1.
Particle physics
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Particle physics is the branch of physics that studies the nature of the particles that constitute matter and radiation. By our current understanding, these particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model, in more technical terms, they are described by quantum state vectors in a Hilbert space, which is also treated in quantum field theory. All particles and their interactions observed to date can be described almost entirely by a field theory called the Standard Model. The Standard Model, as formulated, has 61 elementary particles. Those elementary particles can combine to form composite particles, accounting for the hundreds of species of particles that have been discovered since the 1960s. The Standard Model has been found to agree with almost all the tests conducted to date. However, most particle physicists believe that it is a description of nature. In recent years, measurements of mass have provided the first experimental deviations from the Standard Model. The idea that all matter is composed of elementary particles dates from at least the 6th century BC, in the 19th century, John Dalton, through his work on stoichiometry, concluded that each element of nature was composed of a single, unique type of particle. Throughout the 1950s and 1960s, a variety of particles were found in collisions of particles from increasingly high-energy beams. It was referred to informally as the particle zoo, the current state of the classification of all elementary particles is explained by the Standard Model. It describes the strong, weak, and electromagnetic fundamental interactions, the species of gauge bosons are the gluons, W−, W+ and Z bosons, and the photons. The Standard Model also contains 24 fundamental particles, which are the constituents of all matter, finally, the Standard Model also predicted the existence of a type of boson known as the Higgs boson. Early in the morning on 4 July 2012, physicists with the Large Hadron Collider at CERN announced they had found a new particle that behaves similarly to what is expected from the Higgs boson, the worlds major particle physics laboratories are, Brookhaven National Laboratory. Its main facility is the Relativistic Heavy Ion Collider, which collides heavy ions such as gold ions and it is the worlds first heavy ion collider, and the worlds only polarized proton collider. Its main projects are now the electron-positron colliders VEPP-2000, operated since 2006 and its main project is now the Large Hadron Collider, which had its first beam circulation on 10 September 2008, and is now the worlds most energetic collider of protons. It also became the most energetic collider of heavy ions after it began colliding lead ions and its main facility is the Hadron Elektron Ring Anlage, which collides electrons and positrons with protons
2.
Isospin
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In nuclear physics and particle physics, isospin is a quantum number related to the strong interaction. For example, a pair can be coupled in a state of total isospin 1 or 0. It is a quantity and the name derives from the fact that the mathematical structures used to describe it are very similar to those used to describe the intrinsic angular momentum. This term was derived from isotopic spin, a term to which nuclear physicists prefer isobaric spin. Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons, Isospin symmetry remains an important concept in particle physics. A close examination of this symmetry, historically, led directly to the discovery and understanding of quarks, although the proton has a positive electric charge, and the neutron is neutral, they are almost identical in all other aspects. The strength of the interaction between any pair of nucleons is the same, independent of whether they are interacting as protons or as neutrons. This behavior is not unlike the electron, where there are two states based on their spin. A change in spin turns an electron into a positron and vice versa, other properties of the particle are conserved in this case. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron, in 1937, Eugene Wigner introduced the term isospin to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated. Thus, isospin was introduced as a well before the development of the quark model, in the 1960s. Similar to a spin 1⁄2 particle, which has two states, protons and neutrons were said to be of isospin 1⁄2, the proton and neutron were then associated with different isospin projections I3 = + 1⁄2 and − 1⁄2 respectively. Protons and neutrons were then grouped together as nucleons because they both have nearly the same mass and interact in nearly the way, if the electromagnetic interaction is neglected. It was convenient to them as being different states of the same particle. When constructing a theory of nuclear forces, one could simply assume that it does not depend on isospin. These considerations would also prove useful in the analysis of meson-nucleon interactions after the discovery of the pions in 1947, the three pions could be assigned to an isospin triplet with I =1 and I3 = +1,0 or −1. By assuming that isospin was conserved by nuclear interactions, the new mesons were more easily accommodated by nuclear theory and this multiplet structure was combined with strangeness in Murray Gell-Manns eightfold way, ultimately leading to the quark model and quantum chromodynamics. Observations of the light baryons imply that some of these particles are so similar in terms of their interactions that they can be treated as different states of the same particle
3.
Electric charge
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Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of charges, positive and negative. Like charges repel and unlike attract, an absence of net charge is referred to as neutral. An object is charged if it has an excess of electrons. The SI derived unit of charge is the coulomb. In electrical engineering, it is common to use the ampere-hour. The symbol Q often denotes charge, early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that dont require consideration of quantum effects. The electric charge is a conserved property of some subatomic particles. Electrically charged matter is influenced by, and produces, electromagnetic fields, the interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces. 602×10−19 coulombs. The proton has a charge of +e, and the electron has a charge of −e, the study of charged particles, and how their interactions are mediated by photons, is called quantum electrodynamics. Charge is the property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter. Electric charge is a property of many subatomic particles. The charges of free-standing particles are integer multiples of the charge e. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge, robert Millikans oil drop experiment demonstrated this fact directly, and measured the elementary charge. By convention, the charge of an electron is −1, while that of a proton is +1, charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. The charge of an antiparticle equals that of the corresponding particle, quarks have fractional charges of either −1/3 or +2/3, but free-standing quarks have never been observed. The electric charge of an object is the sum of the electric charges of the particles that make it up. An ion is an atom that has lost one or more electrons, giving it a net charge, or that has gained one or more electrons
4.
Hypercharge
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The concept of hypercharge combines and unifies isospin and flavour into a single charge operator. Hypercharge in particle physics is a number relating the strong interactions of the SU model. Isospin is defined in the SU model while the SU model defines hypercharge, SU weight diagrams are 2-dimensional with the coordinates referring to two quantum numbers, Iz, which is the z-component of isospin and Y, which is the hypercharge. Mathematically, hypercharge is Y = S + C + B ′ + T + B, strong interactions conserve hypercharge, but weak interactions do not. The Gell-Mann–Nishijima formula relates isospin and electric charge Q = I3 +12 Y, isospin creates multiplets of particles whose average charge is related to the hypercharge by, Y =2 Q ¯. Since the hypercharge is the same for all members of a multiplet, the SU model has multiplets characterized by a quantum number J, which is the total angular momentum. Each multiplet consists of 2J +1 substates with equally spaced values of Jz, forming a symmetric arrangement seen in atomic spectra and isospin. This formalizes the observation that certain strong baryon decays were not observed, leading to the prediction of the mass, strangeness, the SU has supermultiplets containing SU multiplets. SU now needs 2 numbers to all its sub-states which are denoted by λ1. Specifies the number of points in the topmost side of the hexagon while specifies the number of points on the bottom side, the nucleon group have an average charge of +1/2, so they both have hypercharge Y =1. From the Gell-Mann–Nishijima formula we know that proton has isospin I3 = +1/2 and this also works for quarks, for the up quark, with a charge of +2/3, and an I3 of +1/2, we deduce a hypercharge of 1/3, due to its baryon number. For a strange quark, with charge −1/3, a number of 1/3 and strangeness of −1 we get a hypercharge Y = −2/3. That means that a strange quark makes a singlet of its own, while up, hypercharge was a concept developed in the 1960s, to organize groups of particles in the particle zoo and to develop ad hoc conservation laws based on their observed transformations. With the advent of the model, it is now obvious that, hypercharge Y is the following combination of the numbers of up, down, strange quarks, charm quarks, top quarks and bottom quarks. Weak hypercharge, however, remains of use in various theories of the electroweak interaction. Introduction to atomic and nuclear physics
5.
