|
Gell-Mann–Nishijima Formula
The Gell-Mann–Nishijima formula (sometimes known as the NNG formula) relates the baryon number ''B'', the strangeness ''S'', the isospin ''I3'' of quarks and hadrons to the electric charge ''Q''. It was originally given by Kazuhiko Nishijima and Tadao Nakano in 1953, and led to the proposal of strangeness as a concept, which Nishijima originally called "eta-charge" after the eta meson. Murray Gell-Mann proposed the formula independently in 1956. The modern version of the formula relates all flavour quantum numbers (isospin up and down, strangeness, charm, bottomness, and topness) with the baryon number and the electric charge. Formula The original form of the Gell-Mann–Nishijima formula is: :Q = I_3 + \frac (B+S)\ This equation was originally based on empirical experiments. It is now understood as a result of the quark model. In particular, the electric charge ''Q'' of a quark or hadron particle is related to its isospin ''I3'' and its hypercharge ''Y'' via the relation: : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baryon Number
In particle physics, the baryon number is a strictly conserved additive quantum number of a system. It is defined as ::B = \frac\left(n_\text - n_\bar\right), where ''n''q is the number of quarks, and ''n'' is the number of antiquarks. Baryons (three quarks) have a baryon number of +1, mesons (one quark, one antiquark) have a baryon number of 0, and antibaryons (three antiquarks) have a baryon number of −1. Exotic hadrons like pentaquarks (four quarks, one antiquark) and tetraquarks (two quarks, two antiquarks) are also classified as baryons and mesons depending on their baryon number. Baryon number vs. quark number Quarks carry not only electric charge, but also charges such as color charge and weak isospin. Because of a phenomenon known as ''color confinement'', a hadron cannot have a net color charge; that is, the total color charge of a particle has to be zero ("white"). A quark can have one of three "colors", dubbed "red", "green", and "blue"; while an antiquar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flavour Quantum Numbers
In particle physics, flavour or flavor refers to the ''species'' of an elementary particle. The Standard Model counts six flavours of quarks and six flavours of leptons. They are conventionally parameterized with ''flavour quantum numbers'' that are assigned to all subatomic particles. They can also be described by some of the family symmetries proposed for the quark-lepton generations. Quantum numbers In classical mechanics, a force acting on a point particle, point-like particle can only alter the particle's dynamical state, i.e., its momentum, angular momentum, etc. Quantum field theory, however, allows interactions that can alter other facets of a particle's nature described by non dynamical, discrete quantum numbers. In particular, the action of the weak interaction, weak force is such that it allows the conversion of quantum numbers describing invariant mass, mass and electric charge of both quarks and leptons from one discrete type to another. This is known as a flavour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether Current
Noether's theorem or Noether's first theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can be determined by the principle of least action. This theorem only applies to continuous and smooth symmetries over physical space. Noether's theorem is used in theoretical physics and the calculus of variations. It reveals the fundamental relation between the symmetries of a physical system and the conservation laws. It also made modern theoretical physicists much more focused on symmetries of physical systems. A generalization of the formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that canno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flavour Symmetry
In particle physics, flavour or flavor refers to the ''species'' of an elementary particle. The Standard Model counts six flavours of quarks and six flavours of leptons. They are conventionally parameterized with ''flavour quantum numbers'' that are assigned to all subatomic particles. They can also be described by some of the family symmetries proposed for the quark-lepton generations. Quantum numbers In classical mechanics, a force acting on a point-like particle can only alter the particle's dynamical state, i.e., its momentum, angular momentum, etc. Quantum field theory, however, allows interactions that can alter other facets of a particle's nature described by non dynamical, discrete quantum numbers. In particular, the action of the weak force is such that it allows the conversion of quantum numbers describing mass and electric charge of both quarks and leptons from one discrete type to another. This is known as a flavour change, or flavour transmutation. Due to their qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SU(3)
In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case. The group operation is matrix multiplication. The special unitary group is a normal subgroup of the unitary group , consisting of all unitary matrices. As a compact classical group, is the group that preserves the standard inner product on \mathbb^n. It is itself a subgroup of the general linear group, \operatorname(n) \subset \operatorname(n) \subset \operatorname(n, \mathbb ). The groups find wide application in the Standard Model of particle physics, especially in the electroweak interaction and in quantum chromodynamics. The groups are important in quantum computing, as they represent the possible quantum logic gate operations in a quantum circuit with n qubits and thus 2^n basis states. (Alternatively, the more general ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called ''color''. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years. QCD exhibits three salient properties: * Color confinement. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quark–antiquark pair is spontaneously produced, turning the initial hadron into a pair of hadrons instead of isolating a color charge. Although ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypercharge
