 107 GeV, most of the signal comes from above or very near the horizon and perhaps prompt MUONs from charm quark decay become a significant background. The importance of the background depends on the magnitude of the flux and detector energy and angular resolution. Fortunately, the sensitivity of AMANDA-II is not impacted by charm contributions for the most of the favored models of charm production in the atmosphere."[14]

## Meteors

"Scaling the lower-latitude, higher-altitude measurements from the Sierra Nevada and Meteor Crater to sea level and high latitude involves choosing an effective geomagnetic latitude for the duration of exposure, determining the contribution of muons to 10Be and 26Al production as a function of altitude and latitude, and determining how instantaneous production rates have changed over the duration of exposure at each site."[17]

By "assuming muon production is inconsequential at sea level (Brown et al., 1995), scaling the three data sets for spallation only, and incorporating a geomagnetically-driven production rate forcing model (Clark et al., 1995; Clapp and Bierman, in review), the three different production rate estimates can be reconciled to within several percent if the exposure age of the Sierra Nevada calibration sites is taken to be 13.5 ky as suggested by Clark et al. (1995)."[17]

## Cosmic rays

"The muons created through decays of secondary pions and kaons are fully polarized, which results in electron/positron decay asymmetry, which in turn causes a difference in their production spectra."[18]

## Neutrals

Single π0 production occurs "in neutral current neutrino interactions with water by a 1.3 GeV wide band neutrino beam."[19]

## Subatomics

"High energy neutrinos may interact to produce a large cascade of particles. In this case, the production of Cherenkov light remains localized and the photons propagation radially outward (well, almost). The effective volume of AMANDA is much smaller for cascades than muons and the angular resolution is very poor, but there are several interesting features of cascades that make them useful to study. First, the energy resolution of the cascade event can be measured with much better precision relative to the muon signature if the vertex of the interaction is contained. Second, the backgrounds from atmospheric electron neutrinos is much smaller than muon neutrinos at these energies because the decay of atmospheric muons is suppressed by time dilation. Third, cascades are produced by electron neutrinos and tau neutrinos so the ratio of cascades to muon neutrino events provides insight on the properties of neutrino oscillation. Fourth, even downgoing neutrinos can be observed if the energy is larger than ~10 TeV. Thus, the cascade technique is sensitive to neutrinos from any direction."[14]

"Like with accelerator physics, most of the interest [in] neutrino astrophysics is at the extreme energy frontier, which we label "extreme high energy" or EHE. Perhaps the most reliable flux predictions (after atmospheric neutrinos) involve the GZK mechanism. Neutrinos are produced by the inevitable collisions between cosmic rays and the cosmic microwave background. Although the physics required by GZK mechanism is straightforward, the GZK mechanism is still in doubt because one of its predictions has not yet been confirmed. The GZK mechanism predicts are rather strong upper limit on the energy of the cosmic ray, but this upper limit has not yet been clearly identified."[14]

"Experimentally, neutrinos at EHE energies are difficult to detect. As the neutrino energies increase to 1 PeV (1015 eV), the earth becomes opaque except near the horizon. We have developed a new technique to search for "downgoing" nearly horizontal muons. They can be distinguished from the blizzard of downgoing muons from cosmic ray collisions because the energies are much higher than muons generated by cosmic ray collisions. Consequently, the topologies of the events [...] are quite different from the typical event. [A] large number of OMs [...] observe Cherenkov light. The effective detection area for muons at these energies is very large, typically 0.2 km2 for AMANDA-B10!"[14]

"The effective detection area of AMANDA-II is even larger than B10. In addition, we upgraded the data acquisition system of AMANDA-II. The new system records the complete waveform from all (usable) OMs in the array. This should dramatically improve the dynamic range of the photon measurement and allow far better energy reconstruction for these high energy events."[14]

"The EHE analysis relies on training a neural net (NN2) to separate background from signal."[14]

Without a nucleus to absorb momentum, a photon decaying into electron-positron pair (or other pairs for that matter such as a muon and anti-muon or a tau and anti-tau can never conserve energy and momentum simultaneously.[20]

## Neutrons

The image is a schematic view of the Mount Norikura solar neutron telescope. Credit: Y. Muraki, K. Murakami, M. Miyazaki, K. Mitsui. S. Shibata, S. Sakakibara, T. Sakai, T. Takahashi, T. Yamada, and K. Yamaguchi.

