Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. In the electroweak theory this symmetry is gauged, and flavour changing processes exist. In quantum chromodynamics, on the other hand, flavour is a global symmetry. CPT-symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously. ... In the standard model of particle physics the Cabibbo Kobayashi Maskawa matrix (CKM matrix, sometimes earlier called KM matrix) is a unitary matrix which contains information on the strength of flavour changing weak decays. ... CP is the product of two symmetries: C for charge conjugation, which transforms a particle into its antiparticle, and P for parity, which creates the mirror image of a physical system. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ... A quantum number is any one of a set of numbers used to specify the full quantum state of any system in quantum mechanics. ... In particle physics, an elementary particle is a particle of which other, larger particles are composed. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In the standard model of particle physics the Cabibbo Kobayashi Maskawa matrix (CKM matrix, sometimes earlier called KM matrix) is a unitary matrix which contains information on the strength of flavour changing weak decays. ... Quantum chromodynamics (QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and neutron). ...

Definition

If there are two or more particles which have identical interactions, then they may be interchanged without affecting the physics. Any (complex) linear combination of these two give the same physics, as long as they are orthogonal to each other. In other words, the theory possesses symmetry transformations such as , where u and d are the two fields, and M is any unitary matrix with a unit determinant. Such matrices form a Lie group called SU(2). This is an example of flavour symmetry. In mathematics, orthogonal is synonymous with perpendicular when used as a simple adjective that is not part of any longer phrase with a standard definition. ... In mathematics, a Lie group is a group whose elements can be continuously parametrized by real numbers, such as the rotation group, which can be parametrized by the Euler angles. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ...

This symmetry is global for strong interactions, and gauged for weak interactions. The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ...

The term "flavour" was first coined for use in the quark model of hadrons in 1968. A name for the set of quantum numbers related to isospin, hypercharge and strangeness is said to have been found on the way to lunch by Murray Gell-Mann and Harald Fritzsch when they passed a Baskin-Robbins advertising 31 flavours. The quark model is a classification scheme for hadrons in terms of their valence quarks, ie, the quarks (and antiquarks) which give rise to the quantum numbers of the hadrons. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... 1968 (MCMLXVIII) was a leap year starting on Monday (the link is to a full 1968 calendar). ... Isospin (isotopic spin, isobaric spin) is a physical quantity which is mathematically analogous to spin. ... In particle physics, the hypercharge (represented by Y) is the sum of the baryon number B and the flavor charges: strangeness S, charm C, bottomness and topness T, although the last one can be omitted given the extremely short life of the top quark (it decays to other quarks before... In particle physics, strangeness is the number of anti-strange quarks minus the number of strange quarks in a particle. ... Murray Gell-Mann at Harvard University Murray Gell-Mann (born September 15, 1929) is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. ... External links Baskin-Robbins official site. ...

Flavour quantum numbers

Leptons

All leptons carry a lepton number L  =  1. In addition, leptons carry weak isospin, which is T_z  =  −½ for the three charged leptons (ie, e, μ and τ) and T_z  =  ½ for the three associated neutrinos. Each doublet of a charged lepton and a neutrino consisting of opposite T_z are said to constitute one generation of leptons. In addition, one defines a quantum number called weak hypercharge, Y_W which is −1 for the charged leptons and +1 for the neutrinos. Weak isospin and weak hypercharge are gauged in the Standard Model. In physics, a particle is a lepton if it has a spin of 1/2 and does not experience the strong nuclear force. ... In high energy physics, the lepton number is the number of leptons minus the number of antileptons. ... The weak isospin in theoretical physics parallels the idea of the isospin under the strong interaction, but applied under the weak interaction. ... According to the standard model of particle physics, all the elementary particles seen in particle collision experiments can be divided into three generations. ... Weak hypercharge is twice the difference between the electrical charge and the weak isospin. ... The weak isospin in theoretical physics parallels the idea of the isospin under the strong interaction, but applied under the weak interaction. ... Weak hypercharge is twice the difference between the electrical charge and the weak isospin. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ...

Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos. These are conserved in electromagnetic interactions, but violated by weak interactions. Therefore, such flavour quantum numbers are not of great use. A quantum number for each generation is more useful. However, neutrinos of different generations can mix; that is, a neutrino of one flavour can transform into another flavour. The strength of such mixings is specified by a matrix called the MNS matrix. Neutrino oscillation is a quantum mechanical phenomenon whereby a neutrino created with a specific lepton flavor (electron, muon, or tau) can later be measured to have a different flavor. ... In the standard model of particle physics the Maki-Nakagawa-Sakata matrix (MNS matrix) is a unitary matrix which contains information on the mismatch between mass and weak flavour quantum states of neutrinos. ...

