Misplaced Pages

#76923

98-825: The physics requirements of a future TeV-scale e + e − {\displaystyle e^{+}e^{-}} machine, such as the ILC, demand extremely high performance calorimetry. This is best achieved using a finely segmented system that allows to reconstruct events using the so-called "particle flow approach" (PFA). The calorimeter systems for high energy physics experiments usually consist of three main subsystems: electromagnetic calorimeter (ECAL) to detect electromagnetic showers produced by electrons (or positrons) and photons, hadronic calorimeter (HCAL) to measure hadron-induced showers, and muon tracker (or so-called tail catcher) to identify highly penetrating particles such as muons . CALICE has developed prototypes of

196-434: 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's but smaller than a proton's. Thus Anderson initially called

294-495: A 5- λ {\displaystyle \lambda } thick tail catcher to measure the hadronic shower leakage. The sampling calorimeter has been calibrated to get its signal vs. the incident particle energy dependence using test beams of different incident particle sorts with known energies in the range from 4 GeV to 120 GeV. The corrections for the calorimeter non-linearity and the external temperature influence have been taken into rooster. For test beams with energy 50 GeV

392-515: A Latin S ( [REDACTED] ). *Upsilon is also derived from waw ( [REDACTED] ). The classical twenty-four-letter alphabet that is now used to represent the Greek language was originally the local alphabet of Ionia . By the late fifth century BC, it was commonly used by many Athenians. In c. 403 BC, at the suggestion of the archon Eucleides , the Athenian Assembly formally abandoned

490-608: A colour-coded map in a seminal 19th-century work on the topic, Studien zur Geschichte des griechischen Alphabets by Adolf Kirchhoff (1867). The "green" (or southern) type is the most archaic and closest to the Phoenician. The "red" (or western) type is the one that was later transmitted to the West and became the ancestor of the Latin alphabet , and bears some crucial features characteristic of that later development. The "blue" (or eastern) type

588-522: A decay like μ → e + γ is technically possible in the Standard Model (for example by neutrino oscillation of a virtual muon neutrino into an electron neutrino), but such a decay is extremely unlikely and therefore should be experimentally unobservable. Fewer than one in 10 muon decays should produce such a decay. Observation of such decay modes would constitute clear evidence for theories beyond

686-606: A distinction between uppercase and lowercase. This distinction is an innovation of the modern era, drawing on different lines of development of the letter shapes in earlier handwriting. The oldest forms of the letters in antiquity are majuscule forms. Besides the upright, straight inscriptional forms (capitals) found in stone carvings or incised pottery, more fluent writing styles adapted for handwriting on soft materials were also developed during antiquity. Such handwriting has been preserved especially from papyrus manuscripts in Egypt since

784-581: A few years previously in Macedonia . By the end of the fourth century BC, it had displaced local alphabets across the Greek-speaking world to become the standard form of the Greek alphabet. When the Greeks adopted the Phoenician alphabet, they took over not only the letter shapes and sound values but also the names by which the sequence of the alphabet could be recited and memorized. In Phoenician, each letter name

882-779: 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 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 . Nonetheless, they are produced in great amounts in high-energy interactions in normal matter, in certain particle accelerator experiments with hadrons , and in cosmic ray interactions with matter. These interactions usually produce pi mesons initially, which almost always decay to muons. As with

980-419: A hundred 3 × 3 cm tiles in the center, surrounded by a large area covered with 6 × 6 cm tiles and finally enclosed by a strip of 12 × 12 cm tiles. These nearly 8000 tiles in total are read out individually by wavelength-shifting fibers which illuminate small silicon photomultipliers mounted on each tile and insensitive to large magnetic fields. The very important experimental part of this project

1078-451: A hydrogen atom than an inert helium atom. Muonic heavy hydrogen atoms with a negative muon may undergo nuclear fusion in the process of muon-catalyzed fusion , after the muon may leave the new atom to induce fusion in another hydrogen molecule. This process continues until the negative muon is captured by a helium nucleus, where it remains until it decays. Negative muons bound to conventional atoms can be captured ( muon capture ) through

