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| {{other uses|Flavour (disambiguation)}}
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| {| align=right
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| |[[Image:Electron.svg|64px]]||[[Image:Muon.svg|64px]]||[[Image:Tau lepton.svg|64px]]
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| |[[Image:Electron neutrino.svg|64px]]||[[Image:Muon neutrino.svg|64px]]||[[Image:Tau neutrino.svg|64px]]
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| | colspan=3 style="font-size:90%" align=center |Six flavours of leptons
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| |}
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| {{Flavour quantum numbers}}
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| In [[particle physics]], '''flavour''' or '''flavor''' refers to a species of an [[elementary particle]]. The [[Standard Model]] counts six flavours of [[quark]]s and six flavours of [[lepton]]s. They are conventionally parametrized with ''flavour [[quantum number]]s'' that are assigned to all [[subatomic particle]]s, including composite ones. For [[hadron]]s, these quantum numbers depend on the number of constituent quarks of particular flavours.
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| ==Intuitive description==
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| Elementary particles are not eternal and undestroyable. Unlike classical mechanics where [[force]]s only change a [[particle]]'s [[momentum]], the [[weak interaction|weak force]] can alter the essence of a particle, even an elementary particle. Namely, it can convert one quark to another quark with different [[mass]] and [[electric charge]], and the same for leptons. From the point of view of [[quantum mechanics]] changing the flavour of a particle with the weak force isn't a different process, in principle, from changing its [[spin (physics)|spin]] with [[electromagnetic interaction]], and should be described with quantum numbers as well. In particular, flavour [[quantum state|states]] may experience [[quantum superposition]].
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| Like the principal quantum number of an [[electron]] in [[atomic physics]] specifies on which [[electron shell|shell]] it resides, that results in different [[energy level]]s for the whole atom, the five flavour quantum numbers of a quark specify which of six flavours (u, d, s, c, b, t) does it have, that results in different types of [[baryon]]s and [[meson]]s with different masses, electric charges, and decay modes.
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| ==Flavour symmetry==<!--'Flavour symmetry' redirects here-->
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| 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 particles give the same physics, as long as they are [[orthogonal]] or perpendicular to each other. In other words, the theory possesses symmetry transformations such as <math>M\left({u\atop d}\right)</math>, where {{mvar|u}} and {{mvar|d}} are the two fields, and {{mvar|M}} is any {{gaps|2|×|2}} [[unitary matrix]] with a unit [[determinant]]. Such matrices form a [[Lie group]] called [[SU(2)]] (see [[special unitary group]]). This is an example of flavour symmetry.
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| In [[quantum chromodynamics]], flavour is a [[global symmetry]]. In the [[electroweak theory]], on the other hand, this symmetry is broken, and flavour changing processes exist, such as [[quark|quark decay]] or [[neutrino oscillation]]s.
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| ==Flavour quantum numbers==
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| ===Leptons===
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| {{offtopic|lepton number|date=February 2014}}
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| All [[lepton]]s carry a [[lepton number]] {{math|1=''L'' = 1}}. In addition, leptons carry [[weak isospin]], {{math|''T''<sub>3</sub>}}, which is −{{sfrac|1|2}} for the three charged leptons (i.e. [[electron]], [[muon]] and [[tau (particle)|tau]]) and +{{sfrac|1|2}} for the three associated [[neutrino]]s. Each doublet of a charged lepton and a neutrino consisting of opposite {{math|''T''<sub>3</sub>}} are said to constitute one [[generation (particle physics)|generation]] of leptons. In addition, one defines a quantum number called [[weak hypercharge]], {{math|''Y''<sub>W</sub>}}, which is −1 for all [[Chirality (physics)|left-handed]] leptons.<ref>See table in
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| {{cite journal
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| |author=S. Raby, R. Slanky
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| |year=1997
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| |title=Neutrino Masses: How to add them to the Standard Model
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| |url=http://theta13.lbl.gov/neutrino_book_pdfs/04_03_Neutrino_Masses.pdf
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| |journal=[[Los Alamos Science]]
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| |volume= |issue=25 |page=64
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| }}</ref> Weak isospin and weak hypercharge are [[Gauge Theory|gauged]] in the [[Standard Model]].
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| 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 separate quantum number for each [[generation (particle physics)|generation]] is more useful: electronic lepton number (+1 for electrons and electron neutrinos), muonic lepton number (+1 for muons and muon neutrinos), and tauonic lepton number (+1 for tau leptons and tau neutrinos). However, even these numbers are not absolutely conserved, as neutrinos of different generations can [[quantum superposition|mix]]; that is, a neutrino of one flavour can [[neutrino oscillation|transform into another flavour]]. The strength of such mixings is specified by a matrix called the [[Pontecorvo–Maki–Nakagawa–Sakata matrix]] (PMNS matrix).
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| ===Quarks===
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| All [[quark]]s carry a [[baryon number]] {{math|1=''B'' = {{sfrac|1|3}}}}. In addition they carry weak isospin, {{math|1=''T''<sub>3</sub> = ±{{sfrac|1|2}}}}. The positive-{{math|''T''<sub>3</sub>}} quarks (up, charm, and top quarks) are called ''up-type quarks'' and negative-{{math|''T''<sub>3</sub>}} ones are called ''down-type quarks''. Each doublet of up and down type quarks constitutes one [[generation (particle physics)|generation]] of quarks.
