2076:
169:
2139:â, 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.
45:
176:
183:
160:
146:
153:
1050:
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
1926:
scale of 250 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
1745:
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 â1 as per the
1879:
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
1769:
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,
789:
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
1819:
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
1910:. 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 (
1654:
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:
1046:). 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
2150:
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.
2285:
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
833:
1868:
1060:
475:
1927:
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
1867:
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
594:, 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
506:
606:
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
1637:
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
2241:, 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
62:
2153:
Heisenberg noted that the mathematical formulation of this symmetry was in certain respects similar to the mathematical formulation of non-relativistic
2367:
2142:
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.
1872:
1821:
470:
2362:
1824:(CKM matrix). This matrix is analogous to the PMNS matrix for neutrinos, and quantifies flavour changes under charged weak interactions of quarks.
1236:
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
2111:
Isospin, strangeness and hypercharge predate the quark model. The first of those quantum numbers, Isospin, was introduced as a concept in 1932 by
1746:
original definition. Strangeness was introduced to explain the rate of decay of newly discovered particles, such as the kaon, and was used in the
2417:
1034:
Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos (
2227:
499:
1888:(electron, muon and tau neutrino), as well as how and why the mass and mixing hierarchy arises among different flavours of these fermions.
1792:
Since first-order processes are more common than second-order processes (involving two quark decays), this can be used as an approximate "
2859:
1609:
represents the number of top antiquarks. However, because of the extremely short half-life of the top quark (predicted lifetime of only
109:
2037:
are much larger than the current quark mass. This indicates that QCD has spontaneous chiral symmetry breaking with the formation of a
81:
128:
480:
492:
2270:
1738:
88:
2874:
2778:
2698:
2310:
1855:. The relations between the hypercharge, electric charge and other flavour quantum numbers hold for hadrons as well as quarks.
1808:
2282:
653:) can characterize the quantum state of quarks, by the degree to which it exhibits six distinct flavours (u, d, c, s, t, b).
66:
2013:
Analysis of experiments indicate that the current quark masses of the lighter flavours of quarks are much smaller than the
2579:
Alonso, Rodrigo; Carmona, Adrian; Dillon, Barry M.; Kamenik, Jernej F.; Camalich, Jorge Martin; Zupan, Jure (2018-10-16).
1994:
1230:
1047:
1003:
845:
95:
2269:
led to a new quantum number that was conserved by the strong interaction: strangeness (or equivalently hypercharge). The
2864:
1977:
1759:
77:
2884:
2176:
2026:
1982:
668:, each possessing unique aggregate characteristics, such as different masses, electric charges, and decay modes. A
55:
2649:
2231:
2381:
2001:(as it does in low-energy QCD). This gives rise to an effective mass for the quarks, often identified with the
1923:
800:
2297:. To better understand the origin of this symmetry, Gell-Mann proposed the existence of up, down and strange
2869:
2395:
2286:
2058:
1747:
778:
31:
2022:
1903:
1403:
886:
642:
237:
1617:), by the time it can interact strongly it has already decayed to another flavour of quark (usually to a
2879:
2325:
was indeed found in 1974, which confirmed the existence of charm quarks. This discovery is known as the
1052:
879:
753:, the individual baryon and lepton number conservation can be violated, if the difference between them (
692:
that commute with the
Hamiltonian. Thus, the eigenvalues of the various charge operators are conserved.
611:
2430:
102:
2787:
2746:
2707:
2658:
2602:
2545:
2470:
2230:) of SU(2). Though there is a difference from the theory of spin: The group action does not preserve
1056:
902:
750:
591:
2273:
was identified in 1953, which relates strangeness and hypercharge with isospin and electric charge.
2376:
1897:
1020:
536:
2674:
2626:
2592:
2561:
2535:
2460:
2425:
2179:) of SU(2), with the proton and neutron being then associated with different isospin projections
2002:
1987:
1755:
1237:
894:
774:
559:
2735:
S.L. Glashow; J. Iliopoulos; L. Maiani (1970). "Weak
Interactions with LeptonâHadron Symmetry".
777:
conserve all flavours, but all flavour quantum numbers are violated (changed, non-conserved) by
2737:
2644:
2618:
2504:
2486:
2372:
2262:
2158:
2112:
2038:
1998:
1035:
673:
563:
1400:. This definition gives the strange quark a strangeness of â1 for the above-mentioned reason.