SECTION 10

#1732887486077

1176-463: 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 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

1274-508: A new experiment at Fermilab using the E821 magnet improved the precision of this measurement. In 2020 an international team of 170 physicists calculated the most accurate prediction for the theoretical value of the muon's anomalous magnetic moment. Greek alphabet The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It was derived from

1372-449: A one cubic-meter steel/scintillator sandwich sampling hadronic calorimeter called physics prototype for study series in various test particle beams . High granularity is achieved by 38 scintillator tile layers . Each layer is a 2-cm thick steel plate 90 × 90 cm followed by a 0.5-cm scintillator plate that consists of more than 200 scintillator tiles. The mosaic of the HCAL layers exhibits

1470-537: 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, τ = ħ / Γ , of

1568-416: A random electron and with this electron forms an exotic atom known as muonium (mu) atom. In this atom, 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 mass of the electron is much smaller than the mass of both the proton and the muon, the reduced mass of muonium, and hence its Bohr radius ,

1666-404: A result of absorption or deflection by other atoms. When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions 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

1764-453: A seventh vowel letter for the long /ɔː/ (Ω, omega ) was introduced. Greek also introduced three new consonant letters for its aspirated plosive sounds and consonant clusters: Φ ( phi ) for /pʰ/ , Χ ( chi ) for /kʰ/ and Ψ ( psi ) for /ps/ . In western Greek variants, Χ was instead used for /ks/ and Ψ for /kʰ/ . The origin of these letters is a matter of some debate. Three of the original Phoenician letters dropped out of use before

1862-428: A time, a writing style with alternating right-to-left and left-to-right lines (called boustrophedon , literally "ox-turning", after the manner of an ox ploughing a field) was common, until in the classical period the left-to-right writing direction became the norm. Individual letter shapes were mirrored depending on the writing direction of the current line. There were initially numerous local (epichoric) variants of

1960-893: A ñ o é as in French é t é Similar to ay as in English overl ay , but without pronouncing y. ai as in English f ai ry ê as in French t ê te [ c ] before [ e ] , [ i ] q as in French q ui ô as in French t ô t r as in Spanish ca r o [ ç ] before [ e ] , [ i ] h as in English h ue Among consonant letters, all letters that denoted voiced plosive consonants ( /b, d, g/ ) and aspirated plosives ( /pʰ, tʰ, kʰ/ ) in Ancient Greek stand for corresponding fricative sounds in Modern Greek. The correspondences are as follows: Among

2058-648: Is also ⟨ ηι, ωι ⟩ , and ⟨ ου ⟩ , pronounced /u/ . The Ancient Greek diphthongs ⟨ αυ ⟩ , ⟨ ευ ⟩ and ⟨ ηυ ⟩ are pronounced [av] , [ev] and [iv] in Modern Greek. In some environments, they are devoiced to [af] , [ef] and [if] . The Modern Greek consonant combinations ⟨ μπ ⟩ and ⟨ ντ ⟩ stand for [b] and [d] (or [mb] and [nd] ); ⟨ τζ ⟩ stands for [d͡z] and ⟨ τσ ⟩ stands for [t͡s] . In addition, both in Ancient and Modern Greek,

SECTION 20

#1732887486077

2156-517: Is attested in early sources as λάβδα besides λάμβδα ; in Modern Greek the spelling is often λάμδα , reflecting pronunciation. Similarly, iota is sometimes spelled γιώτα in Modern Greek ( [ʝ] is conventionally transcribed ⟨γ{ι,η,υ,ει,οι}⟩ word-initially and intervocalically before back vowels and /a/ ). In the tables below, the Greek names of all letters are given in their traditional polytonic spelling; in modern practice, like with all other words, they are usually spelled in

2254-474: Is commonly held to have originated some time in the late ninth or early eighth century BC, conventionally around the year 800 BC. The period between the use of the two writing systems, Linear B and the Greek alphabet, during which no Greek texts are attested, is known as the Greek Dark Ages . The Greeks adopted the alphabet from the earlier Phoenician alphabet , one of the closely related scripts used for