Standard Model
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The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong interactions, as well as classifying all the elementary particles known. It was developed throughout the half of the 20th century. The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks, since then, discoveries of the top quark, the tau neutrino, and the Higgs boson have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results and it does not incorporate the full theory of gravitation as described by general relativity, or account for the accelerating expansion of the Universe. The model does not contain any viable dark matter particle that all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations, the development of the Standard Model was driven by theoretical and experimental particle physicists alike. For theorists, the Standard Model is a paradigm of a field theory. The first step towards the Standard Model was Sheldon Glashows discovery in 1961 of a way to combine the electromagnetic, in 1967 Steven Weinberg and Abdus Salam incorporated the Higgs mechanism into Glashows electroweak interaction, giving it its modern form. The Higgs mechanism is believed to rise to the masses of all the elementary particles in the Standard Model. This includes the masses of the W and Z bosons, the W± and Z0 bosons were discovered experimentally in 1983, and the ratio of their masses was found to be as the Standard Model predicted. The theory of the interaction, to which many contributed, acquired its modern form around 1973–74. At present, matter and energy are best understood in terms of the kinematics, to date, physics has reduced the laws governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. The Standard Model includes members of classes of elementary particles. All particles can be summarized as follows, The Standard Model includes 12 elementary particles of spin known as fermions. According to the theorem, fermions respect the Pauli exclusion principle. Each fermion has a corresponding antiparticle, the fermions of the Standard Model are classified according to how they interact. There are six quarks, and six leptons, pairs from each classification are grouped together to form a generation, with corresponding particles exhibiting similar physical behavior. The defining property of the quarks is that they carry color charge, a phenomenon called color confinement results in quarks being very strongly bound to one another, forming color-neutral composite particles containing either a quark and an antiquark or three quarks
6.
Weak interaction
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In particle physics, the weak interaction is one of the four known fundamental interactions of nature, alongside the strong interaction, electromagnetism, and gravitation. The weak interaction is responsible for radioactive decay, which plays an role in nuclear fission. The theory of the interaction is sometimes called quantum flavourdynamics, in analogy with the terms QCD dealing with the strong interaction. However the term QFD is rarely used because the force is best understood in terms of electro-weak theory. The Standard Model of particle physics, which does not address gravity, provides a framework for understanding how the electromagnetic, weak. An interaction occurs when two particles, typically but not necessarily half-integer spin fermions, exchange integer-spin, force-carrying bosons, the fermions involved in such exchanges can be either elementary or composite, although at the deepest levels, all weak interactions ultimately are between elementary particles. In the case of the interaction, fermions can exchange three distinct types of force carriers known as the W+, W−, and Z bosons. The mass of each of these bosons is far greater than the mass of a proton or neutron, the force is in fact termed weak because its field strength over a given distance is typically several orders of magnitude less than that of the strong nuclear force or electromagnetic force. During the quark epoch of the universe, the electroweak force separated into the electromagnetic. Important examples of the weak interaction include beta decay, and the fusion of hydrogen into deuterium that powers the Suns thermonuclear process, most fermions will decay by a weak interaction over time. Such decay makes radiocarbon dating possible, as carbon-14 decays through the interaction to nitrogen-14. It can also create radioluminescence, commonly used in tritium illumination, quarks, which make up composite particles like neutrons and protons, come in six flavours – up, down, strange, charm, top and bottom – which give those composite particles their properties. The weak interaction is unique in that it allows for quarks to swap their flavour for another, the swapping of those properties is mediated by the force carrier bosons. Also, the interaction is the only fundamental interaction that breaks parity-symmetry, and similarly. In 1933, Enrico Fermi proposed the first theory of the weak interaction and he suggested that beta decay could be explained by a four-fermion interaction, involving a contact force with no range. However, it is described as a non-contact force field having a finite range. The existence of the W and Z bosons was not directly confirmed until 1983, the weak interaction is unique in a number of respects, It is the only interaction capable of changing the flavour of quarks. It is the interaction that violates P or parity-symmetry
7.
Quantum state
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In quantum physics, quantum state refers to the state of an isolated quantum system. A quantum state provides a probability distribution for the value of each observable, knowledge of the quantum state together with the rules for the systems evolution in time exhausts all that can be predicted about the systems behavior. A mixture of states is again a quantum state. Quantum states that cannot be written as a mixture of states are called pure quantum states. Mathematically, a quantum state can be represented by a ray in a Hilbert space over the complex numbers. The ray is a set of nonzero vectors differing by just a scalar factor, any of them can be chosen as a state vector to represent the ray. A unit vector is usually picked, but its phase factor can be chosen freely anyway, nevertheless, such factors are important when state vectors are added together to form a superposition. Hilbert space is a generalization of the ordinary Euclidean space and it all possible pure quantum states of the given system. If this Hilbert space, by choice of representation, is exhibited as a function space, a more complicated case is given by the spin part of a state vector | ψ ⟩ =12, which involves superposition of joint spin states for two particles with spin 1⁄2. A mixed quantum state corresponds to a mixture of pure states, however. Mixed states are described by so-called density matrices, a pure state can also be recast as a density matrix, in this way, pure states can be represented as a subset of the more general mixed states. For example, if the spin of an electron is measured in any direction, e. g. with a Stern–Gerlach experiment, the Hilbert space for the electrons spin is therefore two-dimensional. A mixed state, in case, is a 2 ×2 matrix that is Hermitian, positive-definite. These probability distributions arise for both mixed states and pure states, it is impossible in quantum mechanics to prepare a state in all properties of the system are fixed. This is exemplified by the uncertainty principle, and reflects a difference between classical and quantum physics. Even in quantum theory, however, for every observable there are states that have an exact. In the mathematical formulation of mechanics, pure quantum states correspond to vectors in a Hilbert space. The operator serves as a function which acts on the states of the system
8.