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| For all the quark flavour quantum numbers (strangeness, [[charm (quantum number)|charm]], [[topness]] and [[bottomness]]) the convention is that the flavour charge and the electric charge of a quark have the same [[sign (mathematics)|sign]]. With this, any flavor carried by a charged [[meson]] has the same sign as its charge. Quarks have the following flavour quantum numbers:
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| *[[Isospin]], less ambiguously known as ''isobaric spin'', which has value {{math|1=''I''<sub>3</sub> = {{sfrac|1|2}}}} for the up quark and value {{math|1=''I''<sub>3</sub> = −{{sfrac|1|2}}}} for the down quark.
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| *[[Strangeness]] ({{mvar|S}}): Defined as {{math|1=''S'' = −(''n''<sub>s</sub> − ''n''<sub>s̅</sub>}}), where {{math|''n''<sub>s</sub>}} represents the number of [[strange quark]]s ({{SubatomicParticle|Strange quark}}) and {{math|''n''<sub>s̅</sub>}} represents the number of strange antiquarks ({{SubatomicParticle|Strange antiquark}}). This quantum number was introduced by [[Murray Gell-Mann]]. This definition gives the strange quark a strangeness of −1 for the above-mentioned reason.
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| *Charm ({{mvar|C}}): Defined as {{math|1=''C'' = (''n''<sub>c</sub> − ''n''<sub>c̅</sub>)}}, where {{math|''n''<sub>c</sub>}} represents the number of [[charm quark]]s ({{SubatomicParticle|charm quark}}) and {{math|''n''<sub>c̅</sub>}} represents the number of charm antiquarks. Is +1 for the charm quark.
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| *Bottomness ({{mvar|B′}}): Defined as {{math|1=''B′'' = −(''n''<sub>b</sub> − ''n''<sub>b̅</sub>)}}, where {{math|''n''<sub>b</sub>}} represents the number of [[bottom quark]]s ({{SubatomicParticle|bottom quark}}) and {{math|''n''<sub>b̅</sub>}} represents the number of bottom antiquarks. Sometimes referred to as 'beauty' rather than 'bottomness'.
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| *Topness ({{mvar|T}}): Also called 'truth'. Defined as {{math|1=''T'' = (''n''<sub>t</sub> − ''n''<sub>t̅</sub>)}}, where {{math|''n''<sub>t</sub>}} represents the number of [[top quark]]s ({{SubatomicParticle|top quark}}) and {{math|''n''<sub>t̅</sub>}} represents the number of top antiquarks. However, because of the extremely short half-life of the top quark, by the time it can interact strongly it has already decayed to another flavour of quark (usually to a [[bottom quark]]). For that reason the top quark doesn't [[hadronization|hadronize]], that is it never forms any [[meson]] or [[baryon]].
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| These five quantum numbers, together with baryon number that ''is not a flavour quantum number'', completely specify numbers of all 6 quark flavours separately (as {{math|''n''<sub>q</sub> − ''n''<sub>q̅</sub>}}, i.e. an antiquark is counted with the minus sign). They are conserved by both the electromagnetic and strong interactions (but not the weak interaction). Out of them can be built the derived quantum numbers:
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| *[[Hypercharge]] ({{mvar|Y}}): {{math|1=''Y'' = ''B'' + ''S'' + ''C'' + ''B′'' + ''T''}}
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| *[[Electric charge]]: {{math|1=''Q'' = ''I''<sub>3</sub> + {{sfrac|1|2}}''Y''}} (see [[Gell-Mann–Nishijima formula]])
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| The terms ''strange'' and ''strangeness'' predate the discovery of the quark, and were adopted after its discovery in order to preserve the continuity of the phrase; strangeness of anti-particles being referred to as +1, and particles as −1 as per the original definition. Strangeness was introduced to explain the rate of decay of newly discovered particles and was used in the [[Eightfold Way (physics)|Eightfold Way]] classification of hadrons and in subsequent [[quark model]]s. These quantum numbers are preserved under [[strong interaction|strong]] and [[electromagnetic interaction]]s, but not under [[weak interaction]]s. | |
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| For first-order weak decays, that is processes involving only one quark decay, these quantum numbers (e.g. charm) can only vary by 1 ({{math|{{abs|''C''}} {{=}} ±1}}); {{math|Δ''B′'' {{=}} ±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.
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| A quark of a given flavour is an [[eigenstate]] of the [[weak interaction]] part of the [[Hamiltonian (quantum mechanics)|Hamiltonian]]: it will interact in a definite way with the [[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 [[Cabibbo–Kobayashi–Maskawa matrix]] (CKM matrix). This matrix is analogous to the PMNS matrix for neutrinos, and defines the strength of flavour changes under weak interactions of quarks.
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| The CKM matrix allows for [[CP violation]] if there are at least three generations.