2352-401: Is created by substituting a muon for one of the electrons in helium-4. The muon orbits much closer to the nucleus, so muonic helium can therefore be regarded like an isotope of helium whose nucleus consists of two neutrons, two protons and a muon, with a single electron outside. Chemically, muonic helium, possessing an unpaired valence electron , can bond with other atoms, and behaves more like

2450-447: Is no longer used by the physics community. Muons have a mass of 105.66   MeV/ c , which is approximately 206.768 2827 (46) ‍ times that of the electron, m e . There is also a third lepton, the tau , approximately 17 times heavier than the muon. Due to their greater mass, muons accelerate slower than electrons in electromagnetic fields, and emit less bremsstrahlung (deceleration radiation). This allows muons of

2548-562: Is now in progress: a combined test beam program involving exposure of combined prototype calorimeter system to real particle beams from different accelerators and subsequent data analysis. In test beam studies, the Tile-HCAL with an effective thickness 4.5 nuclear interaction lengths ( λ {\displaystyle \lambda } ) is headed by an electromagnetic calorimeter (Silicon-Tungsten) near 1- λ {\displaystyle \lambda } in thickness and followed by

2646-470: Is still conventionally used for writing Ancient Greek, while in some book printing and generally in the usage of conservative writers it can still also be found in use for Modern Greek. Although it is not a diacritic, the comma has a similar function as a silent letter in a handful of Greek words, principally distinguishing ό,τι ( ó,ti , "whatever") from ότι ( óti , "that"). There are many different methods of rendering Greek text or Greek names in

2744-497: 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 . The E821 experiment at Brookhaven and the Muon g-2 experiment at Fermilab studied the precession of the muon spin in a constant external magnetic field as

2842-408: Is the fraction of muons that are forward-polarized. Integrating this expression over electron energy gives the angular distribution of the daughter electrons: The electron energy distribution integrated over the polar angle (valid for x < 1 {\displaystyle x<1} ) is Because the direction the electron is emitted in (a polar vector) is preferentially aligned opposite

2940-460: Is the one from which the later standard Greek alphabet emerged. Athens used a local form of the "light blue" alphabet type until the end of the fifth century BC, which lacked the letters Ξ and Ψ as well as the vowel symbols Η and Ω. In the Old Attic alphabet, ΧΣ stood for /ks/ and ΦΣ for /ps/ . Ε was used for all three sounds /e, eː, ɛː/ (correspondinɡ to classical Ε, ΕΙ, Η ), and Ο

3038-409: Is used by particle physicists to produce muon beams, such as the beam used for the muon g −2 experiment . 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

CALICE - Misplaced Pages Continue

3136-510: Is very close to that of hydrogen . Therefore this bound muon-electron pair can be treated to a first approximation as a short-lived "atom" that behaves chemically like the isotopes of hydrogen ( protium , deuterium and tritium ). Both positive and negative muons can be part of a short-lived pi-mu atom consisting of a muon and an oppositely charged pion. These atoms were observed in the 1970s in experiments at Brookhaven National Laboratory and Fermilab . The anomalous magnetic dipole moment

3234-518: The Library of Congress , and others. During the Mycenaean period , from around the sixteenth century to the twelfth century BC, a script called Linear B was used to write the earliest attested form of the Greek language, known as Mycenaean Greek . This writing system, unrelated to the Greek alphabet, last appeared in the thirteenth century BC. Inscription written in the Greek alphabet begin to emerge from

3332-588: The West Semitic languages , calling it Greek : Φοινικήια γράμματα 'Phoenician letters'. However, the Phoenician alphabet was limited to consonants. When it was adopted for writing Greek, certain consonants were adapted in order to express vowels. The use of both vowels and consonants makes Greek the first alphabet in the narrow sense, as distinguished from the abjads used in Semitic languages , which have letters only for consonants. Greek initially took over all of