A "new detector to observe solar neutrons [has been in operation] since 1990 October 17 [...] at the Mount Norikura Cosmic Ray Laboratory (CRL) of [the] Institute for cosmic Ray Research, the University of Tokyo."[21]

"The solar neutron telescope [image at right] consists of 10 blocks of scintillator [...] and several lead plates which are used to place kinetic energies Tn of incoming particles into three bands (50-360 MeV, 280-500 MeV, and ≥ 390 MeV)."[21] The telescope is inclined to the direction of the Sun by 15°.[21] The plane area of the detector is 1.0 m2 and protected by lead plates (Pb) to eliminate gamma-ray and muon background from the side of the detector.[21] The anti-coincident counter (A) is used to reject the muons and gamma rays, coming from the side of the detector and the top scintillators.[21] (P) and (G) are used to identify the proton events and gamma rays.[21] The central scintillator blocks are optically separated into 10 units.[21]

"The horizontal scintillator just above the 10 vertical scintillators distinguishes neutral particles (neutrons) from the charged particles (mainly muons, protons and electrons)."[21]

## Protons

Nucleon spin structure describes the partonic structure of proton intrinsic angular momentum (spin). The key question is how the nucleon's spin, whose magnitude is 1/2ħ, is carried by its [suggested] constituent partons (quarks and gluons). In the late 1980s, the European Muon Collaboration (EMC) conducted experiments that suggested the spin carried by quarks is not sufficient to account for the total spin of [protons]. This finding astonished particle physicists at that time, and the problem of where the missing spin lies is sometimes referred to as the "proton spin crisis".

Experimental research on these topics has been continued by the Spin Muon Collaboration (SMC) and the COMPASS experiment at CERN, experiments E154 and E155 at [SLAC National Accelerator Laboratory] SLAC, HERMES at DESY, experiments at [Thomas Jefferson National Accelerator Facility] JLab and RHIC, and others. Global analysis of data from all major experiments confirmed the original EMC discovery and showed that the quark spin may contribute about 30% to the total spin of the nucleon.

For antiproton-proton annihilation at rest, a meson result is, for example,

${\displaystyle p^{+}+{\bar {p}}^{-}\rightarrow \pi ^{+}+\pi ^{-}}$ [22] and
${\displaystyle {\pi }^{+}\rightarrow {\mu }^{+}+{\nu }_{\mu }\rightarrow e^{+}+{\nu }_{e}+{\bar {\nu }}_{\mu }+{\nu }_{\mu }.}$ [23]

## Electrons

The diagram shows a delta electron knocked out by a 180 GeV muon at the SPS at CERN Credit: Wilcokoppert.

"Each [optical module] OM contains a 10 inch [photo-multiplier tube] PMT that detects individual photons of Cerenkov light generated in the optically clear ice by muons and electrons moving with velocities near the speed of light."[24]

## Neutrinos

The diagram plots the measured and expected fluxes of natural and reactor neutrinos. Credit: Christian Spiering.

This is the first neutrino sky map. Credit: Christian Spiering and Krishnaswamy.

One of the first upward moving muons from a neutrino interaction is illustrated. Credit: Christian Spiering.

The figure shows the muon reconstructed zenith. Credit: Christian Spiering.

Equatorial skymap of neutrino-induced muon events from 295 days of ANTARES data in 2007/2008. Credit: Christian Spiering.

A neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor.

The image at right shows the measured "and expected fluxes of natural and reactor neutrinos [...] The energy range from keV to several GeV is the domain of underground detectors. The region from tens of GeV to about 100 PeV, with its much smaller fluxes, is addressed by Cherenkov light detectors underwater and in ice. The highest energies are only accessible with huge detector volumes".[25]

The second image at right is the "first neutrino sky map with the celestial coordinates of 18 KGF neutrino events [...] Due to uncertainties in the azimuth, the coordinates for some events are arcs rather than points. The labels reflect the numbers and registration mode of the events (e.g. "S" for spectrograph). Only for the ringed events the sense of the direction of the registered muon is known."[25]

"Sufficiently energetic muons produced in [...] interactions [in the Earth atmosphere are called] "atmospheric muons [...] Upward-going muons must have been produced in neutrino interactions."[25]

The third image at right illustrates the "Baikal Neutrino Telescope NT200. [...] One of the first upward moving muons from a neutrino interaction recorded with the 4-string stage of the detector in 1996 [...] The Cherenkov light from the muon is recorded by 19 channels."[25]

The fourth image at right contains the number "of reconstructed muons in the 2008 ANTARES data, as a function of the reconstructed zenith angle (black error bars). Also indicated are the simulation results for atmospheric muons (red dashed), and muons induced by atmospheric neutrinos (blue). The shaded band indicates the systematic uncertainties."[25]

The fifth image at right shows an equatorial "skymap of neutrino-induced muon events from 295 days of ANTARES data in 2007/2008. The background color scale indicates the sky visibility in percent of the time. The most significant accumulation of events, marked with a red circle, is fully compatible with the background expectation"[25]

## Gamma rays

"Gamma Ray Bursts (or GRBs) are the most spectacular and powerful explosions in the sky. Their duration lasts from milliseconds to hundreds of seconds, and they tend to cluster into two distinct populations. They are also extremely distant, with redshifts exceeding Z=1, although most of what is known about distances is deduced from the longer duration GRBs. We search for correlation between the GRB event time and location provided by gamma ray satellites. Unfortunately, one of the most powerful detectors (called BATSE on the Compton Gamma Ray Observatory) ceased operation in May of 2000. To increase our search exposure, we have examined BATSE bursts that were uncovered offline by additional analysis (termed "non-triggered" bursts) and GRBs identified by the Interplanetary Network (IPN) of satellites."[14]