Quarks

All quarks carry a baryon number B  =  ⅓. In addition they carry weak isospin, T_z  =  ±½. The positive T_z particles are called up-type quarks and the remainder are down-type quarks. Each doublet of up and down type quarks constitutes one generation of quarks. Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ... In particle physics, the baryon number is an approximate conserved quantum number. ... The weak isospin in theoretical physics parallels the idea of the isospin under the strong interaction, but applied under the weak interaction. ... According to the standard model of particle physics, all the elementary particles seen in particle collision experiments can be divided into three generations. ...

Quarks have the following flavour quantum numbers —

• Isospin which has value I_z = ½ for the up quark and value I_z = −½ for the down quark.
• Strangeness (S): a quantum number introduced by Murray Gell-Mann. The strange antiquark is defined to have strangeness +1. This is a down-type quark.
• Charm (C) number which is +1 for the charm quark. This is an up-type quark.
• Bottom (also called beauty) quantum number, B': which is +1 for the down-type bottom antiquark.
• Top (sometimes called truth) quantum number, T: +1 for the up-type top quark.

These are useful quantum numbers since they are conserved by both the electromagnetic and strong forces. Out of them can be built the derived quantum numbers Isospin (isotopic spin, isobaric spin) is a physical quantity which is mathematically analogous to spin. ... In particle physics, strangeness is the number of anti-strange quarks minus the number of strange quarks in a particle. ... Murray Gell-Mann at Harvard University Murray Gell-Mann (born September 15, 1929) is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. ... For other uses of this term, see: Quark (disambiguation) 1974 discovery photograph of a possible charmed baryon In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ... The bottom quark is a third-generation quark with a charge of -(1/3)e. ... The top quark is a third-generation quark with a charge of +(2/3)e. ...

• hypercharge: Y = B+S+C+B'+T and
• electric charge: Q = I_z+Y/2.

A quark of a given flavour is an eigenstate of the weak interaction part of the Hamiltonian: it will interact in a definite way with the W⁺, W⁻ and Z bosons. On the other hand, a fermion of a fixed mass (an eigenstate of the kinetic and strong interaction parts of the Hamiltonian) is normally a superposition of various flavours. As a result, the flavour content of a quantum state may change as it propagates freely. The transformation from flavour to mass basis for quarks is given by the so-called Cabbibo-Kobayashi-Maskawa matrix (CKM matrix). By definition therefore, this matrix defines the strength of flavour changes under weak interactions of quarks. In particle physics, the hypercharge (represented by Y) is the sum of the baryon number B and the flavor charges: strangeness S, charm C, bottomness and topness T, although the last one can be omitted given the extremely short life of the top quark (it decays to other quarks before... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... In linear algebra, the eigenvectors (from the German eigen meaning inherent, characteristic) of a linear operator are non-zero vectors which, when operated on by the operator, result in a scalar multiple of themselves. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... Please wikify (format) this article as suggested in the Guide to layout and the Manual of Style. ... In physics, bosons, named after Satyendra Nath Bose, are particles with integer spin. ... In particle physics, fermions, (named after Enrico Fermi), are particles with semi-integer spin. ... A quantum state is any possible state in which a quantum mechanical system can be. ... In the standard model of particle physics the Cabibbo Kobayashi Maskawa matrix (CKM matrix, sometimes earlier called KM matrix) is a unitary matrix which contains information on the strength of flavour changing weak decays. ...

The CKM matrix allows for CP violation if there are at least three generations. The connection with the strong CP problem is explored in a separate article. In physics, and specifically particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics. ... In particle physics, the strong CP problem is the puzzling question why Quantum Chromodynamics (QCD) does not seem to break the CP-symmetry. ...

Antiparticles and hadrons

Flavour quantum numbers are additive. Hence antiparticles have flavour equal in magnitude to the particle but opposite in sign. Hadrons inherit their flavour quantum number from their valence quarks: this is the basis of the classification in the quark model. The relations between the hypercharge, electric charge and other flavour quantum numbers hold for hadrons as well as quarks. For each kind of particle, there is an associated antiparticle with the same mass but opposite electromagnetic, weak, and strong charges, as well as spin. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... The quark model is a classification scheme for hadrons in terms of their valence quarks, ie, the quarks (and antiquarks) which give rise to the quantum numbers of the hadrons. ... The quark model is a classification scheme for hadrons in terms of their valence quarks, ie, the quarks (and antiquarks) which give rise to the quantum numbers of the hadrons. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ...

Quantum chromodynamics

(Flavour symmetry is closely related to chiral symmetry. This part of the article is best read along with the one on chirality (physics).) A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ...

Quantum chromodynamics contains six flavours of quarks. However, their masses differ. As a result, they are not strictly interchangeable with each other. Two of the flavours, called up and down, are close to having equal masses, and the theory of these two quarks possesses an approximate SU(2) symmetry. Under some circumstances one can take N_f flavours to have the same masses and obtain an effective SU(N_f) flavour symmetry. Quantum chromodynamics (QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and neutron). ... Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ... Up describes the positive z-value in a gravitational field, just as down represents the negative z-value. ... A down is a hill, usually made of chalk and in southern England. ...