3430-410: The baryons , 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,

3528-415: The electron , with an electric charge of −1  e and spin-1/2 , 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. The muon is an unstable subatomic particle with a mean lifetime of 2.2  μs , much longer than many other subatomic particles. As with the decay of the free neutron (with

3626-413: The polytonic orthography and modern Greek keeping only the stress accent ( acute ) and the diaeresis . Apart from its use in writing the Greek language, in both its ancient and its modern forms, the Greek alphabet today also serves as a source of international technical symbols and labels in many domains of mathematics , science , and other fields. In both Ancient and Modern Greek, the letters of

3724-494: The rough breathing ( ἁ ), marking an /h/ sound at the beginning of a word, or the smooth breathing ( ἀ ), marking its absence. The letter rho (ρ), although not a vowel, also carries rough breathing in a word-initial position. If a rho was geminated within a word, the first ρ always had the smooth breathing and the second the rough breathing (ῤῥ) leading to the transliteration rrh. The vowel letters ⟨ α, η, ω ⟩ carry an additional diacritic in certain words,

3822-497: The speed of light . Although their lifetime without relativistic effects would allow a half-survival distance of only about 456 meters ( 2.197 μs × ln(2) × 0.9997 × c ) 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

3920-410: The weak force by protons in nuclei, in a sort of electron-capture-like process. When this happens, nuclear transmutation results: The proton becomes a neutron and a muon neutrino is emitted. A positive muon, when stopped in ordinary matter, cannot be captured by a proton since the two positive charges can only repel. The positive muon is also not attracted to the nucleus of atoms. Instead, it binds

4018-503: The (positive) muon is 2.196 9811 ± 0.000 0022   μs . The equality of the muon and antimuon lifetimes has been established to better than one part in 10 . Certain neutrino-less decay modes are kinematically allowed but are, for all practical purposes, forbidden in the Standard Model , even given that neutrinos have mass and oscillate. Examples forbidden by lepton flavour conservation are: and Taking into account neutrino mass,

CALICE - Misplaced Pages Continue

4116-432: The 22 letters of Phoenician. Five were reassigned to denote vowel sounds: the glide consonants /j/ ( yodh ) and /w/ ( waw ) were used for [i] (Ι, iota ) and [u] (Υ, upsilon ); the glottal stop consonant /ʔ/ ( aleph ) was used for [a] (Α, alpha ); the pharyngeal /ʕ/ ( ʿayin ) was turned into [o] (Ο, omicron ); and the letter for /h/ ( he ) was turned into [e] (Ε, epsilon ). A doublet of waw

4214-462: The 9th century, Byzantine scribes had begun to employ the lowercase form, which they derived from the cursive styles of the uppercase letters. Sound values and conventional transcriptions for some of the letters differ between Ancient and Modern Greek usage because the pronunciation of Greek has changed significantly between the 5th century BC and today. Additionally, Modern and Ancient Greek now use different diacritics , with ancient Greek using

4312-496: The Byzantine period, to distinguish between letters that had become confusable. Thus, the letters ⟨ο⟩ and ⟨ω⟩ , pronounced identically by this time, were called o mikron ("small o") and o mega ("big o"). The letter ⟨ε⟩ was called e psilon ("plain e") to distinguish it from the identically pronounced digraph ⟨αι⟩ , while, similarly, ⟨υ⟩ , which at this time

4410-444: The Earth's surface are created indirectly as decay products of collisions of cosmic rays with particles of the Earth's atmosphere. About 10,000 muons reach every square meter of the earth's surface a minute; these charged particles form as by-products of cosmic rays colliding with molecules in the upper atmosphere. Traveling at relativistic speeds, muons can penetrate tens of meters into rocks and other matter before attenuating as

