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Pseudorapidity
In experimental particle physics, pseudorapidity, \eta, is a commonly used spatial coordinate describing the angle of a particle relative to the beam axis. It is defined as :\eta \equiv -\ln\left tan\left(\frac\right)\right where \theta is the angle between the particle three-momentum \mathbf and the positive direction of the beam axis.Introduction to High-Energy Heavy-Ion Collisions, by Cheuk-Yin Wong, See page 24 for definition of rapidity. Inversely, :\theta = 2\arctan\left(e^\right). As a function of three-momentum \mathbf, pseudorapidity can be written as :\eta = \frac \ln \left(\frac\right) = \operatorname\left(\frac \right), where p_\text is the component of the momentum along the beam axis (i.e. the ''longitudinal'' momentum – using the conventional system of coordinates for hadron collider physics, this is also commonly denoted p_z). In the limit where the particle is travelling close to the speed of light, or equivalently in the approximation that the mass of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorapidity Plot
In experimental particle physics, pseudorapidity, \eta, is a commonly used spatial coordinate describing the angle of a particle relative to the beam axis. It is defined as :\eta \equiv -\ln\left tan\left(\frac\right)\right where \theta is the angle between the particle three-momentum \mathbf and the positive direction of the beam axis.Introduction to High-Energy Heavy-Ion Collisions, by Cheuk-Yin Wong, See page 24 for definition of rapidity. Inversely, :\theta = 2\arctan\left(e^\right). As a function of three-momentum \mathbf, pseudorapidity can be written as :\eta = \frac \ln \left(\frac\right) = \operatorname\left(\frac \right), where p_\text is the component of the momentum along the beam axis (i.e. the ''longitudinal'' momentum – using the conventional system of coordinates for hadron collider physics, this is also commonly denoted p_z). In the limit where the particle is travelling close to the speed of light, or equivalently in the approximation that the mass of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorapidity
In experimental particle physics, pseudorapidity, \eta, is a commonly used spatial coordinate describing the angle of a particle relative to the beam axis. It is defined as :\eta \equiv -\ln\left tan\left(\frac\right)\right where \theta is the angle between the particle three-momentum \mathbf and the positive direction of the beam axis.Introduction to High-Energy Heavy-Ion Collisions, by Cheuk-Yin Wong, See page 24 for definition of rapidity. Inversely, :\theta = 2\arctan\left(e^\right). As a function of three-momentum \mathbf, pseudorapidity can be written as :\eta = \frac \ln \left(\frac\right) = \operatorname\left(\frac \right), where p_\text is the component of the momentum along the beam axis (i.e. the ''longitudinal'' momentum – using the conventional system of coordinates for hadron collider physics, this is also commonly denoted p_z). In the limit where the particle is travelling close to the speed of light, or equivalently in the approximation that the mass of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorapidity2
In experimental particle physics, pseudorapidity, \eta, is a commonly used spatial coordinate describing the angle of a particle relative to the beam axis. It is defined as :\eta \equiv -\ln\left tan\left(\frac\right)\right where \theta is the angle between the particle three-momentum \mathbf and the positive direction of the beam axis.Introduction to High-Energy Heavy-Ion Collisions, by Cheuk-Yin Wong, See page 24 for definition of rapidity. Inversely, :\theta = 2\arctan\left(e^\right). As a function of three-momentum \mathbf, pseudorapidity can be written as :\eta = \frac \ln \left(\frac\right) = \operatorname\left(\frac \right), where p_\text is the component of the momentum along the beam axis (i.e. the ''longitudinal'' momentum – using the conventional system of coordinates for hadron collider physics, this is also commonly denoted p_z). In the limit where the particle is travelling close to the speed of light, or equivalently in the approximation that the mass of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rapidity
In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates. For one-dimensional motion, rapidities are additive whereas velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are proportional but, for higher velocities, rapidity takes a larger value, with the rapidity of light being infinite. Using the inverse hyperbolic function , the rapidity corresponding to velocity is where ''c'' is the velocity of light. For low speeds, is approximately . Since in relativity any velocity is constrained to the interval the ratio satisfies . The inverse hyperbolic tangent has the unit interval for its domain and the whole real line for its image; that is, the interval maps onto . History In 1908 Hermann Minkowski expl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partons
In particle physics, the parton model is a model of hadrons, such as protons and neutrons, proposed by Richard Feynman. It is useful for interpreting the cascades of radiation (a parton shower) produced from quantum chromodynamics (QCD) processes and interactions in high-energy particle collisions. Model Parton showers are simulated extensively in Monte Carlo event generators, in order to calibrate and interpret (and thus understand) processes in collider experiments. As such, the name is also used to refer to algorithms that approximate or simulate the process. Motivation The parton model was proposed by Richard Feynman in 1969 as a way to analyze high-energy hadron collisions. Any hadron (for example, a proton) can be considered as a composition of a number of point-like constituents, termed "partons". The parton model was immediately applied to electron-proton deep inelastic scattering by Bjorken and Paschos. Component particles A hadron is composed of a number of point- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bjorken Scaling