Quark
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A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, due to a phenomenon known as color confinement, quarks are never directly observed or found in isolation, they can be found only within hadrons, such as baryons and mesons. For this reason, much of what is known about quarks has been drawn from observations of the hadrons themselves, Quarks have various intrinsic properties, including electric charge, mass, color charge, and spin. There are six types of quarks, known as flavors, up, down, strange, charm, top, up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up and down quarks through a process of particle decay, the transformation from a higher mass state to a lower mass state. Because of this, up and down quarks are generally stable and the most common in the universe, whereas strange, charm, bottom, and top quarks can only be produced in high energy collisions. For every quark flavor there is a type of antiparticle, known as an antiquark. The quark model was proposed by physicists Murray Gell-Mann and George Zweig in 1964. Accelerator experiments have provided evidence for all six flavors, the top quark was the last to be discovered at Fermilab in 1995. The Standard Model is the theoretical framework describing all the known elementary particles. This model contains six flavors of quarks, named up, down, strange, charm, bottom, antiparticles of quarks are called antiquarks, and are denoted by a bar over the symbol for the corresponding quark, such as u for an up antiquark. As with antimatter in general, antiquarks have the mass, mean lifetime, and spin as their respective quarks. Quarks are spin- 1⁄2 particles, implying that they are fermions according to the spin-statistics theorem and they are subject to the Pauli exclusion principle, which states that no two identical fermions can simultaneously occupy the same quantum state. This is in contrast to bosons, any number of which can be in the same state, unlike leptons, quarks possess color charge, which causes them to engage in the strong interaction. The resulting attraction between different quarks causes the formation of composite particles known as hadrons, there are two families of hadrons, baryons, with three valence quarks, and mesons, with a valence quark and an antiquark. The most common baryons are the proton and the neutron, the blocks of the atomic nucleus. A great number of hadrons are known, most of them differentiated by their quark content, the existence of exotic hadrons with more valence quarks, such as tetraquarks and pentaquarks, has been conjectured but not proven. However, on 13 July 2015, the LHCb collaboration at CERN reported results consistent with pentaquark states, elementary fermions are grouped into three generations, each comprising two leptons and two quarks
9.
CP violation
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In particle physics, CP violation is a violation of CP-symmetry, the combination of C-symmetry and P-symmetry. CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle while its spatial coordinates are inverted. The discovery of CP violation in 1964 in the decays of neutral kaons resulted in the Nobel Prize in Physics in 1980 for its discoverers James Cronin and Val Fitch. It plays an important role both in the attempts of cosmology to explain the dominance of matter over antimatter in the present Universe, and in the study of weak interactions in particle physics. The strong interaction and electromagnetic interaction seem to be invariant under the combined CP transformation operation, historically, CP-symmetry was proposed to restore order after the discovery of parity violation in the 1950s. The idea behind parity symmetry is that the equations of physics are invariant under mirror inversion. This leads to the prediction that the image of a reaction occurs at the same rate as the original reaction. Parity symmetry appears to be valid for all reactions involving electromagnetism, until 1956, parity conservation was believed to be one of the fundamental geometric conservation laws. They proposed several possible direct experimental tests, overall, the symmetry of a quantum mechanical system can be restored if another symmetry S can be found such that the combined symmetry PS remains unbroken. Simply speaking, charge conjugation is a symmetry between particles and antiparticles, and so CP-symmetry was proposed in 1957 by Lev Landau as the symmetry between matter and antimatter. In other words, a process in which all particles are exchanged with their antiparticles was assumed to be equivalent to the image of the original process. Direct CP violation is allowed in the Standard Model if a complex phase appears in the CKM matrix describing quark mixing, a necessary condition for the appearance of the complex phase is the presence of at least three generations of quarks. The reason why such a complex phase causes CP violation is not immediately obvious, consider any given particles a and b, and their antiparticles a ¯ and b ¯. Now consider the processes a → b and the corresponding antiparticle process a ¯ → b ¯, before CP violation, these terms must be the same complex number. We can separate the magnitude and phase by writing M = | M | e i θ, if a phase term is introduced from the CKM matrix, denote it e i ϕ. Note that M ¯ contains the conjugate matrix to M, so it picks up a phase term e − i ϕ, however, consider that there are two different routes for a → b. In 1964, James Cronin, Val Fitch and coworkers provided clear evidence from kaon decay that CP-symmetry could be broken and this work won them the 1980 Nobel Prize. This discovery showed that weak interactions violate not only the charge-conjugation symmetry C between particles and antiparticles and the P or parity, but also their combination, the discovery shocked particle physics and opened the door to questions still at the core of particle physics and of cosmology today
10.
Makoto Kobayashi (physicist)
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After completing his PhD at Nagoya University in 1972, Kobayashi worked as a research associate on particle physics at Kyoto University. Together, with his colleague Toshihide Maskawa, he worked on explaining CP-violation within the Standard Model of particle physics. Kobayashi and Maskawas theory required that there were at least three generations of quarks, a prediction that was confirmed four years later by the discovery of the bottom quark. Kobayashi and Maskawas article, CP Violation in the Renormalizable Theory of Weak Interaction, the Cabibbo–Kobayashi–Maskawa matrix, which defines the mixing parameters between quarks was the result of this work. Kobayashi and Maskawa were jointly awarded half of the 2008 Nobel Prize in Physics for this work, Kobayashi was born and educated in Nagoya, Japan. He married Sachiko Enomoto in 1975, they had one son, after his first wife died, Kobayashi married Emiko Nakayama in 1990, they had a daughter, Yuka. Progress of Theoretical Physics List of Nobel laureates affiliated with Kyoto University List of Japanese Nobel laureates Progress of Theoretical Physics Makoto Kobayashi, Professor emeritus of KEK
11.