4508-599: The Greek alphabet have fairly stable and consistent symbol-to-sound mappings, making pronunciation of words largely predictable. Ancient Greek spelling was generally near- phonemic . For a number of letters, sound values differ considerably between Ancient and Modern Greek, because their pronunciation has followed a set of systematic phonological shifts that affected the language in its post-classical stages. [ ʝ ] before [ e ] , [ i ] ; [ ŋ ] ~ [ ɲ ] Similar to y as in English y ellow; ng as in English lo ng; ñ as in Spanish

4606-466: The Greek alphabet, which differed in the use and non-use of the additional vowel and consonant symbols and several other features. Epichoric alphabets are commonly divided into four major types according to their different treatments of additional consonant letters for the aspirated consonants (/pʰ, kʰ/) and consonant clusters (/ks, ps/) of Greek. These four types are often conventionally labelled as "green", "red", "light blue" and "dark blue" types, based on

4704-423: The Greek-speaking world and is the version that is still used for Greek writing today. The uppercase and lowercase forms of the 24 letters are: The Greek alphabet is the ancestor of several scripts, such as the Latin , Gothic , Coptic , and Cyrillic scripts. Throughout antiquity, Greek had only a single uppercase form of each letter. It was written without diacritics and with little punctuation . By

4802-673: The Latin script. The form in which classical Greek names are conventionally rendered in English goes back to the way Greek loanwords were incorporated into Latin in antiquity. In this system, ⟨ κ ⟩ is replaced with ⟨c⟩ , the diphthongs ⟨ αι ⟩ and ⟨ οι ⟩ are rendered as ⟨ae⟩ and ⟨oe⟩ (or ⟨æ,œ⟩ ); and ⟨ ει ⟩ and ⟨ ου ⟩ are simplified to ⟨i⟩ and ⟨u⟩ . Smooth breathing marks are usually ignored and rough breathing marks are usually rendered as

4900-627: The Old Attic alphabet and adopted the Ionian alphabet as part of the democratic reforms after the overthrow of the Thirty Tyrants . Because of Eucleides's role in suggesting the idea to adopt the Ionian alphabet, the standard twenty-four-letter Greek alphabet is sometimes known as the "Eucleidean alphabet". Roughly thirty years later, the Eucleidean alphabet was adopted in Boeotia and it may have been adopted

4998-501: The Standard Model . Upper limits for the branching fractions of such decay modes were measured in many experiments starting more than 60 years ago. The current upper limit for the μ → e + γ branching fraction was measured 2009–2013 in the MEG experiment and is 4.2 × 10 . The muon decay width that follows from Fermi's golden rule has dimension of energy, and must be proportional to

SECTION 50

#1732887486077

5096-443: The Standard Model values of Michel parameters is where θ {\displaystyle \theta } is the angle between the muon's polarization vector P μ {\displaystyle \mathbf {P} _{\mu }} and the decay-electron momentum vector, and P μ = | P μ | {\displaystyle P_{\mu }=|\mathbf {P} _{\mu }|}

5194-479: The alphabet took its classical shape: the letter Ϻ ( san ), which had been in competition with Σ ( sigma ) denoting the same phoneme /s/; the letter Ϙ ( qoppa ), which was redundant with Κ ( kappa ) for /k/, and Ϝ ( digamma ), whose sound value /w/ dropped out of the spoken language before or during the classical period. Greek was originally written predominantly from right to left, just like Phoenician, but scribes could freely alternate between directions. For

5292-400: The combinations ⟨ γχ ⟩ and ⟨ γξ ⟩ . In the polytonic orthography traditionally used for ancient Greek and katharevousa , the stressed vowel of each word carries one of three accent marks: either the acute accent ( ά ), the grave accent ( ὰ ), or the circumflex accent ( α̃ or α̑ ). These signs were originally designed to mark different forms of

5390-547: The conventional letter correspondences of Ancient Greek-based transcription systems, and to what degree they attempt either an exact letter-by-letter transliteration or rather a phonetically based transcription. Standardized formal transcription systems have been defined by the International Organization for Standardization (as ISO 843 ), by the United Nations Group of Experts on Geographical Names , by