"The most critical feature of GRB analysis is the very modest background rejection requirements. GRB emit gamma radiation over short duration, typically less than 100s. Satellites provide time and direction information so the analysis needs to reject only non-neutrino events that happen to occur at the right time and reconstruct with the right direction. The upshot: the effective size of AMANDA-II for GRB analysis approaches 50,000 m2 for muons created by neutrinos."[14]

## X-rays

"Resonant formation of dμt molecules in collisions of muonic tritium (μt) on D2 was investigated using a beam of μt atoms, demonstrating a new direct approach in muon catalyzed fusion studies. [...] Reactions of muonic hydrogen atoms and molecules present a sensitive testing ground for few-body theories involving strong, weak, and electromagnetic interactions. [...] muon catalyzed fusion (μCF) in a deuterium–tritium mixture has [...] one muon [...] catalyze more than 100 nuclear fusions between deuteron and triton (d + t → α + n) [1,2]. [...] The Ge detector monitored target impurities via muonic X-rays".[26]

"The muonic X -rays lines serve as highly accurate calibration lines."[27]

## Opticals

"The arrival times of the Cerenkov photons in 6 optical sensors determine the direction of the muon track."[24]

"The optical requirements on the detector medium are severe. A large absorption length is needed because it determines the required spacing of the optical sensors and, to a significant extent, the cost of the detector. A long scattering length is needed to preserve the geometry of the Cerenkov pattern. Nature has been kind and offered ice and water as natural Cerenkov media. Their optical properties are, in fact, complementary. Water and ice have similar attenuation length, with the roles of scattering and absorption reversed. Optics seems, at present, to drive the evolution of ice and water detectors in predictable directions: towards very large telescope area in ice exploiting the long absorption length, and towards lower threshold and good muon track reconstruction in water exploiting the long scattering length."[24]

## Superluminals

"[S]uperluminal neutrinos may lose energy rapidly via the bremsstrahlung [Cherenkov radiation] of electron-positron pairs ${\displaystyle (\nu \rightarrow \nu +e^{-}+e^{+}).}$ "[28]

Assumption:

"muon neutrinos with energies of order tens of GeV travel at superluminal velocity."[28]

For "all cases of superluminal propagation, certain otherwise forbidden processes are kinematically permitted, even in vacuum."[28]

Consider

${\displaystyle \nu _{\mu }\rightarrow {\begin{bmatrix}{\nu _{\mu }+\gamma }&(a)\\{\nu _{\mu }+\nu _{e}+{\overline {\nu }}_{e}}&(b)\\{\nu _{\mu }+e^{+}+e^{-}}&(c)\end{bmatrix}}}$ [28]

"These processes cause superluminal neutrinos to lose energy as they propagate and ... process (c) places a severe constraint upon potentially superluminal neutrino velocities. ... Process (c), pair bremsstrahlung, proceeds through the neutral current weak interaction."[28]

"Throughout the shower development, the electrons and positrons which travel faster than the speed of light in the air emit Cherenkov radiation."[29]

"High energy processes such as Compton, Bhabha, and Moller scattering, along with positron annihilation rapidly lead to a ~20% negative charge asymmetry in the electron-photon part of a cascade ... initiated by a ... 100 PeV neutrino"[30].

## Plasma objects

When analyzing the outcome of some experiments with muons incident on a hydrogen bubble chamber in 1956, muon-catalysis of exothermic p-d, proton and deuteron, nuclear fusion [was observed], which results in a helion, a gamma ray, and a release of about 5.5 MeV of energy.[31]

In muon-catalyzed fusion there are more fusions because the presence of the muon causes deuterium nuclei to be 207 times closer than in ordinary deuterium gas.[32][33]

## Rocky objects

"Isotopes termed "cosmogenic" are produced primarily by four types of interactions between particles and target nuclei: spallation, muon capture, neutron activation, and alpha particle interaction. Different production pathways dominate at different depths below Earth's surface. [...] Muons, charged particles of low mass, can interact with the nucleus of target atoms. For instance, interactions between muons and 40Ca and 28Si produce 36Cl and 26Al, respectively. Muons interact less strongly with matter than fast neutrons; therefore muon-induced isotope production rates are lower and muon penetration depths greater than those characteristic of neutron spallation."[34]

Thermal neutrons which are absorbed to produce 36Cl from 35Cl and 41Ca from 40Ca "result either from the interaction and slowing of fast neutrons and muons or, indirectly, from the decay of U, th, and their daughter nuclides."[34]

"Understanding the depth distribution of cosmogenic isotope production is important for deciphering cosmogenic isotope abundances both in terms of erosion rates and exposure ages."[34]

Isotopes "such as 36Cl and 41Ca [...] are produced in significant quantities by thermal neutron activation [...] the distribution of thermal neutrons with depth is not well modeled by an exponential expression [...] isotope production by thermal neutrons actually increases between the surface and a depth of about 15 cm resulting in the possible overestimation of 36Cl exposure ages if samples are inadvertently collected from ending surfaces."[34]

"In order to measure cosmogenic 26Al reliably, the mineral phase [of quartz] must contain low levels of the stable isotope, 27Al; quartz is ideal as it usually contains less than 100 ppm of Al."[34]