Toshihide Maskawa
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A native of Aichi Prefecture, Maskawa graduated from Nagoya University in 1962 and received a Ph. D in particle physics from the same university in 1967. At Kyoto University in the early 1970s, he collaborated with Makoto Kobayashi on explaining broken symmetry within the Standard Model of particle physics. Maskawa and Kobayashis theory required that there be at least three generations of quarks, a prediction that was confirmed four years later by the discovery of the bottom quark. Maskawa and Kobayashis 1973 article, CP Violation in the Renormalizable Theory of Weak Interaction, is the fourth most cited high energy physics paper of all time as of 2010, the Cabibbo–Kobayashi–Maskawa matrix, which defines the mixing parameters between quarks was the result of this work. Kobayashi and Maskawa were jointly awarded half of the 2008 Nobel Prize in Physics for this work, Maskawa was Director of the Yukawa Institute for Theoretical Physics from 1997 to 2003. Nobel Prize in Physics Japan Order of Culture Asahi Prize Japan Academy Prize Sakurai Prize List of Japanese Nobel laureates List of Nobel laureates affiliated with Kyoto University
12.
Nicola Cabibbo
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Nicola Cabibbo was an Italian physicist, best known for his work on the weak interaction. Cabibbo, son of a Sicilian lawyer, was born in Rome and he graduated in theoretical physics at the Università di Roma “Sapienza University of Rome” in 1958 under the supervision of Bruno Touschek. In 1963, while working at CERN, Cabibbo found the solution to the puzzle of the decays of strange particles. Formulating what came to be known as Cabibbo universality, in 1967 Nicola settled back in Rome where he taught theoretical physics and created a large school with younger colleagues and brilliant students. He was president of the INFN from 1983 to 1992, during which time the Gran Sasso Laboratory was inaugurated. He was also president of the Italian energy agency, ENEA, from 1993 to 1998, in 2004, Cabibbo spent a year at CERN as guest professor. He addressed the issue with a mixing angle θC, between the down and strange quarks. Modern measurements show that θC =13. 04°, before the discovery of the third generation of quarks, this work was extended by Makoto Kobayashi and Toshihide Maskawa to the Cabibbo–Kobayashi–Maskawa matrix. In 2008, Kobayashi and Maskawa shared one half of the Nobel Prize in Physics for their work, some physicists had bitter feelings that the Nobel Prize committee failed to reward Cabibbo for his vital part. Asked for a reaction on the prize, Cabibbo preferred to no comment. According to sources close to him, however, he was embittered, later, Cabibbo researched applications of supercomputers to address problems in modern physics with the experiments APE100 and APE1000. After his death in 2011, the Franklin Institute awarded him with the Benjamin Franklin Medal in Physics and he died from respiratory problems in a Rome hospital on August 16,2010 at the age of 75. For his credits in physics, after his death, the hall of the Physics Department Enrico Fermi of La Sapienza has been nominated after him in his honour. Cabibbo biography from the Istituto e Museo di Storia della Scienza Parisi, Giorgio
13.
Murray Gell-Mann
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Murray Gell-Mann is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. Gell-Mann has spent several periods at CERN, among others as a John Simon Guggenheim Memorial Foundation Fellow in 1972 and he introduced, independently of George Zweig, the quark—constituents of all hadrons—having first identified the SU flavor symmetry of hadrons. This symmetry is now understood to underlie the light quarks, extending isospin to include strangeness and he developed the V−A theory of the weak interaction in collaboration with Richard Feynman. In the 1960s, he introduced current algebra as a method of systematically exploiting symmetries to extract predictions from quark models, Gell-Mann, along with Maurice Lévy, developed the sigma model of pions, which describes low-energy pion interactions. In 1969 he received the Nobel Prize in physics for his contributions and discoveries concerning the classification of elementary particles and their interactions. He is also known to have played a role in keeping string theory alive through the 1970s and early 1980s. Gell-Mann is a proponent of the consistent histories approach to understanding quantum mechanics, Gell-Mann was born in lower Manhattan into a family of Jewish immigrants from the Austro-Hungarian Empire. His parents were Pauline and Arthur Isidore Gell-Mann, who taught English as a Second Language, at Yale, he participated in the William Lowell Putnam Mathematical Competition and was on the team representing Yale University that won the second prize in 1947. Gell-Mann earned a degree in physics from Yale in 1948. His supervisor at MIT was Victor Weisskopf, in 1958, Gell-Mann and Richard Feynman, in parallel with the independent team of George Sudarshan and Robert Marshak, discovered the chiral structures of the weak interaction in physics. This work followed the discovery of the violation of parity by Chien-Shiung Wu, as suggested by Chen Ning Yang and Tsung-Dao Lee. Gell-Manns work in the 1950s involved recently discovered cosmic ray particles that came to be called kaons and hyperons, classifying these particles led him to propose that a quantum number called strangeness would be conserved by the strong and the electromagnetic interactions, but not by the weak interactions. Another of Gell-Manns ideas is the Gell-Mann-Okubo formula, which was, initially, a based on empirical results. Gell-Mann and Abraham Pais were involved in explaining several puzzling aspects of the physics of these particles, in 1961, this led him to introduce a classification scheme for hadrons, elementary particles that participate in the strong interaction. This scheme is now explained by the quark model, Gell-Mann referred to the scheme as the Eightfold Way, because of the octets of particles in the classification. In 1964, Gell-Mann and, independently, George Zweig went on to postulate the existence of quarks, particles of which the hadrons of this scheme are composed. The name was coined by Gell-Mann and is a reference to the novel Finnegans Wake, by James Joyce Zweig had referred to the particles as aces, quarks, antiquarks, and gluons were soon established as the underlying elementary objects in the study of the structure of hadrons. He was awarded a Nobel Prize in physics in 1969 for his contributions and discoveries concerning the classification of elementary particles and their interactions
14.
Matrix (mathematics)
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In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimensions of the matrix below are 2 ×3, the individual items in an m × n matrix A, often denoted by ai, j, where max i = m and max j = n, are called its elements or entries. Provided that they have the size, two matrices can be added or subtracted element by element. The rule for multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second. Any matrix can be multiplied element-wise by a scalar from its associated field, a major application of matrices is to represent linear transformations, that is, generalizations of linear functions such as f = 4x. The product of two matrices is a matrix that represents the composition of two linear transformations. Another application of matrices is in the solution of systems of linear equations, if the matrix is square, it is possible to deduce some of its properties by computing its determinant. For example, a matrix has an inverse if and only if its determinant is not zero. Insight into the geometry of a transformation is obtainable from the matrixs eigenvalues. Applications of matrices are found in most scientific fields, in computer graphics, they are used to manipulate 3D models and project them onto a 2-dimensional screen. Matrix calculus generalizes classical analytical notions such as derivatives and exponentials to higher dimensions, Matrices are used in economics to describe systems of economic relationships. A major branch of analysis is devoted to the development of efficient algorithms for matrix computations. Matrix decomposition methods simplify computations, both theoretically and practically, algorithms that are tailored to particular matrix structures, such as sparse matrices and near-diagonal matrices, expedite computations in finite element method and other computations. Infinite matrices occur in planetary theory and in atomic theory, a simple example of an infinite matrix is the matrix representing the derivative operator, which acts on the Taylor series of a function. A matrix is an array of numbers or other mathematical objects for which operations such as addition and multiplication are defined. Most commonly, a matrix over a field F is an array of scalars each of which is a member of F. Most of this focuses on real and complex matrices, that is, matrices whose elements are real numbers or complex numbers. More general types of entries are discussed below, for instance, this is a real matrix, A =
15.
