View source for Flavour (particle physics)

{{Short description|Species of elementary particle}}
{{Other uses|Flavor (disambiguation)}}
{{Use Oxford spelling|date=August 2016}}
{{more citations needed|date=October 2015}}
{| align=right
 |[[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
 |}
{{Flavour quantum numbers}}

In [[particle physics]], '''flavour''' or '''flavor''' refers to the ''species'' of an [[elementary particle]]. The [[Standard Model]] counts six flavours of [[quark]]s and six flavours of [[lepton]]s. They are conventionally parameterized with ''flavour [[quantum number]]s'' that are assigned to all [[subatomic particle]]s. 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 change, or flavour transmutation. Due to their quantum description, flavour [[quantum state|states]] may also undergo [[quantum superposition]].

In [[atomic physics]] the principal quantum number of an [[electron]] specifies the [[electron shell]] in which it resides, which determines the [[energy level]] of the whole atom. Analogously, the five flavour quantum numbers ([[isospin]], [[strangeness]], [[Charm (quantum number)|charm]], [[bottomness]] or [[topness]]) can characterize the quantum state of quarks, by the degree to which it exhibits six distinct flavours (u, d, s, c, b, t).

Composite particles can be created from multiple quarks, forming [[hadron]]s, such as [[meson]]s and [[baryon]]s, each possessing unique aggregate characteristics, such as different masses, electric charges, and decay modes. A [[hadron]]'s overall flavour quantum numbers depend on the numbers of [[constituent quark]]s of each particular flavour.

=== Conservation laws ===
All of the various charges discussed above are conserved by the fact that the corresponding [[charge (physics)|charge operators]] can be understood as ''generators of symmetries'' that commute with the Hamiltonian. Thus, the eigenvalues of the various charge operators are conserved.

Absolutely conserved quantum numbers in the [[Standard Model]] are:
* [[electric charge]] ({{mvar|Q}})
* [[weak isospin]] ({{math|''T''<sub>3</sub>}})
* [[baryon number]] ({{mvar|B}})<!--including the baryon number for completeness-->
* [[lepton number]] ({{mvar|L}})

In some theories, such as the [[grand unified theory]], the individual baryon and lepton number conservation can be violated, if the difference between them ({{math|[[B − L|''B'' − ''L'']]}}) is conserved (see ''[[Chiral anomaly]]'').

[[Strong interaction]]s conserve all flavours, but all flavour quantum numbers are violated (changed, non-conserved) by [[electroweak interaction]]s.

== Flavour symmetry ==<!--'Flavour symmetry' redirects here-->
If there are two or more particles which have identical interactions, then they may be interchanged without affecting the physics. All (complex) linear combinations of these two particles give the same physics, as long as the combinations 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 (representing the various ''[[generation (particle physics)|generations]]'' of leptons and quarks, see below), 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.

In [[quantum chromodynamics]], flavour is a conserved [[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.

== Flavour quantum numbers ==
=== Leptons ===
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
{{cite journal
 |author      = S. Raby, R. Slanky
 |year        = 1997
 |title       = Neutrino Masses: How to add them to the Standard Model
 |url         = http://theta13.lbl.gov/neutrino_book_pdfs/04_03_Neutrino_Masses.pdf
 |journal     = [[Los Alamos Science]]
 |volume      = 
 |issue       = 25
 |page        = 64
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20110831014543/http://theta13.lbl.gov/neutrino_book_pdfs/04_03_Neutrino_Masses.pdf
 |archive-date = 2011-08-31
 }}</ref> Weak isospin and weak hypercharge are [[Gauge Theory|gauged]] in the [[Standard Model]].

Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos ([[electron neutrino]], [[muon neutrino]] and [[tau neutrino]]). These are conserved in strong and 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).