In particle physics, the hypercharge (a portmanteau of hyperonic and charge) ''Y'' of a particle is a quantum number conserved under the strong interaction. The concept of hypercharge provides a single charge operator that accounts for properties of isospin, electric charge, and flavour. The hypercharge is useful to classify hadrons; the similarly named weak hypercharge has an analogous role in the electroweak interaction. Definition Hypercharge is one of two quantum numbers of the SU(3) model of hadrons, alongside isospin . The isospin alone was sufficient for two quark flavours — namely and — whereas presently 6 flavours of quarks are known. SU(3) weight diagrams (see below) are 2 dimensional, with the coordinates referring to two quantum numbers: (also known as ), which is the component of isospin, and , which is the hypercharge (the sum of strangeness , charm , bottomness , topness , and baryon number ). Mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quark Model
In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)", or the Eightfold Way, the successful classification scheme organizing the large number of lighter hadrons that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental verification beginning in the late 1960s and is a valid effective classification of them to date. The model was independently proposed by physicists Murray Gell-Mann, who dubbed them "quarks" in a concise paper, and George Zweig, who suggested "aces" in a longer manuscript. André Petermann also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation. Today, the model has essentially been absorbed as a component of the established quantum field theory of strong and electroweak particle interactions, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topness
Topness (''T'', also called truth), a flavour quantum number, represents the difference between the number of top quarks (t) and number of top antiquarks () that are present in a particle: :T = n_\text - n_\bar By convention, top quarks have a topness of +1 and top antiquarks have a topness of −1. The term "topness" is rarely used; most physicists simply refer to "the number of top quarks" and "the number of top antiquarks". Conservation Like all flavour quantum numbers, topness is preserved under strong and electromagnetic interactions, but not under weak interaction. However the top quark is extremely unstable, with a half-life under 10−23 s, which is the required time for the strong interaction to take place. For that reason the top quark does not hadronize, that is it never forms any meson or baryon, so the topness of a meson or a baryon is always zero. By the time it can interact strongly it has already decayed to another flavour of quark (usually to a bottom qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bottomness
In physics, bottomness (symbol ''B''′ using a prime as plain ''B'' is used already for baryon number) or beauty is a flavour quantum number reflecting the difference between the number of bottom antiquarks (''n'') and the number of bottom quarks (''n'') that are present in a particle: : B^\prime = -(n_b - n_) Bottom quarks have (by convention) a bottomness of −1 while bottom antiquarks have a bottomness of +1. The convention is that the flavour quantum number sign for the quark is the same as the sign of the electric charge (symbol ''Q'') of that quark (in this case, Q = −). As with other flavour-related quantum numbers, bottomness is preserved under strong and electromagnetic interactions, but not under weak interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the stro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charm (quantum Number)
Charm (symbol ''C'') is a flavour quantum number representing the difference between the number of charm quarks () and charm antiquarks () that are present in a particle: :C = n_\text - n_\ By convention, the sign of flavour quantum numbers agree with the sign of the electric charge carried by the quarks of corresponding flavour. The charm quark, which carries an electric charge (''Q'') of +, therefore carries a charm of +1. The charm antiquarks have the opposite charge (), and flavour quantum numbers (). As with any flavour-related quantum numbers, charm is preserved under strong and electromagnetic interaction, but not under weak interaction (see CKM matrix). For first-order weak decays, that is processes involving only one quark decay, charm can only vary by 1 (). Since first-order processes are more common than second-order processes (involving two quark decays), this can be used as an approximate "selection rule" for weak decays. See also * Quantum number References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gell-Mann–Okubo Mass Formula
In physics, the Gell-Mann–Okubo mass formula provides a sum rule for the masses of hadrons within a specific multiplet, determined by their isospin (''I'') and strangeness (or alternatively, hypercharge) :M = a_0 + a_1 Y + a_2 \left I \left( I + 1 \right)-\frac Y^2 \right, where ''a''0, ''a''1, and ''a''2 are free parameters. The rule was first formulated by Murray Gell-Mann in 1961 and independently proposed by Susumu Okubo in 1962. Isospin and hypercharge are generated by SU(3), which can be represented by eight hermitian and traceless matrices corresponding to the "components" of isospin and hypercharge. Six of the matrices correspond to flavor change, and the final two correspond to the third-component of isospin projection, and hypercharge. Theory The mass formula was obtained by considering the representations of the Lie algebra su(3). In particular, the meson octet corresponds to the root system of the adjoint representation. However, the simplest, lowest-dimensional r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