Rotation matrix
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In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix R = rotates points in the xy-Cartesian plane counter-clockwise through an angle θ about the origin of the Cartesian coordinate system. To perform the rotation using a rotation matrix R, the position of each point must be represented by a vector v. A rotated vector is obtained by using the matrix multiplication Rv, Rotation matrices also provide a means of numerically representing an arbitrary rotation of the axes about the origin, without appealing to angular specification. These coordinate rotations are a way to express the orientation of a camera, or the attitude of a spacecraft. The examples in this article apply to active rotations of vectors counter-clockwise in a coordinate system by pre-multiplication. If any one of these is changed, then the inverse of the matrix should be used. Since matrix multiplication has no effect on the vector, rotation matrices can only be used to describe rotations about the origin of the coordinate system. Rotation matrices provide a description of such rotations, and are used extensively for computations in geometry, physics. Rotation matrices are matrices, with real entries. More specifically, they can be characterized as orthogonal matrices with determinant 1, that is, in some literature, the term rotation is generalized to include improper rotations, characterized by orthogonal matrices with determinant −1. These combine proper rotations with reflections, in other cases, where reflections are not being considered, the label proper may be dropped. This convention is followed in this article, the set of all orthogonal matrices of size n with determinant +1 forms a group known as the special orthogonal group SO. The most important special case is that of the rotation group SO, the set of all orthogonal matrices of size n with determinant +1 or -1 forms the orthogonal group O. In two dimensions, every rotation matrix has the form, R =. This rotates column vectors by means of the matrix multiplication. So the coordinates of the point after rotation are x ′ = x cos θ − y sin θ, y ′ = x sin θ + y cos θ. The direction of rotation is counterclockwise if θ is positive
16.
Absolute value
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In mathematics, the absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign. Namely, |x| = x for a x, |x| = −x for a negative x. For example, the value of 3 is 3. The absolute value of a number may be thought of as its distance from zero, generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, a value is also defined for the complex numbers. The absolute value is related to the notions of magnitude, distance. The term absolute value has been used in this sense from at least 1806 in French and 1857 in English, the notation |x|, with a vertical bar on each side, was introduced by Karl Weierstrass in 1841. Other names for absolute value include numerical value and magnitude, in programming languages and computational software packages, the absolute value of x is generally represented by abs, or a similar expression. Thus, care must be taken to interpret vertical bars as an absolute value sign only when the argument is an object for which the notion of an absolute value is defined. For any real number x the value or modulus of x is denoted by |x| and is defined as | x | = { x, if x ≥0 − x. As can be seen from the definition, the absolute value of x is always either positive or zero. Indeed, the notion of a distance function in mathematics can be seen to be a generalisation of the absolute value of the difference. Since the square root notation without sign represents the square root. This identity is used as a definition of absolute value of real numbers. The absolute value has the four fundamental properties, The properties given by equations - are readily apparent from the definition. To see that equation holds, choose ε from so that ε ≥0, some additional useful properties are given below. These properties are either implied by or equivalent to the properties given by equations -, for example, Absolute value is used to define the absolute difference, the standard metric on the real numbers. Since the complex numbers are not ordered, the definition given above for the absolute value cannot be directly generalised for a complex number
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Kaon
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In particle physics, a kaon /ˈkeɪ. ɒn/, also called a K meson and denoted K, is any of a group of four mesons distinguished by a quantum number called strangeness. In the quark model they are understood to be states of a strange quark. Kaons have proved to be a source of information on the nature of fundamental interactions since their discovery in cosmic rays in 1947. They were essential in establishing the foundations of the Standard Model of particle physics, such as the model of hadrons. Moreover, direct CP violation was discovered in the kaon decays in the early 2000s by the NA48 and KTeV experiments at CERN, the four kaons are, K−, negatively charged has mass 493. 677±0.013 MeV and mean lifetime ×10−8 s. K+ positively charged must have mass and lifetime equal to that of K−, the mass difference is 0. 032±0.090 MeV, consistent with zero. The difference in lifetime is ×10−8 s, K0, neutrally charged has mass 497. 648±0.022 MeV. It has mean squared charge radius of −0. 076±0.01 fm2, K0, neutrally charged has the same mass. It is clear from the quark model assignments that the kaons form two doublets of isospin, that is, they belong to the representation of SU called the 2. One doublet of strangeness +1 contains the K+ and the K0, the antiparticles form the other doublet. No definite lifetime ^ Weak eigenstate, makeup is missing small CP–violating term. ^ The mass of the K0 L and K0 S are given as that of the K0, however, it is known that a difference between the masses of the K0 L and K0 S on the order of 3. 5×10−12 MeV/c2 exists. Although the K0 and its antiparticle K0 are usually produced via the strong force, the short-lived neutral kaon is called the K S, decays primarily into two pions, and has a mean lifetime 8. 958×10−11 s. An experimental observation made in 1964 that K-longs rarely decay into two pions was the discovery of CP violation, main decay modes for K+, Decay modes for the K− are charge conjugates of the ones above. By and large experiments have driven the development, and that major discoveries came unexpectedly or even against expectations expressed by theorists, sanda, CP violation, In 1947, G. D. The estimated mass of the new particles was very rough, about half a protons mass, more examples of these V-particles were slow in coming. The first breakthrough was obtained at Caltech, where a cloud chamber was taken up Mount Wilson, in 1950,30 charged and 4 neutral V-particles were reported. Inspired by this, numerous mountaintop observations were made over the several years, and by 1953
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Fermilab
