Noncentral chi distributionIn probability theory and statistics, the noncentral chi distribution is a noncentral generalization of the chi distribution. It is also known as the generalized Rayleigh distribution. If are k independent, normally distributed random variables with means and variances , then the statistic is distributed according to the noncentral chi distribution. The noncentral chi distribution has two parameters: which specifies the number of degrees of freedom (i.e.
B mesonIn particle physics, B mesons are mesons composed of a bottom antiquark and either an up (_B+), down (_B0), strange (_Strange B0) or charm quark (_Charmed B+). The combination of a bottom antiquark and a top quark is not thought to be possible because of the top quark's short lifetime. The combination of a bottom antiquark and a bottom quark is not a B meson, but rather bottomonium, which is something else entirely. Each B meson has an antiparticle that is composed of a bottom quark and an up (_B-), down (_AntiB0), strange (_Strange antiB0) or charm (_Charmed b-) antiquark respectively.
MesonIn particle physics, a meson (ˈmiːzɒn,_ˈmɛzɒn) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, they have a meaningful physical size, a diameter of roughly one femtometre (10^−15 m), which is about 0.6 times the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few tenths of a nanosecond.
Noncentral chi-squared distributionIn probability theory and statistics, the noncentral chi-squared distribution (or noncentral chi-square distribution, noncentral distribution) is a noncentral generalization of the chi-squared distribution. It often arises in the power analysis of statistical tests in which the null distribution is (perhaps asymptotically) a chi-squared distribution; important examples of such tests are the likelihood-ratio tests. Let be k independent, normally distributed random variables with means and unit variances.
Belle experimentThe Belle experiment was a particle physics experiment conducted by the Belle Collaboration, an international collaboration of more than 400 physicists and engineers, at the High Energy Accelerator Research Organisation (KEK) in Tsukuba, Ibaraki Prefecture, Japan. The experiment ran from 1999 to 2010. The Belle detector was located at the collision point of the asymmetric-energy electron–positron collider, KEKB.
LHCb experimentThe LHCb (Large Hadron Collider beauty) experiment is a particle physics detector experiment collecting data at the Large Hadron Collider at CERN. LHCb is a specialized b-physics experiment, designed primarily to measure the parameters of CP violation in the interactions of b-hadrons (heavy particles containing a bottom quark). Such studies can help to explain the matter-antimatter asymmetry of the Universe. The detector is also able to perform measurements of production cross sections, exotic hadron spectroscopy, charm physics and electroweak physics in the forward region.
Rho mesonIn particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as _Rho+, _Rho0 and _Rho-. Along with pions and omega mesons, the rho meson carries the nuclear force within the atomic nucleus. After the pions and kaons, the rho mesons are the lightest strongly interacting particle, with a mass of 775.45MeV for all three states. The rho mesons have a very short lifetime and their decay width is about 145MeV with the peculiar feature that the decay widths are not described by a Breit–Wigner form.
PionIn particle physics, a pion (or a pi meson, denoted with the Greek letter pi: _Pion) is any of three subatomic particles: _Pion0, _Pion+, and _Pion-. Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more generally, the lightest hadrons. They are unstable, with the charged pions _Pion+ and _Pion- decaying after a mean lifetime of 26.033 nanoseconds (2.6033e-8 seconds), and the neutral pion _Pion0 decaying after a much shorter lifetime of 85 attoseconds (8.
Rice distributionIn probability theory, the Rice distribution or Rician distribution (or, less commonly, Ricean distribution) is the probability distribution of the magnitude of a circularly-symmetric bivariate normal random variable, possibly with non-zero mean (noncentral). It was named after Stephen O. Rice (1907–1986). The probability density function is where I0(z) is the modified Bessel function of the first kind with order zero.
Chi-squared distributionIn probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals.
Chi distributionIn probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable and the origin. It is thus related to the chi-squared distribution by describing the distribution of the positive square roots of a variable obeying a chi-squared distribution.
D mesonThe D mesons are the lightest particle containing charm quarks. They are often studied to gain knowledge on the weak interaction. The strange D mesons (Ds) were called "F mesons" prior to 1986. The D mesons were discovered in 1976 by the Mark I detector at the Stanford Linear Accelerator Center. Since the D mesons are the lightest mesons containing a single charm quark (or antiquark), they must change the charm (anti)quark into an (anti)quark of another type to decay.
Quadratic form (statistics)In multivariate statistics, if is a vector of random variables, and is an -dimensional symmetric matrix, then the scalar quantity is known as a quadratic form in . It can be shown that where and are the expected value and variance-covariance matrix of , respectively, and tr denotes the trace of a matrix. This result only depends on the existence of and ; in particular, normality of is not required. A book treatment of the topic of quadratic forms in random variables is that of Mathai and Provost.
Coupling constantIn physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, , between the bodies; thus: in for Newtonian gravity and in for electrostatic.
Moment-generating functionIn probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple results for the moment-generating functions of distributions defined by the weighted sums of random variables.
Omega mesonThe omega meson (_Omega meson) is a flavourless meson formed from a superposition of an up quark–antiquark and a down quark–antiquark pair. It is part of the vector meson nonet and mediates the nuclear force along with pions and rho mesons. The most common decay mode for the ω meson is _Pion+_Pion0_Pion- at 89.2±0.7%, followed by _Pion0_Gamma at 8.34±0.26%. The quark composition of the _Omega meson meson can be thought of as a mix between _up quark_up antiquark, _down quark_down antiquark and _strange quark_strange antiquark states, but it is very nearly a pure symmetric _up quark_up antiquark-_down quark_down antiquark state.
J/psi mesonThe _J/psi (J/psi) meson ˈdʒeɪ_ˈsaɪ_ˈmiːzɒn is a subatomic particle, a flavor-neutral meson consisting of a charm quark and a charm antiquark. Mesons formed by a bound state of a charm quark and a charm anti-quark are generally known as "charmonium" or psions. The _J/Psi is the most common form of charmonium, due to its spin of 1 and its low rest mass. The _J/Psi has a rest mass of 3.0969GeV/c2, just above that of the _charmed eta (2.9836GeV/c2), and a mean lifetime of 7.2e-21s.
Ratio distributionA ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. Given two (usually independent) random variables X and Y, the distribution of the random variable Z that is formed as the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called the normal ratio distribution), which comes about as the ratio of two normally distributed variables with zero mean.
Tau (particle)The tau (τ), also called the tau lepton, tau particle, tauon or tau electron, is an elementary particle similar to the electron, with negative electric charge and a spin of 1/2. Like the electron, the muon, and the three neutrinos, the tau is a lepton, and like all elementary particles with half-integer spin, the tau has a corresponding antiparticle of opposite charge but equal mass and spin. In the tau's case, this is the "antitau" (also called the positive tau). Tau particles are denoted by the symbol _Tau- and the antitaus by _Tau+.
SupersymmetryIn a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist. Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics.