2827:
2805:
2795:
2754:
2715:
2666:
2610:
2553:
2494:
2478:
2290:
2135:) are almost identical: They are nearly degenerate, and both are thus often referred to as â
1804:
1763:
1397:
1007:
897:, on the other hand, this symmetry is broken, and flavour changing processes exist, such as
685:
684:
All of the various charges discussed above are conserved by the fact that the corresponding
595:
520:
402:
204:
2062:
1696:
890:
703:
603:
319:
2791:
2750:
2711:
2662:
2606:
2549:
2474:
1961:
If all quarks had non-zero but equal masses, then this chiral symmetry is broken to the
2831:
2523:
2499:
2448:
2154:
1922:
Under some circumstances (for instance when the quark masses are much smaller than the
1864:
1812:
1793:
1028:
970:
863:
767:
696:
626:
618:
599:
579:
554:
540:
212:
2075:
2853:
2678:
2630:
2482:
2314:
2238:
1848:
1622:
1348:
1244:
has the same sign as its charge. Quarks have the following flavour quantum numbers:
1076:
1039:
923:
738:
728:
607:
294:
285:
2157:, whence the name "isospin" derives. The neutron and the proton are assigned to the
2565:
2385:
2342:
2301:
which would belong to the fundamental representation of the SU(3) flavor symmetry.
2246:
2219:
2042:
2030:
1863:
The flavour problem (also known as the flavour puzzle) is the inability of current
1840:
1828:
1618:
1510:
1131:
1043:
1024:
933:
713:
630:
303:
2524:"Supersymmetry, Local Horizontal Unification, and a Solution to the Flavor Puzzle"
2614:
2557:
2322:
2318:
2066:
2034:
1852:
1751:
1659:
1439:
1312:
867:
638:
348:
246:
168:
44:
17:
1800:
1470:
791:
646:
328:
264:
2622:
2490:
2293:, and was promptly recognized to correspond to the adjoint representation of
755:
445:
2758:
2391:
2329:. The flavor quantum number associated with the charm quark became known as
2250:
2014:
1581:
1196:
the negatively charged quarks (down, strange, and bottom quarks) are called
871:
2508:
175:
2580:
182:
2317:
was proposed in 1970, which introduced the charm quark and predicted the
1467:
represents the number of charm antiquarks. The charm quark's value is +1.
993:. Each doublet of a charged lepton and a neutrino consisting of opposite
990:
962:
622:
587:
583:
1900:. This part of the article is best read along with the one on chirality.
2800:
2773:
2720:
2693:
2670:
2540:
2242:
2147:
2136:
2116:
2054:
1911:
1876:
1816:
1541:
1249:
650:
634:
255:
221:
159:
2810:
1843:
have flavour equal in magnitude to the particle but opposite in sign.
797:
In other words, the theory possesses symmetry transformations such as
2341:
The bottom and top quarks were predicted in 1973 in order to explain
2128:
1885:
1844:
1630:
1163:
The positively charged quarks (up, charm, and top quarks) are called
919:
669:
665:
657:
548:
2234:(in fact, the group action is specifically an exchange of flavour).
598:
is such that it allows the conversion of quantum numbers describing
145:
2597:
2465:
2249:), where particles with similar mass are assigned an SU(2) isospin
2033:
spring from this fact. The valence quark masses extracted from the
1059:. The strength of such mixings is specified by a matrix called the
2298:
2294:
1986:. The strength of explicit symmetry breaking is controlled by the
1907:
1881:
1815:(charged weak interactions violate flavour). On the other hand, a
1626:
1241:
1072:
898:
875:
661:
633:
of the whole atom. Analogously, the five flavour quantum numbers (
575:
544:
656:
Composite particles can be created from multiple quarks, forming
2266:
2124:
966:
2774:"CP-Violation in the Renormalizable Theory of Weak Interaction"
152:
2070:
38:
1006:
of leptons. In addition, one defines a quantum number called
1993:
Even if quarks are massless, chiral flavour symmetry can be
1781:
likewise, for a decay involving a bottom quark or antiquark
672:'s overall flavour quantum numbers depend on the numbers of
2086: with: Add history of lepton flavours. You can help by
2021:, hence chiral flavour symmetry is a good approximation to
1811:, so will interact in a particularly simple way with the
2418:"Neutrino Masses: How to add them to the Standard Model"
1229:
Each doublet of up and down type quarks constitutes one
2087:
2045:
may break the chiral flavour symmetries in other ways.