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Fermi National Accelerator Laboratory, located just outside Batavia, Illinois, near Chicago, is a United States Department of Energy national laboratory specializing in high-energy particle physics. Since 2007, Fermilab has been operated by the Fermi Research Alliance, a joint venture of the University of Chicago, Fermilab is a part of the Illinois Technology and Research Corridor. Fermilabs Tevatron was a particle accelerator, at 3.9 miles in circumference, it was the worlds fourth-largest particle accelerator. In 1995, the discovery of the top quark was announced by researchers who used the Tevatrons CDF, in addition to high-energy collider physics, Fermilab hosts fixed-target and neutrino experiments, such as MicroBooNE, NOνA and SeaQuest. Completed neutrino experiments include MINOS, MINOS+, MiniBooNE and SciBooNE, the MiniBooNE detector was a 40-foot diameter sphere containing 800 tons of mineral oil lined with 1,520 phototube detectors. An estimated 1 million neutrino events were recorded each year, SciBooNE sat in the same neutrino beam as MiniBooNE but had fine-grained tracking capabilities. In the public realm, Fermilab hosts many events, not only public science lectures and symposia. The site is open dawn to dusk to visitors who present valid photo identification. Asteroid 11998 Fermilab is named in honor of the laboratory, weston, Illinois, was a community next to Batavia voted out of existence by its village board in 1966 to provide a site for Fermilab. The laboratory was founded in 1967 as the National Accelerator Laboratory, the laboratorys first director was Robert Rathbun Wilson, under whom the laboratory opened ahead of time and under budget. Many of the sculptures on the site are of his creation and he is the namesake of the sites high-rise laboratory building, whose unique shape has become the symbol for Fermilab and which is the center of activity on the campus. After Wilson stepped down in 1978 to protest the lack of funding for the lab and it was under his guidance that the original accelerator was replaced with the Tevatron, an accelerator capable of colliding protons and antiprotons at a combined energy of 1.96 TeV. Lederman stepped down in 1989 and remains Director Emeritus, the science education center at the site was named in his honor. The later directors include, John Peoples,1989 to 1999 Michael S, as of 2014, the first stage in the acceleration process takes place in two ion sources which turn hydrogen gas into H− ions. A magnetron generates a plasma to form the ions near the metal surface, at the exit of RFQ, the beam is matched by medium energy beam transport into the entrance of the linear accelerator. The next stage of acceleration is linear particle accelerator and this stage consists of two segments. The first segment has 5 vacuum vessel for drift tubes, operating at 201 MHz, the second stage has 7 side-coupled cavities, operating at 805 MHz. At the end of linac, the particles are accelerated to 400 MeV, immediately before entering the next accelerator, the H− ions pass through a carbon foil, becoming H+ ions
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Leon M. Lederman
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He is Director Emeritus of Fermi National Accelerator Laboratory in Batavia, Illinois, USA. He founded the Illinois Mathematics and Science Academy, in Aurora, Illinois in 1986, in 2012, he was awarded the Vannevar Bush Award for his extraordinary contributions to understanding the basic forces and particles of nature. Lederman was born in New York City, New York, the son of Minna and Morris Lederman, Lederman graduated from the James Monroe High School in the South Bronx. He received his bachelors degree from the City College of New York in 1943 and he then joined the Columbia faculty and eventually became Eugene Higgins Professor of Physics. In 1960, on leave from Columbia, he spent some time at CERN in Geneva as a Ford Foundation Fellow and he took an extended leave of absence from Columbia in 1979 to become director of Fermilab. In 1991, Lederman became President of the American Association for the Advancement of Science, Lederman is also one of the main proponents of the Physics First movement. Also known as Right-side Up Science and Biology Last, this movement seeks to rearrange the current high school curriculum so that physics precedes chemistry. A former president of the American Physical Society, Lederman also received the National Medal of Science, the Wolf Prize, Lederman served as President of the Board of Sponsors of The Bulletin of the Atomic Scientists. He also served on the board of trustees for Science Service, now known as Society for Science & the Public, from 1989 to 1992, among his achievements are the discovery of the muon neutrino in 1962 and the bottom quark in 1977. These helped establish his reputation as among the top particle physicists, in 1977, a group of physicists, the E288 experiment team, led by Leon Lederman announced that a particle with a mass of about 6.0 GeV was being produced by the Fermilab particle accelerator. The particles initial name was the greek letter Upsilon, after taking further data, the group discovered that this particle did not actually exist, and the discovery was named Oops-Leon as a pun on the original name and Ledermans first name. Lederman later wrote his 1993 popular science book The God Particle, If the Universe Is the Answer, – which sought to promote awareness of the significance of such a project – in the context of the projects last years and the changing political climate of the 1990s. The increasingly moribund project was finally shelved that same year after some $2 billion of expenditures, Lederman also received the National Medal of Science, the Elliott Cresson Medal for Physics, the Wolf Prize for Physics and the Enrico Fermi Award. In 1995, he received the Chicago History Museum Making History Award for Distinction in Science Medicine, Lederman was an early supporter of Science Debate 2008, an initiative to get the then-candidates for president, Barack Obama and John McCain, to debate the nations top science policy challenges. Lederman was also a member of the USA Science and Engineering Festivals Advisory Board, Lederman was born in New York to a family of Jewish immigrants from Russia. His father operated a hand laundry while encouraging Leon to pursue his education and he went to elementary school in New York City, continuing on to college and his doctorate in the city. In his book, The God Particle, If the Universe Is the Answer, Lederman wrote that, although he was a chemistry major, he became fascinated with physics, because of the clarity of the logic and the unambiguous results from experimentation. His best friend during his years, Martin Klein, convinced him of the splendors of physics during a long evening over many beers
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Top quark
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The top quark, also known as the t quark or truth quark, is the most massive of all observed elementary particles. Like all quarks, the top quark is a fermion with spin 1/2, and experiences all four fundamental interactions, gravitation, electromagnetism, weak interactions. It has a charge of +2/3 e, It has a large mass of 172.44 ±0.13 ±0.47 GeV/c2. The antiparticle of the top quark is the top antiquark, which differs from it only in some of its properties have equal magnitude. The top quark interacts primarily by the interaction, but can only decay through the weak force. It decays to a W boson and either a quark, a strange quark, or, on the rarest of occasions. The Standard Model predicts its mean lifetime to be roughly 5×10−25 s and this is about a twentieth of the timescale for strong interactions, and therefore it does not form hadrons, giving physicists a unique opportunity to study a bare quark. Because it is so massive, the properties of the top quark allow predictions to be made of the mass of the Higgs boson under certain extensions of the Standard Model, as such, it is extensively studied as a means to discriminate between competing theories. Kobayashi and Maskawa won the 2008 Nobel Prize in Physics for the prediction of the top and bottom quark, in 1973, Makoto Kobayashi and Toshihide Maskawa predicted the existence of a third generation of quarks to explain observed CP violations in kaon decay. The top quark was sometimes called truth quark in the past and this discovery allowed the GIM mechanism to become part of the Standard Model. With the acceptance of the GIM mechanism, Kobayashi and Maskawas prediction also gained in credibility and their case was further strengthened by the discovery of the tau by Martin Lewis Perls team at SLAC between 1974 and 1978. This announced a third generation of leptons, breaking the new symmetry between leptons and quarks introduced by the GIM mechanism, restoration of the symmetry implied the existence of a fifth and sixth quark. It was in not long until a fifth quark, the bottom, was discovered by the E288 experiment team. This strongly suggested that there must also be a sixth quark and it was known that this quark would be heavier than the bottom, requiring more energy to create in particle collisions, but the general expectation was that the sixth quark would soon be found. However, it took another 18 years before the existence of the top was confirmed, early searches for the top quark at SLAC and DESY came up empty-handed. When, in the eighties, the Super Proton Synchrotron at CERN discovered the W boson. As the SPS gained competition from the Tevatron at Fermilab there was no sign of the missing particle. After a race between CERN and Fermilab to discover the top, the accelerator at CERN reached its limits without creating a single top, the Tevatron was the only hadron collider powerful enough to produce top quarks