Atmospheric "production of [...] 36Cl is significant [...] For young samples, exposed at low elevations, radiogenic production can account for significant portion of the measured 36Cl".[34]

Several "boulders in a roadcut through a moraine in the Bishop Creek drainage, east side of the Sierra Nevada, California [...] shielded by >8 m of till, have ratios of 36Cl/Cl between 50 and 100 x 10-15, of which only about half can be explained by radiogenic production."[34]

"Some isotopes, such as 36Cl and 26Al, have important muon production pathways and are produced in significant abundances several meters below the ground surface. As a result, one would suspect that the likelihood of inheriting 36Cl or 26Al might be higher [than] the likelihood of inheriting 14C from a prior exposure. [... There is] the potential for significant 36Cl inheritance if boulders had previous exposure histories within several meters of Earth's surface."[34]

"Cosmogenically determined (36Cl) erosion rates for granitic landforms in the southern United States are similar to those reported from other locations."[34]

## Astrochemistry

"There is both direct and indirect evidence that magnetic field intensity and therefore isotope production rates have changed significantly and irregularly over the Pleistocene Epoch [...] There is also evidence for short periods of exceptionally high rates of isotope production [...] if an accurate, average production rate could be determined for the past 30 kyr, production rate variations would result in age deviations no larger than 16 % for Holocene samples and less than 10 % for Pleistocene samples [... For] samples younger than 15 kyr [...], a period of higher than average field strength and thus lower than average isotope production [may have yielded different production rate calibrations]."[34]

Combining isotope dating techniques may often lead to consistent results. For example, prior "exposure of clasts on alluvial fans and beach ridges is suggested by the 26Al and 10Be data [...] and by the depth/production rate calculations for 36Cl".[34]

## Hydrogens

Muonium is an exotic atom made up of an antimuon and an electron[35]

During the muon's 2.2 µs lifetime, muonium can enter into compounds such as muonium chloride (MuCl) or sodium muonide (NaMu).[36] Due to the mass difference between the antimuon and the electron, muonium (${\displaystyle {\bar {\mu }}^{+}e^{-}}$ ) is more similar to atomic hydrogen (p+e-) than positronium] (e+e-). Its Bohr radius and ionization energy are within 0.5% of hydrogen, deuterium, and tritium.[37]

Although muonium is short-lived, physical chemists use it in a modified form of electron spin resonance spectroscopy for the analysis of chemical transformations and the structure of compounds with novel or potentially valuable electronic properties. (This form of electron spin resonance (eSR) is called muon spin resonance (μSR).)

There are variants of μSR, e.g. muon spin rotation, which is affected by the presence of a magnetic field applied transverse to the muon beam direction (since muons are typically produced in a spin-polarized state from the decay of pions), and avoided level crossing (ALC), which is also called level crossing resonance (LCR).

The latter employs a magnetic field applied longitudinally to the beam direction, and monitors the relaxation of muon spins caused by magnetic oscillations with another magnetic nucleus.

Because the muon is a lepton, the atomic energy levels of muonium can be calculated with great precision from quantum electrodynamics (QED), unlike the case of hydrogen, where the precision is limited by uncertainies related to the internal structure of the proton. For this reason, muonium is an ideal system for studying bound-state QED and also for searching for physics beyond the standard model.[38]

## Nitrogens

"The [cosmic-ray] shower can be observed by: i) sampling the electromagnetic and hadronic components when they reach the ground with an array of particle detectors such as scintillators, ii) detecting the fluorescent light emitted by atmospheric nitrogen excited by the passage of the shower particles, iii) detecting the Cerenkov light emitted by the large number of particles at shower maximum, and iv) detecting muons and neutrinos underground."[24]

## Ions

"Muons are the most numerous energetic charged particles at sea level. A charged particle cannot avoid losing energy by ionization. As it passes through matter the charged particle interacts with the electric fields and typically knocks loose some of the loosely bound outer electrons. A muon interacts very little with matter except by ionization. Because of this, muons can travel large distances and commonly reach the ground. However, they lose energy proportional to the amount of matter they pass. This is proportional to the density (g/cm3) times the path length (cm). This "interaction length" has units of grams per square centimeter."[39]

"Muons lose energy at a fairly constant rate of about 2 MeV per g/cm2. Since the vertical depth of the atmosphere is about 1000 g/cm2, muons will lose about 2 GeV to ionization before reaching the ground. The mean energy of muons at sea level is still 4 GeV. Therefore the mean energy at creation is probably about 6 GeV."[39]

"The atmosphere is so tenuous at higher altitudes that even at 15,000 m it is still only 175 g/cm2 deep. Typically, it is about here that most muons are generated. Muons arrive at sea level with an average flux of about 1 muon per square centimeter per minute. This is about half of the typical total natural radiation background."[39]

"Muons (and other particles) are generated within a cone-shaped shower, with all particles staying within about 1 degree of the primary particle's path."[39]

"Muons arriving at some angle q from the vertical will have traveled a pathlength that increases as 1/cos (q). [...] This assumes that the Earth is essentially flat (less than 1% error for q < 70°) and that muons do not decay over the extended path length."[39]

"If we assume that twice the path length would attenuate the muons to half as many, then we would expect the muon flux to vary as the cos (q). However, the observed distribution is proportional to cos2 (q). This is a difference of less than 10% at an angle of 27° and 20% at 43°. This disparity may be primarily due to the impending decays of muons, as the path length exceeds their range."[39]

## Atmospheres

The figure shows the differential flux of atmospheric neutrinos. Credit: Amanda Collaboration.