1980:
of the quarks. This reduction of symmetry is a form of
2844:
2345:, which also implied two new flavor quantum numbers:
2115:, to explain symmetries of the then newly discovered
803:
2025:
for the up, down and strange quarks. The success of
1884:(up-down, charm-strange, and top-bottom quarks) and
69:. Unsourced material may be challenged and removed.
827:
1851:: this is the basis of the classification in the
1976:, which applies the same transformation to both
1847:inherit their flavour quantum number from their
1023:leptons. Weak isospin and weak hypercharge are
2146:Protons and neutrons were grouped together as
1376:represents the number of strange antiquarks (
843:are the two fields (representing the various
551:. They are conventionally parameterized with
500:
8:
2522:Babu, K. S.; Mohapatra, R. N. (1999-09-27).
2218:respectively. The pions are assigned to the
1839:Flavour quantum numbers are additive. Hence
1754:. These quantum numbers are preserved under
1750:classification of hadrons and in subsequent
695:Absolutely conserved quantum numbers in the
562:. They can also be described by some of the
2694:"Charge Independence Theory of V Particles"
2581:"A clockwork solution to the flavor puzzle"
1538:represents the number of bottom antiquarks.
882:). This is an example of flavour symmetry.
566:proposed for the quark-lepton generations.
1799:A special mixture of quark flavours is an
629:in which it resides, which determines the
507:
493:
195:
2834:, University of Wisconsin, 18th Dec. 2009
2809:
2799:
2719:
2596:
2539:
2498:
2464:
2363:Standard Model (mathematical formulation)
1831:if there are at least three generations.
1621:). For that reason the top quark doesn't
1396:). This quantum number was introduced by
1055:; that is, a neutrino of one flavour can
828:{\displaystyle M\left({u \atop d}\right)}
811:
802:
129:Learn how and when to remove this message
1240:. Thus any flavour carried by a charged
189:
2407:
2245:discovered in the 1950s and 1960s (see
2237:When constructing a physical theory of
1997:if the vacuum of the theory contains a
1896:Flavour symmetry is closely related to
1875:matrices. These free parameters - the
849:of leptons and quarks, see below), and
462:
340:
277:
210:
198:
2647:(1932). "Ăber den Bau der Atomkerne".
1061:PontecorvoâMakiâNakagawaâSakata matrix
2281:Once the kaons and their property of
7:
961:for the three charged leptons (i.e.
67:adding citations to reliable sources
2772:Kobayashi, M.; Maskawa, T. (1973).
2447:Feruglio, Ferruccio (August 2015).
2309:To explain the observed absence of
794:, or perpendicular, to each other.
621:the principal quantum number of an
812:
25:
2398:in experimental particle physics.
2277:The eightfold way and quark model
2368:CabibboâKobayashiâMaskawa matrix
2311:flavor-changing neutral currents
2074:
1965:of the "diagonal flavour group"
1822:CabibboâKobayashiâMaskawa matrix
181:
174:
167:
158:
151:
144:
43:
2779:Progress of Theoretical Physics
2699:Progress of Theoretical Physics
2453:The European Physical Journal C
2390:Quark flavour tagging, such as
1906:(QCD) contains six flavours of
78:"Flavour" particle physics
54:needs additional citations for
2585:Journal of High Energy Physics
2483:10.1140/epjc/s10052-015-3576-5
2449:"Pieces of the Flavour Puzzle"
1057:transform into another flavour
749:In some theories, such as the
586:'s dynamical state, i.e., its
140:
27:Species of elementary particle
1:
1625:, that is it never forms any
932:. In addition, leptons carry
1760:electromagnetic interactions
676:of each particular flavour.
2828:Lessons in Particle Physics
2558:10.1103/PhysRevLett.83.2522
2416:S. Raby, R. Slanky (1997).
2271:Gell-MannâNishijima formula
2257:Strangeness and hypercharge
1957:Vector symmetry description
1918:Chiral symmetry description
1739:Gell-MannâNishijima formula
1002:are said to constitute one
2901:
2860:Flavour (particle physics)
2177:fundamental representation
2052:
2027:chiral perturbation theory
1983:explicit symmetry breaking
1895:
1827:The CKM matrix allows for
1252:(usually just "isospin") (
574:In classical mechanics, a
29:
1835:Antiparticles and hadrons
1580:represents the number of
1509:represents the number of
1438:represents the number of
1347:represents the number of
1104:and all anti-quarks have
989:for the three associated
889:, flavour is a conserved
590:, angular momentum, etc.
558:that are assigned to all
2845:The particle data group.