Under some circumstances, the masses of the quarks can be neglected entirely. In that case, each flavour of quark possesses a chiral symmetry. One can then make flavour transformations independently on the left- and right-handed parts of each quark field. The flavour group is then a chiral group . A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ...

If all quarks have equal mass, then this chiral symmetry is broken to the vector symmetry of the diagonal flavour group which applies the same transformation to both helicities of the quarks. Such a reduction of the symmetry is called explicit symmetry breaking. The amount of explicit symmetry breaking is controlled by the current quark masses in QCD. this page is about helicity in fluid mechanics. ... The current quark mass is also called the mass of the naked quarks. ...

Even if quarks are massless, chiral flavour symmetry can be spontaneously broken if for some reason the vacuum of the theory contains a chiral condensate (as it does in low-energy QCD). This gives rise to an effective mass for the quarks, often identified with the valence quark mass in QCD. This article or section should be merged with fermionic condensate In a theory with two chiral fields, ψ1 and ψ2 with a global symmetry relating the relative phases of both fields, but at low temperatures, the correlation function is nonzero, then we say a fermion condensate (also called chiral condensate... Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ...

Symmetries of QCD

Analysis of experiments indicate that the current quark masses of the lighter flavours of quarks are much smaller than the QCD scale, Λ_QCD, hence chiral flavour symmetry is a good approximation to QCD for the up, down and strange quarks. The success of chiral perturbation theory and the even more naive chiral models spring from this fact. The valence quark masses extracted from the quark model are much larger than the current quark mass. This indicates that QCD has spontaneous chiral symmetry breaking with the formation of a chiral condensate. Other phases of QCD may break the chiral flavour symmetries in other ways. In particle physics, QCD scale is the energy scale (or length scale) associated with the processes of Quantum chromodynamics (QCD), i. ... Quantum chromodynamics (QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and neutron). ... Chiral perturbation theory is an effective field theory constructed on a lagrangian consistent with the (approximate) chiral symmetry of quantum chromodynamics. ... In nuclear physics, the chiral model is a phenemological model describing mesons in the chiral limit where the masses of the quarks goes to zero (without mentioning quarks at all). ... The quark model is a classification scheme for hadrons in terms of their valence quarks, ie, the quarks (and antiquarks) which give rise to the quantum numbers of the hadrons. ... This article or section should be merged with fermionic condensate In a theory with two chiral fields, ψ1 and ψ2 with a global symmetry relating the relative phases of both fields, but at low temperatures, the correlation function is nonzero, then we say a fermion condensate (also called chiral condensate... Quark Matter refers to any of a number of phases of matter built out of quarks and gluons. ...

Conservation laws

Absolutely conserved flavour quantum numbers are

• the electric charge Q
• the difference of the baryon number and the lepton number: B−L

All other flavour quantum numbers are violated by the electroweak interactions. Baryon number and lepton number are separately violated in the electroweak interactions through the chiral anomaly. Strong interactions conserve all flavours. Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... In particle physics, the baryon number is an approximate conserved quantum number. ... In high energy physics, the lepton number is the number of leptons minus the number of antileptons. ... In high energy physics, B−L (pronounced bee minus ell) is the baryon number minus the lepton number. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... In particle physics, the baryon number is an approximate conserved quantum number. ... In high energy physics, the lepton number is the number of leptons minus the number of antileptons. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... A chiral anomaly is the anomalous nonconservation of a chiral current. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ...

History

Some of the historical events that lead to the development of flavour symmetry are discussed in the article on isospin. Isospin (isotopic spin, isobaric spin) is a physical quantity which is mathematically analogous to spin. ...

See also

• Field theoretical formulation of the standard model
• Weak interactions, flavour changing processes and CP violation
• Quantum chromodynamics, strong CP problem and chirality (physics)
• Chiral symmetry breaking and quark matter
• Quarks, leptons and hadrons.
• Quark flavor tagging is an example of particle identification in experimental particle physics.

This is a detailed description of the standard model (SM) of particle physics. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... In the standard model of particle physics the Cabibbo Kobayashi Maskawa matrix (CKM matrix, sometimes earlier called KM matrix) is a unitary matrix which contains information on the strength of flavour changing weak decays. ... In physics, and specifically particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics. ... Quantum chromodynamics (QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and neutron). ... In particle physics, the strong CP problem is the puzzling question why Quantum Chromodynamics (QCD) does not seem to break the CP-symmetry. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ... In particle physics, chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the chiral symmetry of gauge theory such as Quantum Chromodynamics. ... Quark Matter refers to any of a number of phases of matter built out of quarks and gluons. ... Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ... In physics, a particle is a lepton if it has a spin of 1/2 and does not experience the strong nuclear force. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... Particle identification refers to the process of using information left by an elementary particle passing through a particle detector to identify the type of particle. ... From Latin ex- + -periri (akin to periculum attempt). ...

References and external links

• The particle data group.