5488-415: 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 . Muon  g −2 ,

5586-457: The earlier Phoenician alphabet , and is the earliest known alphabetic script to have developed distinct letters for vowels as well as consonants . In Archaic and early Classical times, the Greek alphabet existed in many local variants , but, by the end of the 4th century BC, the Ionic -based Euclidean alphabet , with 24 letters, ordered from alpha to omega , had become standard throughout

5684-463: The eighth century BC onward. While early evidence of Greek letters may date no later than 770 BC, the oldest known substantial and legible Greek alphabet texts, such as the Dipylon inscription and Nestor's cup , date from c.  740 /30 BC. It is accepted that the introduction of the alphabet occurred some time prior to these inscriptions. While earlier dates have been proposed, the Greek alphabet

5782-424: 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 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

5880-504: The energy reconstruction. The unprecedented granularity of the CALICE calorimeter prototype provides an opportunity to test the particle flow concept. These days the work is in progress to check the output quality of the PFA programs. Due to large amount of test beam data, it becomes possible to use real events instead of simulated ones as input information for that programs. Since in the test beams all

5978-585: 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)

SECTION 60

#1732887486077

6076-410: The following group of consonant letters, the older forms of the names in Ancient Greek were spelled with -εῖ , indicating an original pronunciation with -ē . In Modern Greek these names are spelled with -ι . The following group of vowel letters were originally called simply by their sound values as long vowels: ē, ō, ū, and ɔ . Their modern names contain adjectival qualifiers that were added during

6174-444: The following letters are more or less straightforward continuations of their Phoenician antecedents. Between Ancient and Modern Greek, they have remained largely unchanged, except that their pronunciation has followed regular sound changes along with other words (for instance, in the name of beta , ancient /b/ regularly changed to modern /v/, and ancient /ɛː/ to modern /i/, resulting in the modern pronunciation vita ). The name of lambda

6272-408: 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 . The fact that the mesotron (i.e.

6370-439: The historical sound system in pronouncing Ancient Greek. Several letter combinations have special conventional sound values different from those of their single components. Among them are several digraphs of vowel letters that formerly represented diphthongs but are now monophthongized. In addition to the four mentioned above ( ⟨ ει , οι, υι⟩ , pronounced /i/ and ⟨ αι ⟩ , pronounced /e/ ), there

6468-474: The letter ⟨ γ ⟩ , before another velar consonant , stands for the velar nasal [ŋ] ; thus ⟨ γγ ⟩ and ⟨ γκ ⟩ are pronounced like English ⟨ng⟩ like in the word finger (not like in the word thing). In analogy to ⟨ μπ ⟩ and ⟨ ντ ⟩ , ⟨ γκ ⟩ is also used to stand for [g] before vowels [a] , [o] and [u] , and [ɟ] before [e] and [i] . There are also

6566-654: The letter ⟨h⟩ . In modern scholarly transliteration of Ancient Greek, ⟨ κ ⟩ will usually be rendered as ⟨k⟩ , and the vowel combinations ⟨ αι , οι, ει, ου⟩ as ⟨ai, oi, ei, ou⟩ . The letters ⟨ θ ⟩ and ⟨ φ ⟩ are generally rendered as ⟨th⟩ and ⟨ph⟩ ; ⟨ χ ⟩ as either ⟨ch⟩ or ⟨kh⟩ ; and word-initial ⟨ ρ ⟩ as ⟨rh⟩ . Transcription conventions for Modern Greek differ widely, depending on their purpose, on how close they stay to

6664-408: The mediator of the nuclear force postulated by Yukawa. Yukawa's predicted particle, the pi meson , was finally identified in 1947 (again from cosmic ray interactions). 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

6762-414: The much larger mass of the muon gives it a much more localized 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. Nonetheless, in such cases, the orbital of the muon continues to be smaller and far closer to

6860-476: 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 ) predicted by special relativity , for the first time. Muons arriving on