The zenith angle distribution is compared with [Monte Carlo] MC predictions in the figure. Credit: Amanda Collaboration.

"The figure [at right] shows the differential flux of atmospheric neutrinos. The enormous effective volume allows AMANDA-II to measure the flux to much higher energies than any previous detector. The solid black lines show the theoretical expectation for both horizontal (upper) and vertical (lower) orientations."[14]

"The atmospheric neutrino analysis concentrates on signal purity. The distribution [shown] on the right is from [the] 2000 data sample. It is consistent with expectations from atmospheric neutrinos because 1) the observed events are distributed approximately isotropically, 2) the distribution of the number of [optical modules] OMs participating in the event (which is correlated with energy) is consistent with a soft spectra, 3) the shape of the zenith angle distribution of events is consistent with expectation (see figure for Diffuse Flux), 4) the absolute number of events is within 30% of expectation, consistent with systematic uncertainty of the predictions, and 5) upon visual inspection, the events topology is consistent with upgoing neutrino events. Recently, we have developed an accurate energy estimator, allowing us to plot the differential flux of the sum of atmospheric muon neutrinos and anti-neutrinos."[14]

"The zenith angle distribution is compared with [Monte Carlo] MC predictions in the [second figure at the right]. Horizontal events have sin(declination)=0, and upward vertical events have sin(declination)= +1. AMANDA-II has vastly improved sensitivity near the horizon compared to AMANDA-B10 due to the fact that it is much wider. Note that AMANDA-II has very little sensitivity to neutrino oscillations due to its relatively large energy threshold, although we have included such effects in the predicted flux."[14]

"The major problems associated with the balloon borne positron measurements are (i) the unique identification against a vast background of protons, and (ii) corrections for the positrons produced in the residual atmosphere."[40]

"[T]o account for the atmospheric corrections ... first [use] the instrument to determine the negative muon spectrum at float altitude. ... [Use this] spectrum ... to normalize the analytically determined atmospheric electron-positron spectra. ... most of the atmospheric electrons and positrons at small atmospheric depths are produced from muon decay at [the energies from 0.85 to 14 GeV]."[40]

## Spectrometers

This is the HiFi muon spectrometer. Credit: Peter Baker and James Lord.

"Positive muons are used to investigate magnetic order and dynamics in many magnetic systems. They are implanted into the sample where they stop at sites of high electronegativity and the time-evolution of their spin direction is monitored by measuring the direction of positrons emitted when they subsequently decay. Previously there had not been any studies of magnetization plateaux using the technique and it was interesting to find out what information could be obtained from such an experiment. Ca3Co2O6 was an ideal starting point because it has a broad magnetization plateau in a field range accessible to the new HiFi muon spin relaxation spectrometer at ISIS."[41]

## Coronal clouds

"Neutrinos can be produced by energetic protons accelerated in solar magnetic fields. Such protons produce pions, and therefore muons, hence also neutrinos as a decay product, in the solar atmosphere."[42]

## Earth

A "measurement of the ratio of positive to negative muon fluxes from cosmic ray interactions in the atmosphere [has been made], using data collected by the CMS detector both at ground level and in the underground experimental cavern at the CERN LHC. Muons were detected in the momentum range from 5 GeV/c to 1 TeV/c. The surface flux ratio is measured to be 1.2766±0.0032 (stat.) ±0.0032 (syst.), independent of the muon momentum, below 100 GeV/c."[43]

"The muon charge ratio R is defined as the ratio of the number of positive- to negative-charge atmospheric muons arriving at the Earth’s surface."[43]

"These muons arise from showers produced in interactions of high-energy cosmic ray particles with air nuclei in the upper layers of the atmosphere. The magnitude and the momentum dependence of R are determined by the production and interaction cross sections of mesons (mainly pions and kaons), and by their decay lengths. As most cosmic rays and the nuclei with which they interact are positively charged, positive meson production is favoured, hence more positive muons are expected. Previous measurements from various experiments [1–8] showed the muon charge ratio to be constant up to a momentum of about 200 GeV/c, and then to increase at higher momenta, in agreement with the predicted rise in the fraction of muons from kaon decays. Measurements of the charge ratio can be used to constrain hadronic interaction models and to predict better the atmospheric neutrino flux."[43]

"The Compact Muon Solenoid (CMS) [9] is one of the detectors installed at the Large Hadron Collider (LHC) [10] at CERN. The main goal of the CMS experiment is to search for signals of new physics in proton-proton collisions at centre-of-mass energies from 7 to 14 TeV [11]."[43]