2429:(25): 64. Archived from
2382:Chiral symmetry breaking
2029:and the even more naive
1924:chiral symmetry breaking
779:electroweak interactions
690:generators of symmetries
190:Six flavours of leptons
2759:10.1103/PhysRevD.2.1285
2615:10.1007/JHEP10(2018)099
2528:Physical Review Letters
2396:particle identification
2305:GIM-Mechanism and charm
2127:of the neutron and the
2059:Eightfold way (physics)
1248:The third component of
909:Flavour quantum numbers
870:. Such matrices form a
543:counts six flavours of
481:Flavour complementarity
278:Related quantum numbers
32:Flavor (disambiguation)
2875:Quantum chromodynamics
2650:Zeitschrift fĂŒr Physik
2337:Bottomness and topness
2228:adjoint representation
2055:Isospin § History
1904:Quantum chromodynamics
1892:Quantum chromodynamics
1019:, which is â1 for all
887:quantum chromodynamics
829:
2830:Luis Anchordoqui and
2692:Nishijima, K (1955).
1284:for the up quark and
903:neutrino oscillations
880:special unitary group
830:
688:can be understood as
612:quantum superposition
1995:spontaneously broken
1988:current quark masses
1130:They also all carry
801:
765:) is conserved (see
751:grand unified theory
592:Quantum field theory
547:and six flavours of
63:improve this article
30:For other uses, see
2865:Physical quantities
2792:1973PThPh..49..652K
2751:1970PhRvD...2.1285G
2712:1955PThPh..13..285N
2663:1932ZPhy...77....1H
2607:2018JHEP...10..099A
2550:1999PhRvL..83.2522B
2475:2015EPJC...75..373F
2394:, is an example of
2377:chirality (physics)
2327:November Revolution
2043:Other phases of QCD
1796:" for weak decays.
1309:for the down quark.
1259:), which has value
775:Strong interactions
582:can only alter the
580:point-like particle
560:subatomic particles
537:elementary particle
2801:10.1143/PTP.49.652
2721:10.1143/PTP.13.285
2671:10.1007/BF01342433
2426:Los Alamos Science
2003:valence quark mass
895:electroweak theory
825:
674:constituent quarks
2885:Conservation laws
2738:Physical Review D
2534:(13): 2522â2525.
2373:Strong CP problem
2263:strange particles
2261:The discovery of
2113:Werner Heisenberg
2104:
2103:
2039:chiral condensate
2009:Symmetries of QCD
1999:chiral condensate
1764:weak interactions
1036:electron neutrino
819:
680:Conservation laws
610:may also undergo
564:family symmetries
517:
516:
194:
193:
139:
138:
131:
113:
16:(Redirected from
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2513:
2512:
2502:
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2438:
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2422:
2412:
2291:Murray Gell-Mann
2217:
2216:
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2170:
2169:
2165:
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2096:
2078:
2071:
1975:
1952:
1947:
1936:
1805:weak interaction
1791:
1789:
1780:
1778:
1762:, but not under
1736:
1735:
1731:
1729:
1728:
1725:
1722:
1702:
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1692:
1665:
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1600:
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1458:
1457:
1450:
1449:
1434:
1430:
1425:
1418:
1414:
1409:
1398:Murray Gell-Mann
1395:
1394:
1393:
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1372:
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1273:
1263:
1255:
1228:
1226:
1224:
1223:
1220:
1217:
1213:
1204:
1198:down-type quarks
1195:
1193:
1191:
1190:
1187:
1184:
1180:
1171:
1162:
1160:
1158:
1157:
1154:
1151:
1147:
1138:
1129:
1127:
1125:
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1121:
1118:
1114:
1108:
1103:
1101:
1099:
1098:
1095:
1092:
1088:
1082:
1018:
1008:weak hypercharge
1001:
988:
986:
985:
982:
979:
960:
958:
957:
954:
951:
944:
931:
862:
861:
858:
852:
842:
838:
834:
832:
831:
826:
824:
820:
785:Flavour symmetry
764:
744:
734:
724:
709:
686:charge operators
521:particle physics
509:
502:
495:
403:Weak hypercharge
205:particle physics
196:
185:
178:
171:
162:
155:
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141:
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127:
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120:
114:
112:
71:
47:
39:
21:
18:Flavour symmetry
2900:
2899:
2895:
2894:
2893:
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2890:
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2824:
2822:Further reading
2819:
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2642:
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2415:
2413:
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2339:
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2279:
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2214:
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2207:
2205:
2199:
2195:
2192:
2190:
2188:
2181:
2180:
2167:
2163:
2162:
2132:
2109:
2100:
2094:
2091:
2084:needs expansion
2069:
2063:Chiral symmetry
2051:
2020:
2011:
1973:
1966:
1963:vector symmetry
1959:
1950:
1945:
1943:
1939:
1934:
1932:
1928:
1920:
1901:
1898:chiral symmetry
1894:
1861:
1859:Flavour problem
1837:
1783:
1782:
1772:
1771:
1726:
1723:
1720:
1719:
1717:
1715:
1705:
1704:
1700:
1697:Electric charge
1668:
1667:
1663:
1651:
1646:
1644:
1639:
1638:
1612:
1610:
1608:
1603:
1598:
1596:
1595:
1594:
1590:
1588:
1587:
1586:
1585:
1579:
1574:
1570:
1565:
1563:
1558:
1554:
1553:
1549:
1537:
1532:
1527:
1525:
1524:
1523:
1519:
1517:
1516:
1515:
1514:
1508:
1503:
1499:
1494:
1492:
1487:
1483:
1482:
1478:
1466:
1461:
1456:
1454:
1453:
1452:
1448:
1446:
1445:
1444:
1443:
1437:
1432:
1428:
1423:
1421:
1416:
1412:
1411:
1407:
1392:
1390:
1389:
1388:
1385:
1382:
1380:
1379:
1378:
1377:
1375:
1370:
1365:
1363:
1362:
1361:
1357:
1355:
1354:
1353:
1352:
1346:
1341:
1337:
1332:
1330:
1325:
1321:
1320:
1316:
1302:
1299:
1296:
1295:
1293:
1291:
1286:
1285:
1277:
1274:
1271:
1270:
1268:
1266:
1261:
1260:
1258:
1253:
1221:
1218:
1215:
1214:
1211:
1209:
1207:
1202:
1201:
1188:
1185:
1182:
1181:
1178:
1176:
1174:
1169:
1168:
1155:
1152:
1149:
1148:
1145:
1143:
1141:
1136:
1135:
1122:
1119:
1116:
1115:
1112:
1110:
1106:
1105:
1096:
1093:
1090:
1089:
1086:
1084:
1080:
1079:
1069:
1063:(PMNS matrix).
1017:
1011:
1000:
994:
983:
980:
977:
976:
974:
955:
952:
949:
948:
946:
943:
937:
926:
916:
911:
891:global symmetry
859:
856:
854:
850:
840:
836:
807:
799:
798:
787:
754:
742:
732:
723:
717:
707:
704:electric charge
682:
604:electric charge
572:
570:Quantum numbers
555:quantum numbers
513:
443:
430:
419:
411:
396:
320:Electric charge
316:
234:
213:quantum numbers
203:
135:
124:
118:
115:
72:
70:
60:
48:
35:
28:
23:
22:
15:
12:
11:
5:
2898:
2896:
2888:
2887:
2882:
2877:
2872:
2870:Standard Model
2867:
2862:
2852:
2851:
2848:
2847:
2840:
2839:External links
2837:
2836:
2835:
2832:Francis Halzen
2823:
2820:
2818:
2817:
2786:(2): 652â657.
2764:
2727:
2706:(3): 285â304.
2684:
2645:Heisenberg, W.
2636:
2571:
2541:hep-ph/9906271
2514:
2439:
2436:on 2011-08-31.