6958-635: The muon spin (an axial vector ), the decay is an example of non-conservation of parity by the weak interaction. This is essentially the same experimental signature as used by the original demonstration . More generally in the Standard Model, all charged leptons decay via the weak interaction and likewise violate parity symmetry. The muon was the first elementary particle discovered that does not appear in ordinary atoms . Negative muons can form muonic atoms (previously called mu-mesic atoms), by replacing an electron in ordinary atoms. Muonic hydrogen atoms are much smaller than typical hydrogen atoms because

7056-458: The muon) was not Yukawa's particle was established in 1946 by an experiment conducted by Marcello Conversi , Oreste Piccioni , and Ettore Pancini in Rome. In this experiment, which Luis Walter Alvarez called the "start of modern particle physics" in his 1968 Nobel lecture, they showed that the muons from cosmic rays were decaying without being captured by atomic nuclei, contrary to what was expected of

7154-517: The muons circulated in a confining storage ring. The Muon g-2 collaboration reported in 2021: The prediction for the value of the muon anomalous magnetic moment includes three parts: 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

7252-461: 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 that 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

7350-415: 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

7448-456: The nucleus than the atomic orbitals of the electrons. Spectroscopic measurements in muonic hydrogen have been used to produce a precise estimate of the proton radius . The results of these measurements diverged from the then accepted value giving rise to the so called proton radius puzzle . Later this puzzle found its resolution when new improved measurements of the proton radius in the electronic hydrogen became available. Muonic helium

7546-441: The other charged leptons, the muon has an associated muon neutrino , denoted by ν μ , which differs from the electron neutrino and participates in different nuclear reactions. Muons were discovered by Carl D. Anderson and Seth Neddermeyer at Caltech in 1936 while studying cosmic radiation . Anderson noticed particles that curved differently from electrons and other known particles when passed through

7644-518: The other, as was observed in the decay of other charged mesons. In the eventual Standard Model 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 – 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

7742-420: The particles are almost at the same coordinate position, artificial events are created consisting of several incoming particles separated by some distance in order to check if the PFA program can reconstruct the incoming particles correctly. Muons A muon ( / ˈ m ( j ) uː . ɒ n / M(Y)OO -on ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to

7840-418: The phonological pitch accent in Ancient Greek. By the time their use became conventional and obligatory in Greek writing, in late antiquity, pitch accent was evolving into a single stress accent , and thus the three signs have not corresponded to a phonological distinction in actual speech ever since. In addition to the accent marks, every word-initial vowel must carry either of two so-called "breathing marks":

7938-503: 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

8036-446: The precision of incoming particle energy reconstruction was estimated to be near 4%. Given some number of unknown incoming particles, it is possible to reconstruct their energies using the picture of particle showers from the calorimeter. That picture has to be analyzed by a PFA program. In addition, novel deep analysis (DA) algorithms have been developed to separate different sorts of secondary particles inside showers in order to improve

8134-533: 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.,

8232-411: The pronunciation alone, while the reverse mapping, from spelling to pronunciation, is usually regular and predictable. The following vowel letters and digraphs are involved in the mergers: Modern Greek speakers typically use the same, modern symbol–sound mappings in reading Greek of all historical stages. In other countries, students of Ancient Greek may use a variety of conventional approximations of

8330-477: 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 and spin: the antimuon (also called a positive muon ). Muons are denoted by μ and antimuons by μ . Formerly, muons were called mu mesons , but are not classified as mesons by modern particle physicists (see § History ) , and that name

8428-462: The simplified monotonic system. In the cases of the three historical sibilant letters below, the correspondence between Phoenician and Ancient Greek is less clear, with apparent mismatches both in letter names and sound values. The early history of these letters (and the fourth sibilant letter, obsolete san ) has been a matter of some debate. Here too, the changes in the pronunciation of the letter names between Ancient and Modern Greek are regular. In

8526-434: The so-called iota subscript , which has the shape of a small vertical stroke or a miniature ⟨ ι ⟩ below the letter. This iota represents the former offglide of what were originally long diphthongs, ⟨ ᾱι, ηι, ωι ⟩ (i.e. /aːi, ɛːi, ɔːi/ ), which became monophthongized during antiquity. Another diacritic used in Greek is the diaeresis ( ¨ ), indicating a hiatus . This system of diacritics