"Cosmic rays were used extensively to commission the CMS detector [12, 13]. These data can also be used to performmeasurements of physical quantities related to cosmic ray muons."[43]

"About 25 million cosmic-muon events were recorded [on the Earth's surface] during the first phase of the MTCC with the magnet at a number of field values ranging from 3.67 to 4.00 T."[43]

"The CRAFT08 campaign was a sustained data-taking exercise in October and November 2008 with the CMS detector fully assembled in its final underground position. The full detector, ready for collecting data from LHC, participated in the run, with the magnet at the nominal field of 3.8 T. Approximately 270 million cosmic-muon events were recorded."[43]

"Single cosmic muons are simulated using the Monte Carlo event generator CMSCGEN [18, 19], which makes use of parameterizations of the distributions of the muon energy and incidence angle based on the air shower program CORSIKA [20]. The CMS detector response is simulated using the GEANT4 program [21], which takes into account the effects of energy loss, multiple scattering, and showering in the detector. A map [19] describing the various materials between the Earth’s surface and the CMS detector is used to obtain the average expected energy loss of simulated muons as a function of their energy, impact point, and incidence direction at the surface."[43]

"Muon tracking in CMS can be performed with the all-silicon tracker at the heart of the detector, and with either three or four stations of muon chambers installed outside the solenoid, sandwiched between steel layers serving both as hadron absorbers and as a return yoke for the magnetic field."[43]

"Three types of muon-track reconstruction were designed for cosmic muons not originating from an LHC proton-proton collision [22]: a standalone-muon track includes only hits from the muon detectors; a tracker track includes only hits from the silicon tracker; and a global muon track combines hits from the muon system and the silicon tracker in a combined track fit. For a cosmic muon that crosses the whole CMS detector, illustrated in Fig. 1 (top), each of the above types of tracks can be fitted separately in the top and bottom halves of CMS. Alternatively, a single track fit can be made including hits from the top and bottom halves of CMS. The direction of the muon is assumed to be downwards, and the muon charge is defined accordingly."[43]

"The analysis based on 2006 MTCC data uses standalone muons."[43]

"Since the muons were measured only in one half of the detector, the momentum resolution is poorer than in the standalone-muon analysis using the complete detector. Having the detector on the surface, however, permitted the collection of a large number of low-momentum muons, down to a momentum of 5 GeV/c, allowing for a precise measurement of the charge ratio in the low-momentum range."[43]

## Moon

This is a contour plot of the muon deficit measured by IceCube in the region around the Moon's position. Credit: Silvia Bravo.

At right of the top of the resource is an image of the Moon's cosmic ray shadow, as seen in secondary muons generated by cosmic rays in the atmosphere, and detected 700 meters below ground, at the Soudan II detector.

"Earth-based telescopes such as IceCube use the cosmic-ray shadow cast by the Moon to calibrate their angular resolution and their pointing accuracy for identifying point-like sources. The first impacts on the size of source signal in the detector, while the second constrains the precision with which the detector can estimate the direction of the incoming particles."[44]

"The observation of a cosmic-ray deficit from the direction of the Moon with the IceCube Neutrino Observatory is thus an important milestone in proving its potential in the search for point-like sources of astrophysical neutrinos. A recent measurement of the Moon shadow in TeV cosmic rays with the IceCube telescope sets an upper limit on the detector’s absolute pointing accuracy to 0.2 degrees. The Antarctic telescope has observed the Moon shadow with a high significance (over 6 sigma), and the Moon’s center has been measured to be statistically consistent with its actual location."[44]

"The search for neutrinos coming from gamma-ray bursts (GRBs), for example, is very sensitive to the absolute pointing accuracy of IceCube."[44]

"In this case, the position in the sky of the GRB is compared to nearby events detected within a time window around the burst. If off by a few degrees, the sensitivity of IceCube to detect these potential sources of high-energy neutrinos would be significantly reduced."[45]

"The importance of the pointing accuracy is also highlighted in studies such as the cosmic-ray anisotropy map, which IceCube measured for the first time in the Southern Hemisphere."[44]

"Even though the search for point-like sources of astrophysical neutrinos uses data samples with a different energy distribution, the Moon shadow results indicate that high-energy neutrinos detected with IceCube will allow for identifying astrophysical point sources if enough statistics are available."[44]

"Two independent analysis methods were applied to data taken between April 2008 and May 2010, before the completion of the IceCube neutrino telescope. Both methods and data samples show consistent results, and they are the first statistically significant detection of the shadow of the Moon using a high-energy neutrino telescope."[44]

"The Moon shadow was measured as a deficit of downgoing muon events, which are the majority of events detected by IceCube and are generated by the interaction of cosmic rays with the Earth’s atmosphere. Only muons reaching the detector when the Moon was at least 15 degrees above the horizon were selected for analysis. Over 300 million events passed this initial cut, with about 68% of the events estimated to be produced by proton cosmic rays and another 23% by helium cosmic rays."[44]

"The width of the Moon shadow as measured by IceCube in its partial 40-string and 59-string configurations was around 0.7 degrees, in agreement with simulation studies."[44]

## Technology

This diagram depicts an air shower resulting from cosmic rays. Credit: Konrad Bernlöhr.