=== Quarks ===
All [[quark]]s carry a [[baryon number]] {{nowrap| {{mvar|B}} {{=}} {{sfrac|+|1|3}} ,}} and all anti-quarks have {{nowrap| {{mvar|B}} {{=}} {{sfrac|&minus;|1|3}} .}} They also all carry [[weak isospin]], {{nowrap| {{mvar|T}}<sub>3</sub> {{=}} {{sfrac|±|1|2}} .}} The positively charged quarks (up, charm, and top quarks) are called ''up-type quarks'' and have {{nowrap| {{mvar|T}}<sub>3</sub> {{=}} {{sfrac|+|1|2}} ;}} the negatively charged quarks (down, strange, and bottom quarks) are called ''down-type quarks'' and have {{nowrap|{{mvar|T}}<sub>3</sub> {{=}} {{sfrac|&minus;|1|2}} .}} Each doublet of up and down type quarks constitutes one [[generation (particle physics)|generation]] of quarks.

For all the quark flavour quantum numbers listed below, the convention is that the flavour charge and the electric charge of a quark have the same [[sign (mathematics)|sign]]. Thus any flavour carried by a charged [[meson]] has the same sign as its charge. Quarks have the following flavour quantum numbers: 
* The third component of [[isospin]] (usually just "isospin") ({{mvar|I}}{{sub|3}}), which has value {{nowrap| {{mvar|I}}{{sub|3}} {{=}} {{sfrac|1|2}} }} for the up quark and {{nowrap| {{mvar|I}}{{sub|3}} {{=}} &minus;{{sfrac|1|2}} }} for the down quark.
* [[Strangeness]] ({{mvar|S}}): Defined as {{nowrap| {{mvar|S}} {{=}} &minus;{{mvar|n}}{{sub| s}} + {{mvar|n}}{{sub| s&#773;}} ,}} where {{mvar|n}}{{sub|s}} represents the number of [[strange quark]]s ({{SubatomicParticle|Strange quark}}) and {{mvar|n}}{{sub|s&#773;}} 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.
* [[Charm (quantum number)|Charm]] ({{mvar|C}}): Defined as {{nowrap| {{mvar|C}} {{=}} {{mvar|n}}{{sub| c}} − {{mvar|n}}{{sub| c&#773;}} ,}} where {{mvar|n}}{{sub|c}} represents the number of [[charm quark]]s ({{SubatomicParticle|charm quark}}) and {{mvar|n}}{{sub|c&#773;}} represents the number of charm antiquarks. The charm quark's value is +1.
* [[Bottomness]] (or ''beauty'') ({{mvar|B&prime;}}): Defined as {{nowrap| {{mvar|B&prime;}} {{=}} &minus;{{mvar|n}}{{sub| b}} + {{mvar|n}}{{sub| b&#773;}} ,}} where {{mvar|n}}{{sub|b}} represents the number of [[bottom quark]]s ({{SubatomicParticle|bottom quark}}) and {{mvar|n}}{{sub|b&#773;}} represents the number of bottom antiquarks.
* [[Topness]] (or ''truth'') ({{mvar|T}}): Defined as {{nowrap| {{mvar|T}} {{=}} {{mvar|n}}{{sub| t}} − {{mvar|n}}{{sub| t&#773;}} ,}} where {{mvar|n}}{{sub|t}} represents the number of [[top quark]]s ({{SubatomicParticle|top quark}}) and {{mvar|n}}{{sub|t&#773;}} represents the number of top antiquarks. However, because of the extremely short half-life of the top quark (predicted lifetime of only {{val |5|e=-25|u=s}}), 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]].

These five quantum numbers, together with baryon number (which is not a flavour quantum number), completely specify numbers of all 6 quark flavours separately (as {{nowrap| {{mvar|n}}{{sub| q}} − {{mvar|n}}{{sub| q&#773;}} ,}} 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). From them can be built the derived quantum numbers:
* [[Hypercharge]] ({{mvar|Y}}): {{nowrap| {{math|''Y'' {{=}} ''B'' + ''S'' + ''C'' + ''B&prime;'' + ''T''}} }}
* [[Electric charge]] ({{mvar|Q}}): {{nowrap| {{math|''Q'' {{=}} ''I''<sub>3</sub> + {{sfrac|1|2}}''Y''}} }} (see [[Gell-Mann–Nishijima formula]])

The terms "strange" and "strangeness" predate the discovery of the quark, but continued to be used after its discovery for the sake of continuity (i.e. the strangeness of each type of hadron remained the same); 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, such as the kaon, 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.