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| ===Antiparticles and hadrons===
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| Flavour quantum numbers are additive. Hence [[antiparticle]]s have flavour equal in magnitude to the particle but opposite in sign. [[Hadron]]s inherit their flavour quantum number from their [[valence quark]]s: 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.
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| ==Quantum chromodynamics==
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| :''Flavour symmetry is closely related to [[chirality (physics)|chiral symmetry]]. This part of the article is best read along with the one on [[chirality (physics)|chirality]].''
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| [[Quantum chromodynamics]] (QCD) contains six flavours of [[quark]]s. However, their masses differ and as a result they are not strictly interchangeable with each other. The up and down flavours are close to having equal masses, and the theory of these two quarks possesses an approximate SU(2) symmetry ([[isospin]] symmetry).
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| Under some circumstances, the masses of the quarks can be neglected entirely. 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 {{math|SU<sub>L</sub>(''N''<sub>f</sub>) × SU<sub>R</sub>(''N''<sub>f</sub>)}}.
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| If all quarks had non-zero but equal masses, then this chiral symmetry is broken to the ''vector symmetry'' of the "diagonal flavour group" {{math|SU(''N''<sub>f</sub>)}}, which applies the same transformation to both [[helicity (particle physics)|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 mass]]es in QCD.
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| Even if quarks are massless, chiral flavour symmetry can be [[spontaneous symmetry breaking|spontaneously broken]] if 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.
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| ===Symmetries of QCD===
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| Analysis of experiments indicate that the current quark masses of the lighter flavours of quarks are much smaller than the [[QCD scale]], Λ<sub>QCD</sub>, hence chiral flavour symmetry is a good approximation to [[Quantum chromodynamics|QCD]] for the up, down and strange quarks. The success of [[chiral perturbation theory]] and the even more naive [[chiral model]]s 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]]. [[Quark matter|Other phases of QCD]] may break the chiral flavour symmetries in other ways.
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| ==Conservation laws==
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| Absolutely conserved flavour quantum numbers are
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| *[[electric charge]] ({{mvar|Q}})
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| *[[weak isospin]] ({{math|''I''<sub>3</sub>}})
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| *[[baryon number]] ({{mvar|B}})
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| *[[lepton number]] ({{mvar|L}})
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| In some theories, the individual baryon and lepton number conservation can be violated, if the difference between them ([[B − L|{{math|''B'' − ''L''}}]]) is conserved (see [[chiral anomaly]]). All other flavour quantum numbers are violated by the [[electroweak interaction]]s. [[Strong interaction]]s conserve all flavours.
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| ==History==
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| Some of the historical events that lead to the development of flavour symmetry are discussed in the article on [[isospin]].
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| ==See also==
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| *[[Standard Model (mathematical formulation)]]
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| *[[Cabibbo–Kobayashi–Maskawa matrix]]
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| *[[Strong CP problem]] and [[chirality (physics)]]
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| *[[Chiral symmetry breaking]] and [[quark matter]]
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| *Quark flavour tagging, such as [[B-tagging]], is an example of [[particle identification]] in experimental particle physics.
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| == References ==
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| <references/>
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| ==Further reading==
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| * [http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf Lessons in Particle Physics] Luis Anchordoqui and Francis Halzen, University of Wisconsin, 18th Dec. 2009
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| == External links ==
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| *[http://pdg.lbl.gov/ The particle data group.]
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| [[Category:Concepts in physics]]
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| [[Category:Standard Model]]
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| [[Category:Quantum chromodynamics]]
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| [[Category:Quark matter]]
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| [[Category:Conservation laws]]
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Is a upcoming condominium located within the neighbourhood of Hillview The Singapore authorities has put in place a new subsidised pancreas transplant programme (Thinkstock photograph). Within the newest effort to spur funding in blighted areas of one of many city's poorest neighborhoods, Chicago plans to sell several hundred properties for the price of a sweet bar.
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The Shiny Hill Drive condominium is an exciting upcoming development in Upper Thomson space by UVD Pte Ltd, a three way partnership between Singapore Land and UOL Group Limited. Located along Vibrant Hill Drive, this web site is well located with close proximity to Thomson Plaza and the future Higher Thomson MRT. Get pleasure from a green and healthy lifestyle with visits to MacRitchie Reservoir, Lower Peirce Reservoir, Bishan Park and Singapore Island Golf Course which are just minutes' drive away
Freehold built-in growth at Jalan Lokam, near Bartley MRT. Nice comfort with shopping and dining at your step. Total of 141 residential and fifty seven business units. Upcoming Condominium at Mount Vernon Highway, 2 minutes walk to Bartley MRT. Enormous growth potential below Master Plan. Whole of 868 units from 1BR to 4BR. City fringe dwelling at low costs. ALL ITEMS ABSOLUTELY OFFERED view this undertaking This site at Woodlands Avenue 5 obtained 7 bids and it's awarded to QingJian Realty Pte Ltd at a price of $216m or $341.2psf ppr with an estimated break-even price of $617psf. Extra Business Areas in Woodlands, apart from Primz Biz Hub, Woodlands Horizon, alongside Woodlands Avenue 5, Avenue 6 and at Gambas to be developed below Master Plan 2013
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