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Vector boson
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In particle physics, a vector boson is a boson with the spin equal to 1. Some composite particles are bosons, for instance any vector meson. During the 1970s and 1980s, intermediate vector bosons of intermediate mass —drew much attention in particle physics. The Z and W particles interact with the recently confirmed Higgs Boson, the name vector boson arises from quantum field theory. The component of such a particles spin along any axis has the three eigenvalues −ħ,0, and +ħ, meaning that any measurement of its spin can only yield one of these values. The space of spin states therefore is a degree of freedom consisting of three states, the same as the number of components of a vector in three-dimensional space. Quantum superpositions of states can be taken such that they transform under rotations just like the spatial components of a rotating vector. If the vector boson is taken to be the quantum of a field, the field is a vector field, hence the name
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Complex plane
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In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis. It can be thought of as a modified Cartesian plane, with the part of a complex number represented by a displacement along the x-axis. The concept of the plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors, in particular, multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is known as the Argand plane. These are named after Jean-Robert Argand, although they were first described by Norwegian-Danish land surveyor, Argand diagrams are frequently used to plot the positions of the poles and zeroes of a function in the complex plane. In this customary notation the number z corresponds to the point in the Cartesian plane. In the Cartesian plane the point can also be represented in coordinates as = =. In the Cartesian plane it may be assumed that the arctangent takes values from −π/2 to π/2, and some care must be taken to define the real arctangent function for points when x ≤0. Here |z| is the value or modulus of the complex number z, θ, the argument of z, is usually taken on the interval 0 ≤ θ < 2π. Notice that without the constraint on the range of θ, the argument of z is multi-valued, because the exponential function is periodic. Thus, if θ is one value of arg, the values are given by arg = θ + 2nπ. The theory of contour integration comprises a part of complex analysis. In this context the direction of travel around a curve is important – reversing the direction in which the curve is traversed multiplies the value of the integral by −1. By convention the direction is counterclockwise. Almost all of complex analysis is concerned with complex functions – that is, here it is customary to speak of the domain of f as lying in the z-plane, while referring to the range or image of f as a set of points in the w-plane. In symbols we write z = x + i y, f = w = u + i v and it can be useful to think of the complex plane as if it occupied the surface of a sphere. We can establish a correspondence between the points on the surface of the sphere minus the north pole and the points in the complex plane as follows
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BaBar experiment
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Its design was motivated by the investigation of Charge Parity violation. BaBar is located at the SLAC National Accelerator Laboratory, which is operated by Stanford University for the Department of Energy in California, BaBar was set up to understand the disparity between the matter and antimatter content of the universe by measuring Charge Parity violation. CP symmetry is a combination of Charge-conjugation symmetry and Parity symmetry, BaBar focuses on the study of CP violation in the B meson system. The name of the experiment is derived from the nomenclature for the B meson, the experiments mascot was accordingly chosen to be Babar the Elephant. If CP symmetry holds, the rate of B mesons. Consistent results were found by the Belle experiment at the KEK laboratory in Japan, CP violation was already predicted by the Standard Model of particle physics, and well established in the neutral kaon system. The BaBar experiment has increased the accuracy to which this effect has been experimentally measured, currently, results are consistent with the Standard Model, but further investigation of a greater variety of decay modes may reveal discrepancies in the future. The BaBar detector is a particle detector. The BaBar detector ceased operation on 7 April 2008, but data analysis is ongoing, the BaBar detector is cylindrical with the interaction region at the center. In the interaction region,9 GeV electrons collide with 3.1 GeV antielectrons to produce a collision energy of 10.58 GeV. The ϒ decays immediately into a pair of B mesons – half the time B+B−, to detect the particles there are a series of subsystems arranged cylindrically around the interaction region. Drift Chamber Less expensive than silicon, the 40 layers of wires in this gas chamber detect charged particle tracks out to a larger radius. In addition, the DCH also measures the energy loss of the particles as they pass through matter, detector of Internally Reflected Cherenkov Light The DIRC is composed of 144 fused silica bars which radiate and focus Cherenkov radiation to differentiate between kaons and pions. Magnet The Magnet produces a 1.5 T field inside the detector, instrumented Flux Return The IFR is designed to return the flux of the 1.5 T magnet, so it is mostly iron but there is also instrumentation to detect muons and long kaons. The IFR is broken into 6 sextants and two endcaps, each of the sextants has empty spaces which held the 19 layers of Resistive Plate Chambers, which were replaced in 2004 and 2006 with Limited Streamer Tubes interleaved with brass. The brass is there to add mass for the length since the LST modules are so much less massive than the RPCs. On 9 October 2005, BaBar recorded a record luminosity just over 1 ×1034 cm−2s−1 delivered by the PEP-II positron-electron collider, in 2008, BaBar physicists detected the lowest energy particle in the bottomonium quark family. Spokesman Hassan Jawahery said, These results were highly sought after for over 30 years, in May 2012 BaBar reported that their recently analyzed data may suggest possible flaws in the Standard Model of particle physics
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LHCb experiment