For first-order weak decays, that is processes involving only one quark decay, these quantum numbers (e.g. charm) can only vary by 1, that is, for a decay involving a charmed quark or antiquark either as the incident particle or as a decay byproduct, {{nowrap| {{math|Δ''C'' {{=}} ±1}} ;}} likewise, for a decay involving a bottom quark or antiquark {{nowrap| {{math|Δ''B&prime;'' {{=}} ±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.

A special mixture of quark flavours is an [[eigenstate]] of the [[weak interaction]] part of the [[Hamiltonian (quantum mechanics)|Hamiltonian]], so will interact in a particularly simple way with the [[W and Z bosons|W bosons]] (charged weak interactions violate flavour). On the other hand, a [[fermion]] of a fixed mass (an eigenstate of the kinetic and strong interaction parts of the Hamiltonian) is an eigenstate of flavour. The transformation from the former basis to the flavour-eigenstate/mass-eigenstate basis for quarks underlies the [[Cabibbo–Kobayashi–Maskawa matrix]] (CKM matrix). This matrix is analogous to the PMNS matrix for neutrinos, and quantifies flavour changes under charged weak interactions of quarks.

The CKM matrix allows for [[CP violation]] if there are at least three generations.

=== Antiparticles and hadrons ===
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.

== Flavour problem ==
The Flavour problem (also known as the Flavour puzzle) is the inability of current [[Standard Model]] flavour physics to explain why the free parameters of particles in the Standard Model have the values they have, and why there are specified values for mixing angles in the [[Pontecorvo–Maki–Nakagawa–Sakata matrix|PMNS]] and [[Cabibbo–Kobayashi–Maskawa matrix|CKM]] matrices.  These free parameters - the [[fermion]] masses and their mixing angles - appear to be specifically tuned. Understanding the reason for such tuning would be the solution to the flavor puzzle. There are very fundamental questions involved in this puzzle such as why there are three generations of                 [[quark]]s (up-down, charm-strange, and top-bottom quarks) and [[lepton]]s (electron, muon and tau neutrino), as well as how and why the mass and mixing hierarchy arises among different flavours of these fermions.<ref>{{Cite journal|last=Feruglio|first=Ferruccio|date=August 2015|title=Pieces of the Flavour Puzzle|journal=The European Physical Journal C|volume=75|issue=8|pages=373|doi=10.1140/epjc/s10052-015-3576-5|pmid=26300692|issn=1434-6044|pmc=4538584|arxiv=1503.04071|bibcode=2015EPJC...75..373F}}</ref><ref>{{Cite journal|last1=Babu|first1=K. S.|last2=Mohapatra|first2=R. N.|date=1999-09-27|title=Supersymmetry, Local Horizontal Unification, and a Solution to the Flavor Puzzle|url=https://link.aps.org/doi/10.1103/PhysRevLett.83.2522|journal=Physical Review Letters|volume=83|issue=13|pages=2522–2525|doi=10.1103/PhysRevLett.83.2522|arxiv=hep-ph/9906271|bibcode=1999PhRvL..83.2522B|s2cid=1081641}}</ref><ref>{{Cite journal|last1=Alonso|first1=Rodrigo|last2=Carmona|first2=Adrian|last3=Dillon|first3=Barry M.|last4=Kamenik|first4=Jernej F.|last5=Camalich|first5=Jorge Martin|last6=Zupan|first6=Jure|date=2018-10-16|title=A clockwork solution to the flavor puzzle|url=https://doi.org/10.1007/JHEP10(2018)099|journal=Journal of High Energy Physics|language=en|volume=2018|issue=10|pages=99|doi=10.1007/JHEP10(2018)099|issn=1029-8479|arxiv=1807.09792|bibcode=2018JHEP...10..099A|s2cid=119410222}}</ref>

== Quantum chromodynamics ==
{{hatnote|Flavour symmetry is closely related to [[chirality (physics)|chiral symmetry]]. This part of the article is best read along with the one on chirality.}}

[[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).