James Daniel "BJ" Bjorken (born 1934) is an American theoretical physicist. He was a Putnam Fellow in 1954, received a BS in physics from MIT in 1956, and obtained his PhD from Stanford University in 1959. He was a visiting scholar at the Institute for Advanced Study in the fall of 1962. Bjorken is Emeritus Professor in the SLAC Theory Group at the Stanford Linear Accelerator Center, and was a member of the Theory Department of the Fermi National Accelerator Laboratory (1979–1989). He was awarded the Dirac Medal of the ICTP in 2004; and, in 2015, the Wolf Prize in Physics and the EPS High Energy and Particle Physics Prize. Early life and education James Bjorken's father, J. Daniel Bjorken, was an immigrant from Sweden near Lake Siljan. He changed his surname from "Björkén" to Bjorken upon arriving in the US; he moved to Chicago to work as an electrical engineer, which is where he met his future wife, Edith. James Bjorken grew up in Chicago and enjoyed mathematics, chemi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Transformation
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz. The most common form of the transformation, parametrized by the real constant v, representing a velocity confined to the -direction, is expressed as \begin t' &= \gamma \left( t - \frac \right) \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end where and are the coordinates of an event in two frames with the origins coinciding at 0, where the primed frame is seen from the unprimed frame as moving with speed along the -axis, where is the speed of light, and \gamma = \left ( \sqrt\right )^ is the Lorentz factor. When speed is much smaller than , the Lorentz factor is negligibly different from 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transverse Mass
The transverse mass is a useful quantity to define for use in particle physics as it is invariant under Lorentz boost along the z direction. In natural units, it is: m_T^2 = m^2 + p_x^2 + p_y^2 = E^2 - p_z^2 *where the z-direction is along the beam pipe and so *p_x and p_y are the momentum perpendicular to the beam pipe and *m is the (invariant) mass. This definition of the transverse mass is used in conjunction with the definition of the (directed) transverse energy \vec_T = E \frac = \frac\vec_T with the transverse momentum vector \vec_T = (p_x, p_y). It is easy to see that for vanishing mass (m = 0) the three quantities are the same: E_T = p_T = m_T. The transverse mass is used together with the rapidity, transverse momentum and polar angle in the parameterization of the four-momentum of a single particle: (E, p_x, p_y, p_z) = (m_T \cosh y,\ p_T \cos\phi,\ p_T \sin\phi,\ m_T \sinh y) Using these definitions (in particular for E_) gives for the mass of a two particle system: :M_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Units
In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a Coherence (units of measurement), coherent unit of a quantity. For example, the elementary charge may be used as a natural unit of electric charge, and the speed of light may be used as a natural unit of speed. A purely natural system of units has all of its units defined such that each of these can be expressed as a product of powers of defining physical constants. Through nondimensionalization, physical quantities may then redefined so that the defining constants can be omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of constants, such as and , unless it is ''known'' which units (in dimensionf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four Momentum
In special relativity, four-momentum (also called momentum-energy or momenergy ) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant vector, contravariant four-momentum of a particle with relativistic energy and three-momentum , where is the particle's three-velocity and the Lorentz factor, is p = \left(p^0 , p^1 , p^2 , p^3\right) = \left(\frac E c , p_x , p_y , p_z\right). The quantity of above is ordinary Momentum#Single particle, non-relativistic momentum of the particle and its rest mass. The four-momentum is useful in relativistic calculations because it is a Lorentz covariant vector. This means that it is easy to keep track of how it transforms under Lorentz transformations. The above definition applies under the coordinate convention that . Some authors use the convention , which yields a modified definition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laboratory Frame Of Reference
In theoretical physics, a local reference frame (local frame) refers to a coordinate system or frame of reference that is only expected to function over a small region or a restricted region of space or spacetime. The term is most often used in the context of the application of local inertial frames to small regions of a gravitational field. Although gravitational tidal forces will cause the background geometry to become noticeably non-Euclidean over larger regions, if we restrict ourselves to a sufficiently small region containing a cluster of objects falling together in an ''effectively'' uniform gravitational field, their physics can be described as the physics of that cluster in a space free from explicit background gravitational effects. Equivalence principle When constructing his general theory of relativity, Einstein made the following observation: a freely falling object in a gravitational field will not be able to detect the existence of the field by making local meas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
