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, this symmetry is a global (chiral) 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 mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. ... CP-symmetry is a symmetry obtained by a combination of the C-symmetry and the P-symmetry. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The fundamental laws of physics may be chiral, as the weak charge is not invariant under a reflection unless particles are replaced by their antiparticles as well, and kaon decay appears... A quantum number is a number used to parametrise certain properties of particles or other systems 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. ... Quantum chromodynamics (QCD) is the physical theory describing one of the fundamental forces, the strong interaction. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The fundamental laws of physics may be chiral, as the weak charge is not invariant under a reflection unless particles are replaced by their antiparticles as well, and kaon decay appears...

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 matrix with an 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 an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ... 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 force or strong interaction (the term interaction is more precise), also called color force is a fundamental interaction of nature which can be split up into two sub forces: The fundamental strong force and the residual strong force. ... 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 and hypercharge 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. Wikipedia does not have an article with this exact name. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... 1968 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... 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. ...

Weak interactions

Quarks come in 6 flavours: 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ...

• up u (B=1/3, Q=2/3, I_z=1/2, Y=1/3, Y_W=1/3)
• down d (B=1/3, Q=-1/3, I_z=-1/2, Y=1/3, Y_W=1/3)
• strange s (B=1/3, Q=-1/3, I=0, Y=-2/3, Y_W=1/3)
• charm c (B=1/3, Q=2/3, C=1, Y_W=1/3)
• bottom (also called beauty) b (B=1/3, Q=-1/3, B'=-1, Y_W=1/3)
• top (was sometimes called truth) t (B=1/3, Q=2/3, T=1, Y_W=1/3)

Here B is the baryon number, Q the electric charge, I is the isospin, Y the hypercharge, S, C, B', T are the flavour charges strangeness, charm, bottomness and topness. Y_W is the weak hypercharge. 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. ... Strange is a British television drama series, produced by the independent production company Big Bear Productions for the BBC One network. ... Charms - so Russian poet Daniil Kharms spelled his pseudonym Charm can have the following meanings: In the world of paranormal magic, a charm can mean either: An amulet or talisman, or a spell. ... Bottom can refer to: Buttocks In general, the lowermost part (see Wiktionary:Bottom). ... This page is about the pleasant phenomenon. ... This article is about the toy. ... This article is primarily concerned with truth as it is used in the evaluation of propositions, sentences, and similar items. ... In particle physics, the baryon number is an approximate conserved quantum number. ... Electric charge is a fundamental FATTY STASHEconserved property of some subatomic particles, which determines their electromagnetic interactions. ... 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... Charge is a word with many different meanings. ... Weak hypercharge is twice the difference between the electrical charge and the weak isospin. ...

Hadrons inherit their flavour quantum number from their valence quarks: this is the basis of the classification called the Eightfold way or the quark model. The following relations hold for hadrons as well as quarks: Y=B+S+C+B'+T and Q=I_z+Y/2. In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... If in relation to baryons or mesons the term quark is use, then usually the valence quarks are meant. ... The Noble Eightfold Path, according to Buddhism and as taught by Gautama Buddha, is the way to the cessation of suffering, the fourth part of the Four Noble Truths. ... Wikipedia does not have an article with this exact name. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ...

Leptons occur in six other flavours: A lepton is also a unit of currency. ...

• electron e, muon μ, tau τ (L=1, Q=-1, Y_W=-1)
• electron neutrino ν_e, muon neutrino ν_μ, tau neutrino ν_τ (L=1, Q=0, Y_W=-1)

Here L is the lepton number. Properties The electron is a subatomic particle. ... In the Standard Model of particle physics, a muon (Greek μείον = minus) is a semistable fundamental particle with negative electric charge and a spin of 1/2. ... Tau (upper case Τ, lower case τ) is the 19th letter of the Greek alphabet. ... The neutrino is an elementary particle. ... The neutrino is an elementary particle. ... The neutrino is an elementary particle. ... In high energy physics, the lepton number is the number of leptons minus the number of antileptons. ...