=== Chiral symmetry description ===
Under some circumstances (for instance when the quark masses are much smaller than the [[chiral symmetry breaking]] scale of 250&nbsp;MeV), the masses of quarks do not substantially contribute to the system's behavior, and to zeroth approximation the masses of the lightest quarks can be ignored for most purposes, as if they had zero mass. The simplified behavior of flavour transformations can then be successfully modeled as acting independently on the left- and right-handed parts of each quark field. This approximate description of the flavour symmetry is described by a chiral group {{math|SU<sub>L</sub>({{mvar|N}}<sub>f</sub>) × SU<sub>R</sub>({{mvar|N}}<sub>f</sub>)}}.

=== Vector symmetry description ===
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. This reduction of symmetry is a form of ''[[explicit symmetry breaking]]''. The strength of explicit symmetry breaking is controlled by the [[current quark mass]]es in QCD.

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.

=== 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<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.

== History ==
{{See also|Isospin#History|Eightfold way (physics)|Chiral symmetry|J/psi meson}}

{{expand section|date=March 2017|Add history of lepton flavours}}

=== Isospin ===
Isospin, strangeness and hypercharge predate the quark model. The first of those quantum numbers, Isospin, was introduced as a concept in 1932 by [[Werner Heisenberg]],<ref>
{{cite journal
 |last=Heisenberg |first=W. |author-link=Werner Heisenberg
 |year=1932
 |title=Über den Bau der Atomkerne
 |journal=[[Zeitschrift für Physik]]
 |volume=77 |issue=1–2 |pages=1–11
 |doi=10.1007/BF01342433
 |bibcode = 1932ZPhy...77....1H |s2cid=186218053 |language=de
}}</ref> to explain symmetries of the then newly discovered [[neutron]] (symbol n):
* The [[mass]] of the neutron and the [[proton]] (symbol {{math|p}}) are almost identical: They are nearly degenerate, and both are thus often referred to as “[[nucleon]]s”, a term that ignores their differences. Although the proton has a positive electric charge, and the neutron is neutral, they are almost identical in all other aspects, and their nuclear binding-force interactions (old name for the residual color force) are so strong compared to the electrical force between some, that there is very little point in paying much attention to their differences.
* The strength of the strong interaction between any pair of nucleons is the same, independent of whether they are interacting as protons or as neutrons.

Protons and neutrons were grouped together as [[nucleon]]s and treated as different states of the same particle, because they both have nearly the same mass and interact in nearly the same way, if the (much weaker) electromagnetic interaction is neglected.

Heisenberg noted that the mathematical formulation of this symmetry was in certain respects similar to the mathematical formulation of non-relativistic [[Spin (physics)|spin]], whence the name "isospin" derives. The neutron and the proton are assigned to the [[doublet (physics)|doublet]] (the spin-{{frac|1|2}}, '''2''', or [[fundamental representation]]) of SU(2), with the proton and neutron being then associated with different isospin projections {{nowrap|{{math|''I''}}{{sub|3}} {{=}} {{frac|+|1|2}}}} and {{frac|−|1|2}} respectively. The pions are assigned to the [[spin triplet|triplet]] (the spin-1, '''3''', or [[adjoint representation of a Lie group|adjoint representation]]) of SU(2). Though there is a difference from the theory of spin: The group action does not preserve [[flavor (particle physics)|flavor]] (in fact, the group action is specifically an exchange of flavour).