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The LHCb experiment is one of seven particle physics detector experiments collecting data at the Large Hadron Collider accelerator at CERN. LHCb is a specialized b-physics experiment, that is measuring the parameters of CP violation in the interactions of b-hadrons, such studies can help to explain the Matter-Antimatter asymmetry of the Universe. The detector is able to perform measurements of production cross sections. Approximately 840 people from 60 scientific institutes, representing 16 countries, form the collaboration who built, as of 2014, the spokesperson for the collaboration is Guy Wilkinson. The experiment is located at point 8 on the LHC tunnel close to Ferney-Voltaire, the MoEDAL experiment shares the same cavern. The experiment has wide physics program covering many important aspects of Heavy Flavor, Electroweak, six key measurements have been identified involving B mesons. These are described in a document that form the core physics programme for the first high energy LHC running in 2010–2012. They include, Measuring the branching ratio of the rare Bs → μ+ μ− decay, Measuring the forward-backward asymmetry of the muon pair in the flavour changing neutral current Bd → K* μ+ μ− decay. Measuring the CP violating phase in the decay Bs → J/ψ φ and this phase is one of the CP observables with the smallest theoretical uncertainty in the Standard Model, and can be significantly modified by new Physics. Measuring properties of radiative B decays, i. e, B meson decays with photons in the final states. Specifically, these are again flavour changing neutral current decays, tree-level determination of the unitarity triangle angle γ. The fact that the two b-hadrons are predominantly produced in the same forward cone is exploited in the layout of the LHCb detector. The LHCb detector is a single arm forward spectrometer with a polar angular coverage from 10 to 300 milliradians in the horizontal and 250 mrad in the vertical plane. The asymmetry between the horizontal and vertical plane is determined by a dipole magnet with the main field component in the vertical direction. The vertex detector is built around the interaction region. It is used to measure the particle trajectories close to the point in order to precisely separate primary and secondary vertices. The detector operates at 7 millimetres from the LHC beam and this implies an enormous flux of particles, The VELO has been designed to withstand integrated fluences of more than 1014 p/cm2 per year for a period of about three years. The detector operates in vacuum and is cooled to approximately −25 °C using a biphase CO2 system, the data of the VELO detector are amplified and read out by the Beetle ASIC
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Euler angles
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The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They can also represent the orientation of a frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra. Any orientation can be achieved by composing three elemental rotations, i. e. rotations about the axes of a coordinate system, Euler angles can be defined by three of these rotations. They can also be defined by geometry and the geometrical definition demonstrates that three rotations are always sufficient to reach any frame. The three elemental rotations may be extrinsic, or intrinsic, Euler angles are typically denoted as α, β, γ, or φ, θ, ψ. Different authors may use different sets of rotation axes to define Euler angles, therefore, any discussion employing Euler angles should always be preceded by their definition. Tait–Bryan angles are also called Cardan angles, nautical angles, heading, elevation, and bank, or yaw, pitch, sometimes, both kinds of sequences are called Euler angles. In that case, the sequences of the first group are called proper or classic Euler angles, the axes of the original frame are denoted as x, y, z and the axes of the rotated frame are denoted as X, Y, Z. The geometrical definition begins defining the line of nodes as the intersection of the planes xy, using it, the three Euler angles can be defined as follows, α is the angle between the x axis and the N axis. β is the angle between the z axis and the Z axis, γ is the angle between the N axis and the X axis. Euler angles between two frames are defined only if both frames have the same handedness. Intrinsic rotations are elemental rotations occur about the axes of a coordinate system XYZ attached to a moving body. Therefore, they change their orientation after each elemental rotation, the XYZ system rotates, while xyz is fixed. Starting with XYZ overlapping xyz, a composition of three intrinsic rotations can be used to any target orientation for XYZ. Euler angles can be defined by intrinsic rotations, the rotated frame XYZ may be imagined to be initially aligned with xyz, before undergoing the three elemental rotations represented by Euler angles. Hence, N can be simply denoted x’, moreover, since the third elemental rotation occurs about Z, it does not change the orientation of Z. Extrinsic rotations are elemental rotations occur about the axes of the fixed coordinate system xyz. The XYZ system rotates, while xyz is fixed, starting with XYZ overlapping xyz, a composition of three extrinsic rotations can be used to reach any target orientation for XYZ
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Nobel Prize in Physics
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The Nobel Prize in Physics is a yearly award given by the Royal Swedish Academy of Sciences for those who conferred the most outstanding contributions for mankind in the field of physics. The first Nobel Prize in Physics was awarded to German/Dutch physicist Wilhelm Röntgen in recognition of the services he has rendered by the discovery of the remarkable rays. This award is administered by the Nobel Foundation and widely regarded as the most prestigious award that a scientist can receive in physics and it is presented in Stockholm at an annual ceremony on December 10, the anniversary of Nobels death. Through 2016, a total of 203 individuals have been awarded the prize, only two women have won the Nobel Prize in Physics, Marie Curie in 1903, and Maria Goeppert Mayer in 1963. Though Nobel wrote several wills during his lifetime, the last one was written a year before he died and was signed at the Swedish-Norwegian Club in Paris on 27 November 1895. Nobel bequeathed 94% of his assets,31 million Swedish kronor, to establish. Due to the level of surrounding the will, it was not until April 26,1897 that it was approved by the Storting. The executors of his will were Ragnar Sohlman and Rudolf Lilljequist, the members of the Norwegian Nobel Committee who were to award the Peace Prize were appointed shortly after the will was approved. The prize-awarding organisations followed, the Karolinska Institutet on June 7, the Swedish Academy on June 9, the Nobel Foundation then reached an agreement on guidelines for how the Nobel Prize should be awarded. In 1900, the Nobel Foundations newly created statutes were promulgated by King Oscar II, according to Nobels will, The Royal Swedish Academy of sciences were to award the Prize in Physics. A maximum of three Nobel laureates and two different works may be selected for the Nobel Prize in Physics, compared with other Nobel Prizes, the nomination and selection process for the prize in Physics is long and rigorous. This is a key reason why it has grown in importance over the years to become the most important prize in Physics, the Nobel laureates are selected by the Nobel Committee for Physics, a Nobel Committee that consists of five members elected by The Royal Swedish Academy of Sciences. In the first stage begins in September, around 3,000 people – selected university professors, Nobel Laureates in Physics and Chemistry. The completed nomination forms arrive at the Nobel Committee no later than 31 January of the following year and these nominees are scrutinized and discussed by experts who narrow it to approximately fifteen names. The committee submits a report with recommendations on the candidates into the Academy. The Academy then makes the selection of the Laureates in Physics through a majority vote. The names of the nominees are never announced, and neither are they told that they have been considered for the prize. Nomination records are sealed for fifty years, while posthumous nominations are not permitted, awards can be made if the individual died in the months between the decision of the prize committee and the ceremony in December