The Cherenkov telescopes do not actually detect the gamma rays directly but instead detect the flashes of visible light produced when gamma rays are absorbed by the Earth's atmosphere.[46]

## Observatories

This is an architecture diagram of IceCube. Credit: Nasa-verve.

This is the MAGIC telescope at La Palma, Canary Islands. Credit: Pachango.

VERITAS is located at the basecamp of the Smithsonian Astrophysics Observatory's Fred Lawrence Whipple Observatory (FLWO) in southern Arizona. Credit: VERITAS.

Two HEGRA reflectors, with the Nordic Optical Telescope (NOT) in the background. Credit: Bob Tubbs.

All four of the HESS telescope array in Namibia are in operation at night. Credit: H.E.S.S. collaboration.

"The IceCube Neutrino Observatory (or simply IceCube) is a neutrino telescope constructed at the Amundsen-Scott South Pole Station in Antarctica.[1] Similar to its predecessor, the Antarctic Muon And Neutrino Detector Array (AMANDA), IceCube contains thousands of spherical optical sensors called Digital Optical Modules (DOMs), each with a photomultiplier tube (PMT)[47] and a single board data acquisition computer which sends digital data to the counting house on the surface above the array.[48] IceCube was completed on 18 December, 2010, New Zealand time.[49]

As it rockets through the ice at nearly the speed of light, a muon produces a trail of blue light known as Cherenkov radiation that acts like an arrow pointing back in the direction of the neutrino’s origin."[50]

"The trick is to distinguish muons coming from the relatively few high-energy neutrinos from a sea of background muons, generated constantly by showers of lower-energy atmospheric neutrinos and other subatomic interactions. To help differentiate cosmic neutrinos from the background, IceCube’s DOMs are positioned to “look down” through the planet to the Northern Hemisphere. In effect, Earth’s interior acts as a filter. Because muons decay over distances of only a few kilometers, any muons that arrive at the detector from below must arise from neutrinos that have passed through the planet."[50]

"Neutrinos are further differentiated based on their energy: In general, the more energy a neutrino has, the more energy it imparts to a muon and the more blue light is emitted and detected. Still, sorting the data gathered by the detector is not simple, and a high degree of precision is required. Complex algorithms are needed to discern the direction and arrival times of thousands of muons per second."[50]

"A few hours later [after being turned on], ANTARES looked up at the sky for the first time and caught sight of its first muons."[51]

The Cherenkov telescopes do not actually detect the gamma rays directly but instead detect the flashes of visible light produced when gamma rays are absorbed by the Earth's atmosphere.[46]

The first astronomical observations started in the fall of 2004. However, the facility had its last observing runs in November 2005 as funds for observational operations from the National Science Foundation were no longer available.

CACTUS [Converted Atmospheric Cherenkov Telescope Using Solar-2] is sensitive in the 50-500 GeV energy range.[52]

"The CACTUS atmospheric Cherenkov telescope collaboration recently reported a gamma-ray excess from the Draco dwarf spheroidal galaxy."[53] "[T]he bulk of the signal detected by CACTUS [may come] from direct [weakly interacting massive particles (WIMPs)] WIMP annihilation to two photons"[53].

The Pierre Auger Observatory is an international cosmic ray observatory designed to detect ultra-high-energy cosmic rays: single sub-atomic particles (protons or atomic nuclei) with energies beyond 1020 eV (about the energy of a tennis ball traveling at 80 km/h). These high energy particles have an estimated arrival rate of just 1 per km2 per century, therefore the Auger Observatory has created a detection area the size of Rhode Island — over 3,000 km2 (1,200 sq mi) — in order to record a large number of these events. It is located in western Argentina's Mendoza Province, in one of the South American Pampas.

The basic set-up consists of 1600 water tanks (water Cherenkov Detectors, similar to the Haverah Park experiment) distributed over 3,000 square kilometres (1,200 sq mi), along with four atmospheric fluorescence detectors (similar to the High Resolution Fly's Eye) overseeing the surface array.

MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov Telescopes) is a system of two Imaging Atmospheric Cherenkov telescopes situated at the Roque de los Muchachos Observatory on [La Palma, one of the Canary Islands, at about 2200 m above sea level. MAGIC detects particle showers released by gamma rays, using the Cherenkov radiation, i.e., faint light radiated by the charged particles in the showers. With a diameter of 17 meters for the reflecting surface, it is the largest in the world. ... MAGIC is sensitive to cosmic gamma rays with energies between 50 GeV and 30 TeV due to its large mirror; other ground-based gamma-ray telescopes typically observe gamma energies above 200-300 GeV. Satellite-based detectors detect gamma-rays in the energy range from keV up to several GeV. ... MAGIC has found pulsed gamma-rays at energies higher than 25 GeV coming from the Crab Pulsar.[54] The presence of such high energies indicates that the gamma-ray source is far out in the pulsar's magnetosphere, in contradiction with many models. ... A much more controversial observation is an energy dependence in the speed of light of cosmic rays coming from a short burst of the blazar Markarian 501 on July 9, 2005. Photons with energies between 1.2 and 10 TeV arrived 4 minutes after those in a band between .25 and .6 TeV. The average delay was .030±.012 seconds per GeV of energy of the photon. If the relation between the space velocity of a photon and its energy is linear, then this translates into the fractional difference in the speed of light being equal to minus the photon's energy divided by 2 x 1017 GeV.