8624-604: The square of the amplitude, and thus the square of Fermi's coupling constant ( G F {\displaystyle G_{\text{F}}} ), with over-all dimension of inverse fourth power of energy. By dimensional analysis, this leads to Sargent's rule of fifth-power dependence on m μ , where I ( x ) = 1 − 8 x − 12 x 2 ln ⁡ x + 8 x 3 − x 4 {\displaystyle I(x)=1-8x-12x^{2}\ln x+8x^{3}-x^{4}} , and: The decay distributions of

8722-447: 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

8820-500: The three main calorimetric subsystems of a future detector: an ECAL followed by an HCAL and a tail catcher/muon tracker (TCMT), and is evaluating the performance of alternative technological solutions within this combined system. The collaboration studies the performance of such calorimeters within a long, detailed program for an ECAL and several options of high granular analogue and digital calorimeters with sensitive layers of gas or plastic scintillator . The Tile subgroup [2] has built

8918-403: 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 . As more types of mesons were discovered in accelerator experiments later, it was eventually found that the mu meson significantly differed not only from

9016-459: The vowel symbols, Modern Greek sound values reflect the radical simplification of the vowel system of post-classical Greek, merging multiple formerly distinct vowel phonemes into a much smaller number. This leads to several groups of vowel letters denoting identical sounds today. Modern Greek orthography remains true to the historical spellings in most of these cases. As a consequence, the spellings of words in Modern Greek are often not predictable from

9114-414: Was a word that began with the sound represented by that letter; thus ʾaleph , the word for "ox", was used as the name for the glottal stop /ʔ/ , bet , or "house", for the /b/ sound, and so on. When the letters were adopted by the Greeks, most of the Phoenician names were maintained or modified slightly to fit Greek phonology; thus, ʾaleph, bet, gimel became alpha, beta, gamma . The Greek names of

9212-489: Was adopted for official use in Modern Greek by the Greek state. It uses only a single accent mark, the acute (also known in this context as tonos , i.e. simply "accent"), marking the stressed syllable of polysyllabic words, and occasionally the diaeresis to distinguish diphthongal from digraph readings in pairs of vowel letters, making this monotonic system very similar to the accent mark system used in Spanish . The polytonic system

9310-400: Was also borrowed as a consonant for [w] (Ϝ, digamma ). In addition, the Phoenician letter for the emphatic glottal /ħ/ ( heth ) was borrowed in two different functions by different dialects of Greek: as a letter for /h/ (Η, heta ) by those dialects that had such a sound, and as an additional vowel letter for the long /ɛː/ (Η, eta ) by those dialects that lacked the consonant. Eventually,

9408-506: Was first developed by the scholar Aristophanes of Byzantium ( c.  257 – c.  185/180 BC), who worked at the Musaeum in Alexandria during the third century BC. Aristophanes of Byzantium also was the first to divide poems into lines, rather than writing them like prose, and also introduced a series of signs for textual criticism . In 1982, a new, simplified orthography, known as "monotonic",

9506-531: Was pronounced [ y ] , was called y psilon ("plain y") to distinguish it from the identically pronounced digraph ⟨οι⟩ . Some dialects of the Aegean and Cypriot have retained long consonants and pronounce [ˈɣamːa] and [ˈkapʰa] ; also, ήτα has come to be pronounced [ˈitʰa] in Cypriot. Like Latin and other alphabetic scripts, Greek originally had only a single form of each letter, without

9604-399: Was used for all of /o, oː, ɔː/ (corresponding to classical Ο, ΟΥ, Ω ). The letter Η (heta) was used for the consonant /h/ . Some variant local letter forms were also characteristic of Athenian writing, some of which were shared with the neighboring (but otherwise "red") alphabet of Euboia : a form of Λ that resembled a Latin L ( [REDACTED] ) and a form of Σ that resembled

#76923