When constructing a physical theory of [[nuclear force]]s, one could simply assume that it does not depend on isospin, although the total isospin should be conserved. The concept of isospin proved useful in classifying [[hadrons]] discovered in the 1950s and 1960s (see [[particle zoo]]), where particles with similar mass are assigned an SU(2) isospin [[multiplet]].

=== Strangeness and hypercharge ===
The discovery of [[strange particles]] like the [[kaon]] led to a new quantum number that was conserved by the strong interaction: strangeness (or equivalently hypercharge). The [[Gell-Mann–Nishijima formula]] was identified in 1953, which relates strangeness and hypercharge with isospin and electric charge.<ref>
{{cite journal
 |last=Nishijima |first=K
 |year=1955
 |title=Charge Independence Theory of V Particles
 |journal=[[Progress of Theoretical Physics]]
 |volume=13 |issue=3 |pages=285–304 
 |doi=10.1143/PTP.13.285
|bibcode = 1955PThPh..13..285N |doi-access=free}}</ref>

=== The eightfold way and quark model ===
Once the kaons and their property of [[Strangeness (particle physics)|strangeness]] became better understood, it started to become clear that these, too, seemed to be a part of an enlarged symmetry that contained isospin as a subgroup. The larger symmetry was named the [[Eightfold way (physics)|Eightfold Way]] by [[Murray Gell-Mann]], and was promptly recognized to correspond to the adjoint representation of [[SU(3)]]. To better understand the origin of this symmetry, Gell-Mann proposed the existence of up, down and strange [[quark]]s which would belong to the fundamental representation of the SU(3) flavor symmetry.

=== GIM-Mechanism and charm ===
To explain the observed absence of [[flavor-changing neutral current]]s, the [[GIM mechanism]] was proposed in 1970, which introduced the charm quark and predicted the [[J/psi meson]].<ref>
{{cite journal
 |doi=10.1103/PhysRevD.2.1285
 |author1=S.L. Glashow |author2=J. Iliopoulos |author3=L. Maiani |year=1970
 |title=Weak Interactions with Lepton–Hadron Symmetry
 |journal=[[Physical Review D]]
 |volume=2 |pages=1285
|bibcode = 1970PhRvD...2.1285G
 |issue=7 }}</ref> The [[J/psi meson]] was indeed found in 1974, which confirmed the existence of charm quarks. This discovery is known as the ''November Revolution''. The flavor quantum number associated with the charm quark became known as ''charm''.

=== Bottomness and topness ===
The bottom and top quarks were predicted in 1973 in order to explain [[CP violation]],<ref>
{{cite journal
 |first1=M. |last1=Kobayashi |first2=T. |last2=Maskawa
 |title=CP-Violation in the Renormalizable Theory of Weak Interaction
 |url=http://ptp.ipap.jp/link?PTP/49/652/pdf
 |journal=[[Progress of Theoretical Physics]]
 |volume=49 |issue=2 |pages=652–657
 |year=1973
 |doi=10.1143/PTP.49.652
|bibcode = 1973PThPh..49..652K 
 |doi-access=free
 |hdl=2433/66179|hdl-access=free}}</ref> which also implied two new flavor quantum numbers: ''bottomness'' and ''topness''.

== See also ==
* [[Standard Model (mathematical formulation)]]
* [[Cabibbo–Kobayashi–Maskawa matrix]]
* [[Strong CP problem]] and [[chirality (physics)]]
* [[Chiral symmetry breaking]] and [[quark matter]]
* Quark flavour tagging, such as [[B-tagging]], is an example of [[particle identification]] in experimental particle physics.

== References ==
<references/>

== Further reading ==
* [https://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

== External links ==
* [http://pdg.lbl.gov/ The particle data group.]

[[Category:Flavour (particle physics)| ]]
[[Category:Physical quantities]]
[[Category:Standard Model]]
[[Category:Quantum chromodynamics]]
[[Category:Quark matter]]
[[Category:Conservation laws]]