"VERITAS (Very Energetic Radiation Imaging Telescope Array System) is a ground-based gamma-ray instrument operating at the Fred Lawrence Whipple Observatory (FLWO) in southern Arizona, USA. It is an array of four 12m optical reflectors for gamma-ray astronomy in the GeV - TeV energy range. These imaging Cherenkov [a bluish light] telescopes are deployed such that they have the highest sensitivity in the VHE energy band (50 GeV - 50 TeV), with maximum sensitivity from 100 GeV to 10 TeV. This VHE observatory effectively complements the NASA Fermi mission."[55]

The Collaboration between Australia and Nippon for a Gamma Ray Observatory in the Outback, (CANGAROO) is for very high energy cosmic gamma ray observation by telescope detecting Cherenkov light. It is located on the Woomera Prohibited Area in South Australia. [56]

HEGRA, which stands for High-Energy-Gamma-Ray Astronomy, was an atmospheric Cherenkov telescope for Gamma-ray astronomy. With its various types of detectors, HEGRA took data between 1987 and 2002, at which point it was dismantled in order to build its successor, MAGIC, at the same site. HEGRA is at 2200 masl.

High Energy Stereoscopic System or H.E.S.S. is a next-generation system of Imaging Atmospheric Cherenkov Telescopes (IACT) for the investigation of cosmic gamma rays in the 100 GeV and TeV energy range. The acronym was chosen in honour of Victor Hess, who was the first to observe cosmic rays.

The name also emphasizes two main features of the currently-operating installation, namely the simultaneous observation of air showers with several telescopes, under different viewing angles, and the combination of telescopes to a large system to increase the effective detection area for gamma rays. H.E.S.S. permits the exploration of gamma-ray sources with intensities at a level of a few thousandth parts of the flux of the Crab Nebula.

H.E.S.S. is located on the Cranz family farm, Göllschau, in Namibia, near the Gamsberg, an area well known for its excellent optical quality. The first of the four telescopes of Phase I of the H.E.S.S. project went into operation in Summer 2002; all four were operational in December 2003.

## Detectors

The Compact Muon Solenoid (CMS) is an example of a large particle detector. Notice the person for scale. Credit: CERN.

"With γ ray energy 50 times higher than the muon energy and a probability of muon production by the γ's of about 1%, muon detectors can match the detection efficiency of a GeV satellite detector if their effective area is larger by 104."[1]

## Hypotheses

1. Muons may be the key to sustained fusion at any temperature.

## References

1. Francis Halzen, Todor Stanev, Gaurang B. Yodh (April 1, 1997). "γ ray astronomy with muons". Physical Review D Particles, Fields, Gravitation, and Cosmology 55 (7): 4475-9. doi:10.1103/PhysRevD.55.4475. Retrieved 2013-01-18.
2. Paolo Strolin (August 15, 2013). The secret life of volcanoes: using muon radiography. EIROforum. Retrieved 2014-03-22.
3. Terry W. Swanson and Marc L. Caffee (2001). "Determination of 36Cl Production Rates Derived from the Well-Dated Deglaciation Surfaces of Whidbey and Fidalgo Islands, Washington". Quaternary Research 56: 366-82. doi:10.1006/qres.2001.2278. Retrieved 2013-10-31.
4. B. Pontecorvo (1957). "Mesonium and anti-mesonium". Zh. Eksp. Teor. Fiz. 33: 549–551.  reproduced and translated in Sov. Phys. JETP 6: 429. 1957.  and B. Pontecorvo (1967). "Neutrino Experiments and the Problem of Conservation of Leptonic Charge". Zh. Eksp. Teor. Fiz. 53: 1717.  reproduced and translated in Sov. Phys. JETP 26: 984. 1968.
5. Derek Fabel (December 18, 2008). In-situ produced terrestrial cosmogenic nuclides. University of Glasgow. Retrieved 2014-03-21.
6. Poccil (18 October 2004). "muon". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 17 July 2019.
7. Vedant Koladiya (11 July 2019). "muon". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 17 July 2019.
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9. Equinox (5 October 2008). "antimuon". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 17 July 2019.
10. Conrad Ranzan (4 June 2016). "The Nature of Gravitational Collapse". American Journal of Astronomy and Astrophysics 4 (2): 15-33. doi:10.11648/j.ajaa.20160402.11. Retrieved 16 July 2019.
11. Pasquale Di Bari and Stephen F. King (2 October 2015). "Successful N2 leptogenesis with flavour coupling effects in realistic unified models". Journal of Cosmology and Astroparticle Physics 10: 008. doi:10.1088/1475-7516/2015/10/008. Retrieved 16 July 2019.
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