2406:
2404:
2401:
2400:
2399:
2388:
2379:
2370:
2365:
2358:
2355:
2338:
2335:
2306:
2303:
2278:
2275:
2258:
2255:
2239:nuclear forces
2186:
2144:
2143:
2140:
2108:
2105:
2102:
2101:
2081:
2079:
2050:
2047:
2018:
2010:
2007:
1971:
1958:
1955:
1948:
1941:
1937:
1930:
1919:
1916:
1893:
1890:
1865:Standard Model
1860:
1857:
1849:valence quarks
1836:
1833:
1794:selection rule
1743:
1742:
1713:
1694:
1649:
1642:
1635:
1634:
1606:
1597:
1589:
1577:
1568:
1561:
1552:): Defined as
1539:
1535:
1526:
1518:
1506:
1497:
1490:
1481:): Defined as
1468:
1464:
1455:
1447:
1435:
1426:
1419:
1410:): Defined as
1401:
1391:
1381:
1373:
1364:
1356:
1349:strange quarks
1344:
1335:
1328:
1319:): Defined as
1310:
1289:
1264:
1256:
1210:−
1205:
1172:
1165:up-type quarks
1139:
1111:−
1068:
1065:
1029:Standard Model
1015:
998:
941:
915:
912:
910:
907:
864:unitary matrix
823:
818:
815:
810:
806:
786:
783:
768:Chiral anomaly
747:
746:
736:
726:
721:
711:
697:Standard Model
681:
678:
627:electron shell
625:specifies the
619:atomic physics
571:
568:
541:Standard Model
531:refers to the
515:
514:
512:
511:
504:
497:
489:
486:
485:
484:
483:
478:
473:
465:
464:
463:Flavour mixing
460:
459:
458:
457:
456:
455:
441:
432:
428:
417:
409:
400:
399:
398:
394:
381:
343:
342:
338:
337:
336:
335:
326:
317:
314:
301:
292:
280:
279:
275:
274:
273:
272:
262:
253:
244:
235:
232:
216:
215:
208:
207:
192:
191:
187:
186:
179:
172:
164:
163:
156:
149:
137:
136:
51:
49:
42:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2897:
2886:
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2866:
2863:
2861:
2858:
2857:
2855:
2846:
2843:
2842:
2838:
2833:
2829:
2826:
2825:
2821:
2812:
2807:
2802:
2797:
2793:
2789:
2785:
2781:
2780:
2775:
2768:
2765:
2760:
2756:
2752:
2748:
2744:
2740:
2739:
2731:
2728:
2722:
2717:
2713:
2709:
2705:
2701:
2700:
2695:
2688:
2685:
2680:
2676:
2672:
2668:
2664:
2660:
2657:(1â2): 1â11.
2656:
2653:(in German).
2652:
2651:
2646:
2640:
2637:
2632:
2628:
2624:
2620:
2616:
2612:
2608:
2604:
2599:
2594:
2590:
2586:
2582:
2575:
2572:
2567:
2563:
2559:
2555:
2551:
2547:
2542:
2537:
2533:
2529:
2525:
2518:
2515:
2510:
2506:
2501:
2496:
2492:
2488:
2484:
2480:
2476:
2472:
2467:
2462:
2458:
2454:
2450:
2443:
2440:
2432:
2428:
2427:
2419:
2414:See table in
2411:
2408:
2402:
2397:
2393:
2389:
2387:
2383:
2380:
2378:
2374:
2371:
2369:
2366:
2364:
2361:
2360:
2356:
2354:
2352:
2348:
2344:
2336:
2334:
2332:
2328:
2324:
2320:
2316:
2315:GIM mechanism
2312:
2304:
2302:
2300:
2296:
2292:
2288:
2287:Eightfold Way
2284:
2276:
2274:
2272:
2268:
2264:
2256:
2254:
2252:
2248:
2244:
2240:
2235:
2233:
2229:
2225:
2222:(the spin-1,
2221:
2184:
2178:
2174:
2160:
2156:
2151:
2149:
2141:
2138:
2130:
2126:
2122:
2121:
2120:
2118:
2114:
2106:
2098:
2089:
2085:
2082:This section
2080:
2077:
2073:
2072:
2068:
2064:
2060:
2056:
2048:
2046:
2044:
2040:
2036:
2032:
2031:chiral models
2028:
2024:
2016:
2008:
2006:
2004:
2000:
1996:
1991:
1989:
1985:
1984:
1979:
1970:
1964:
1956:
1954:
1925:
1917:
1915:
1913:
1909:
1905:
1899:
1891:
1889:
1887:
1883:
1878:
1874:
1870:
1866:
1858:
1856:
1854:
1850:
1846:
1842:
1841:antiparticles
1834:
1832:
1830:
1825:
1823:
1818:
1814:
1810:
1806:
1802:
1797:
1795:
1787:
1776:
1767:
1765:
1761:
1757:
1753:
1749:
1748:Eightfold Way
1740:
1734:
1712:
1708:
1698:
1695:
1691:
1687:
1683:
1679:
1675:
1671:
1661:
1658:
1657:
1656:
1632:
1628:
1624:
1620:
1583:
1547:
1543:
1540:
1512:
1511:bottom quarks
1476:
1472:
1469:
1441:
1405:
1402:
1399:
1350:
1314:
1311:
1251:
1247:
1246:
1245:
1243:
1239:
1234:
1232:
1199:
1166:
1133:
1078:
1077:baryon number
1074:
1066:
1064:
1062:
1058:
1054:
1049:
1045:
1041:
1040:muon neutrino
1037:
1032:
1030:
1026:
1022:
1014:
1009:
1005:
997:
992:
972:
968:
964:
940:
935:
929:
925:
924:lepton number
921:
913:
908:
906:
904:
900:
896:
892:
888:
883:
881:
877:
873:
869:
865:
848:
847:
821:
816:
813:
808:
804:
795:
793:
784:
782:
780:
776:
772:
770:
769:
763:
762:
758:
752:
740:
739:lepton number
737:
730:
729:baryon number
727:
720:
715:
712:
705:
702:
701:
700:
698:
693:
691:
687:
679:
677:
675:
671:
667:
663:
659:
654:
652:
648:
644:
640:
636:
632:
628:
624:
620:
615:
613:
609:
605:
601:
597:
593:
589:
585:
581:
577:
569:
567:
565:
561:
557:
556:
550:
546:
542:
538:
534:
530:
526:
522:
510:
505:
503:
498:
496:
491:
490:
488:
487:
482:
479:
477:
474:
472:
469:
468:
467:
466:
461:
453:
452:
448:
440:
436:
433:
427:
423:
416:
413:
412:
408:
404:
401:
393:
389:
385:
382:
379:
375:
371:
367:
363:
359:
356:
355:
354:
350:
347:
346:
345:
344:
339:
334:
330:
327:
325:
321:
318:
313:
309:
305:
302:
300:
296:
295:Lepton number
293:
291:
287:
286:Baryon number
284:
283:
282:
281:
276:
270:
266:
263:
261:
257:
254:
252:
248:
245:
243:
239:
236:
231:
227:
223:
220:
219:
218:
217:
214:
209:
206:
201:
197:
188:
184:
180:
177:
173:
170:
166:
165:
161:
157:
154:
150:
147:
143:
142:
133:
130:
122:
111:
108:
104:
101:
97:
94:
90:
87:
83:
80: â
79:
75:
74:Find sources:
68:
64:
58:
57:
52:This article
50:
46:
41:
40:
37:
33:
19:
2880:Quark matter
2783:
2777:
2767:
2742:
2736:
2730:
2703:
2697:
2687:
2654:
2648:
2639:
2588:
2584:
2574:
2531:
2527:
2517:
2456:
2452:
2442:
2431:the original
2424:
2410:
2386:quark matter
2350:
2346:
2343:CP violation
2340:
2330:
2326:
2308:
2280:
2260:
2247:particle zoo
2236:
2223:
2182:
2172:
2152:
2145:
2119:(symbol n):
2110:
2092:
2088:adding to it
2083:
2012:
1992:
1981:
1968:
1962:
1960:
1921:
1902:
1862:
1838:
1829:CP violation
1826:
1807:part of the
1798:
1785:
1774:
1768:
1752:quark models
1744:
1732:
1710:
1706:
1689:
1685:
1681:
1677:
1673:
1669:
1636:
1619:bottom quark
1545:
1474:
1440:charm quarks
1235:
1197:
1164:
1132:weak isospin
1070:
1044:tau neutrino
1033:
1012:
995:
945:, which is â
938:
934:weak isospin
927:
917:
884:
866:with a unit
844:
796:
788:
773:
766:
760:
756:
748:
718:
714:weak isospin
694:
689:
683:
655:
631:energy level
616:
578:acting on a
573:
552:
532:
528:
524:
518:
450:
446:
438:
434:
425:
421:
414:
406:
391:
387:
383:
377:
373:
369:
365:
361:
357:
352:
341:Combinations
332:
323:
311:
307:
304:Weak isospin
298:
289:
268:
259:
250:
241:
229:
225:
199:
125:
119:October 2015
116:
106:
99:
92:
85:
73:
61:Please help
56:verification
53:
36:
2745:(7): 1285.
2323:J/psi meson
2319:J/psi meson
2283:strangeness
2067:J/psi meson
2035:quark model
1914:symmetry).
1853:quark model
1809:Hamiltonian
1660:Hypercharge
1313:Strangeness
1233:of quarks.
1021:left-handed
899:quark decay
868:determinant
846:generations
639:strangeness
476:PMNS matrix
349:Hypercharge
247:Strangeness
2854:Categories
2811:2433/66179
2598:1807.09792
2591:(10): 99.
2466:1503.04071
2459:(8): 373.