Antiparticles have the opposite quantum number of the corresponding particle. For example, the positron (which is the anti-electron) has L=-1 and Q=1. 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. ...

The six flavours of quarks are grouped into three generations: (u,d), (c,s), (t,b). The first member of each generation has charge Q=2/3 and second has Q=-1/3. The leptons are grouped into three generations: (e,ν_e), (μ,&nu_μ), (τ,ν_τ). The first member has Q=-1 and the second has Q=0. The number of generations of quarks and leptons must match in order to cancel the chiral anomaly. Chiral anomaly is the anomalous nonconservation of charge in a quantized theory of chiral fermions coupled to a background gauge field. ...

A fermion 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 part 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). The equivalent for neutrinos is the MNS matrix. 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. ... Bosons, named after Satyendra Nath Bose, are particles which form totally-symmetric composite quantum states. ... In physics, Hamiltonian has distinct but closely related meanings. ... Quite literally, quantum state describes the state of a quantum system. ... 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 mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. ... The neutrino is an elementary particle. ...

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. CP-symmetry is a symmetry obtained by a combination of the C-symmetry and the P-symmetry. ... In particle physics, the strong CP problem is the puzzling question why Quantum Chromodynamics (QCD) does not seem to break the CP-symmetry. ...

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 fundamental laws of physics may be chiral, as the weak charge is not invariant under a reflection unless particles are replaced by their antiparticles as well, and kaon decay appears... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The fundamental laws of physics may be chiral, as the weak charge is not invariant under a reflection unless particles are replaced by their antiparticles as well, and kaon decay appears...

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 be nearly degenerate and obtain an effective SU(N_f) flavour symmetry. Quantum chromodynamics (QCD) is the physical theory describing one of the fundamental forces, the strong interaction. ... 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ... Up describes the positive z-value in a gravitational field, just as down represents the negative z-value. ...

Under some circumstances, the masses of the quarks can be neglected. In that case, each flavour of quarks possesses a chiral symmetry. One can then make flavour transformations independently on the left and right handed quarks. 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 fundamental laws of physics may be chiral, as the weak charge is not invariant under a reflection unless particles are replaced by their antiparticles as well, and kaon decay appears...

If all quarks have equal mass, then this chiral symmetry is broken to the vector symmetry of the diagonal flavour group which involves the same transformation to the two 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. The current quark mass is also called the mass of the naked quarks. ... The acronym QCD can mean: Quantum chromodynamics Quintessential Player This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

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. 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... The acronym QCD can mean: Quantum chromodynamics Quintessential Player This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

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. 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. The current quark mass is also called the mass of the naked quarks. ... In particle physics, QCD scale is the energy scale (or length scale) associated with the processes of Quantum chromodynamics (QCD), i. ... The acronym QCD can mean: Quantum chromodynamics Quintessential Player This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... Wikipedia does not have an article with this exact name. ... The current quark mass is also called the mass of the naked quarks. ... The acronym QCD can mean: Quantum chromodynamics Quintessential Player This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... 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 FATTY STASHEconserved 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 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. ... Chiral anomaly is the anomalous nonconservation of charge in a quantized theory of chiral fermions coupled to a background gauge field. ... 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. ...

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.

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. ... CP-symmetry is a symmetry obtained by a combination of the C-symmetry and the P-symmetry. ... Quantum chromodynamics (QCD) is the physical theory describing one of the fundamental forces, the strong interaction. ... 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 fundamental laws of physics may be chiral, as the weak charge is not invariant under a reflection unless particles are replaced by their antiparticles as well, and kaon decay appears... Quark Matter refers to any of a number of phases of matter built out of quarks and gluons. ... 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ... 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. ...

References and external links

• The particle data group (http://pdg.lbl.gov/)