2403:References
2347:bottomness
2161:(the spin-
2095:March 2017
2053:See also:
1978:helicities
1801:eigenstate
1582:top quarks
1471:Bottomness
1231:generation
1048:generation
1004:generation
792:orthogonal
660:, such as
647:bottomness
596:weak force
471:CKM matrix
376:′ +
265:Bottomness
89:newspapers
2679:186218053
2631:119410222
2623:1029-8479
2491:1434-6044
2392:B-tagging
2265:like the
2251:multiplet
2015:QCD scale
1623:hadronize
1615:10 s
1486:= −
1324:= −
1292:= −
1200:and have
1167:and have
991:neutrinos
893:. In the
872:Lie group
2509:26300692
2357:See also
2148:nucleons
2137:nucleons
2131:(symbol
2005:in QCD.
1990:in QCD.
1813:W bosons
1786:B′
1686:B′
1484:B′
1479:B′
1177:+
1144:±
1085:+
1075:carry a
963:electron
922:carry a
835:, where
623:electron
588:momentum
584:particle
553:flavour
329:X-charge
211:Flavour
2788:Bibcode
2747:Bibcode
2708:Bibcode
2659:Bibcode
2603:Bibcode
2566:1081641
2546:Bibcode
2500:4538584
2471:Bibcode
2351:topness
2243:hadrons
2220:triplet
2213:⁄
2198:⁄
2166:⁄
2159:doublet
2117:neutron
2107:Isospin
2049:History
1912:isospin
1886:leptons
1877:fermion
1845:Hadrons
1817:fermion
1803:of the
1779: ;
1730:
1718:
1650:q̅
1607:t̅
1569:t̅
1542:Topness
1536:b̅
1498:b̅
1465:c̅
1427:c̅
1374:s̅
1336:s̅
1306:
1294:
1281:
1269:
1250:isospin
1225:
1194: ;
1192:
1159:
1126:
1100:
1027:in the
987:
975:
973:) and +
959:
947:
920:leptons
914:Leptons
874:called
853:is any
666:baryons
658:hadrons
651:topness
635:isospin
549:leptons
533:species
525:flavour
271:′
256:Topness
222:Isospin
200:Flavour
103:scholar
2677:
2629:
2621:
2564:
2507:
2497:
2489:
2321:. The
2313:, the
2299:quarks
2232:flavor
2129:proton
2065:, and
1940:) Ă SU
1908:quarks
1882:quarks
1756:strong
1631:baryon
1602:) and
1573:where
1531:) and
1502:where
1475:beauty
1460:) and
1431:where
1369:) and
1340:where
1073:quarks
1067:Quarks
1025:gauged
670:hadron
662:mesons
608:states
545:quarks
539:. The
535:of an
529:flavor
105:
98:
91:
84:
76:
2675:S2CID
2627:S2CID
2593:arXiv
2562:S2CID
2536:arXiv
2461:arXiv
2434:(PDF)
2421:(PDF)
2331:charm
2295:SU(3)
2226:, or
2175:, or
1737:(see
1627:meson
1546:truth
1404:Charm
1242:meson
878:(see
876:SU(2)
699:are:
643:charm
576:force
444:= 5 (
420:= 2 (
386:= 2 (
238:Charm
110:JSTOR
96:books
2619:ISSN
2589:2018
2505:PMID
2487:ISSN
2384:and
2375:and
2349:and
2267:kaon
2204:and
2155:spin
2125:mass
2123:The
1871:and
1869:PMNS
1788:= ±1
1777:= ±1
1758:and
1544:(or
1473:(or
1238:sign
1071:All
1051:can
1042:and
969:and
967:muon
918:All
839:and
664:and
602:and
600:mass
82:news
2806:hdl
2796:doi
2755:doi
2716:doi
2667:doi
2611:doi
2554:doi
2495:PMC
2479:doi
2289:by
2090:.
2023:QCD
2019:QCD
2017:, Î
1967:SU(
1873:CKM
1703:):
1666:):
1629:or
1548:) (
1477:) (
1053:mix
971:tau
930:= 1
901:or
885:In
771:).
649:or
617:In
527:or
519:In
437:+ 2
360:= (
310:or
228:or
65:by
2856::
2804:.
2794:.
2784:49
2782:.
2776:.
2753:.
2741:.
2714:.
2704:13
2702:.
2696:.
2673:.
2665:.
2655:77
2625:.
2617:.
2609:.
2601:.
2587:.
2583:.
2560:.
2552:.
2544:.
2532:83
2530:.
2526:.
2503:.
2493:.
2485:.
2477:.
2469:.
2457:75
2455:.
2451:.
2423:.
2353:.
2333:.
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