3469:
3194:
3203:
2931:
3464:{\displaystyle \vert \mathrm {n} \uparrow \rangle ={\frac {1}{3{\sqrt {2}}}}\left({\begin{array}{ccc}\vert \mathrm {udd} \rangle &\vert \mathrm {dud} \rangle &\vert \mathrm {ddu} \rangle \end{array}}\right)\left({\begin{array}{ccc}2&-1&-1\\-1&2&-1\\-1&-1&2\end{array}}\right)\left({\begin{array}{c}\left\vert \downarrow \uparrow \uparrow \right\rangle \\\left\vert \uparrow \downarrow \uparrow \right\rangle \\\left\vert \uparrow \uparrow \downarrow \right\rangle \end{array}}\right).}
3189:{\displaystyle \vert \mathrm {p} \uparrow \rangle ={\frac {1}{3{\sqrt {2}}}}\left({\begin{array}{ccc}\vert \mathrm {duu} \rangle &\vert \mathrm {udu} \rangle &\vert \mathrm {uud} \rangle \end{array}}\right)\left({\begin{array}{ccc}2&-1&-1\\-1&2&-1\\-1&-1&2\end{array}}\right)\left({\begin{array}{c}\left\vert \downarrow \uparrow \uparrow \right\rangle \\\left\vert \uparrow \downarrow \uparrow \right\rangle \\\left\vert \uparrow \uparrow \downarrow \right\rangle \end{array}}\right)}
2417:
into each other, but can never leave the space (since the subspace is in fact invariant). This is reflective of the symmetry present. The fact that unitary matrices will commute with the
Hamiltonian means that the physical quantities calculated do not change even under unitary transformation. In the case of isospin, this machinery is used to reflect the fact that the mathematics of the strong force behaves the same if a proton and neutron are swapped around (in the modern formulation, the up and down quark).
3846:
2826:
2854:
3632:
3841:{\displaystyle {\begin{aligned}\vert \pi ^{+}\rangle &=\vert \mathrm {u{\overline {d}}} \rangle \\\vert \pi ^{0}\rangle &={\tfrac {1}{\sqrt {2}}}\left(\vert \mathrm {u{\overline {u}}} \rangle -\vert \mathrm {d{\overline {d}}} \rangle \right)\\\vert \pi ^{-}\rangle &=-\vert \mathrm {d{\overline {u}}} \rangle .\end{aligned}}}
3620:. Although these superpositions are the technically correct way of denoting a proton and neutron in terms of quark flavour and spin eigenstates, for brevity, they are often simply referred to as "uud" and "udd". The derivation above assumes exact isospin symmetry and is modified by SU(2)-breaking terms.
2812:
were discovered a short time later, and were quickly identified as
Sakurai's vector bosons. The couplings of the rho to the nucleons and to each other were verified to be universal, as best as experiment could measure. The fact that the diagonal isospin current contains part of the electromagnetic
406:
Before the concept of quarks was introduced, particles that are affected equally by the strong force but had different charges (e.g. protons and neutrons) were considered different states of the same particle, but having isospin values related to the number of charge states. A close examination of
2416:
SU(2). In this context, an invariant subspace is spanned by basis vectors which correspond to particles in a family. Under the action of the Lie algebra SU(2), which generates rotations in isospin space, elements corresponding to definite particle states or superpositions of states can be rotated
2766:
suggested that the notion of protons and neutrons, which are continuously rotated into each other by isospin, should be allowed to vary from point to point. To describe this, the proton and neutron direction in isospin space must be defined at every point, giving local basis for isospin. A
2922:) followed from the up and down quark content of particles; uud for the proton and udd for the neutron. Technically, the nucleon doublet states are seen to be linear combinations of products of 3-particle isospin doublet states and spin doublet states. That is, the (spin-up) proton
2461:
They could be treated as the same particle, with the difference in charge being due to the particle being in different states. Isospin was introduced in order to be the variable that defined this difference of state. In an analogue to spin, an isospin projection (denoted
4024:
which connects quark and lepton doublets of left-handed particles in all generations; for example, up and down quarks, top and bottom quarks, electrons and electron neutrinos. By contrast (strong) isospin connects only up and down quarks, acts on both
2471:) is associated to each charged state; since there were four Deltas, four projections were needed. Like spin, isospin projections were made to vary in increments of 1. Hence, in order to have four increments of 1, an isospin value of
2637:
In the isospin picture, the four Deltas and the two nucleons were thought to simply be the different states of two particles. The Delta baryons are now understood to be made of a mix of three up and down quarks – uuu
1886:
1008:
431:
have the same mass: they can be interpreted as two states of the same particle. These states have different values for an internal isospin coordinate. The mathematical properties of this coordinate are completely analogous to
2411:
The power of isospin symmetry and related methods comes from the observation that families of particles with similar masses tend to correspond to the invariant subspaces associated with the irreducible representations of the
1196:
with the same quark content but different total isospin can be distinguished experimentally, verifying that flavour is actually a vector quantity, not a scalar (up vs down simply being a projection in the quantum mechanical
1208:, but there are two different ways the isospin values can combine – either adding (due to being flavour-aligned) or cancelling out (due to being in opposite flavour directions). The isospin-1 state (the
1956:
1519:
925:
700:
604:
1559:
flavour symmetry is very badly broken in nature (at least at low energies), and assuming this symmetry leads to qualitatively and quantitatively incorrect predictions. In modern applications, such as
399:; for example, a proton–neutron pair can be coupled either in a state of total isospin 1 or in one of 0). But unlike angular momentum, it is a dimensionless quantity and is not actually any type of
3591:
3637:
3563:
1180:
1539:
Although isospin symmetry is actually very slightly broken, SU(3) symmetry is more badly broken, due to the much higher mass of the strange quark compared to the up and down. The discovery of
3937:
3854:
led to reinterpretation of mesons as a vector bound state of a quark and an antiquark, it is sometimes still useful to think of them as being the gauge bosons of a hidden local symmetry.
2896:
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
3531:
3499:
1756:
1722:
2016:: a single electron was shared by two protons. Heisenberg's theory had several problems, most notable it incorrectly predicted the exceptionally strong binding energy of He,
1192:) could either be aligned between a pair of quarks, or face the opposite direction, giving different possible values for total isospin for any combination of quark flavours.
2020:. However, its equal treatment of the proton and neutron gained significance when several experimental studies showed these particles must bind almost equally. In response,
739:
470:
934:
531:
4014:
3984:
3618:
1287:). In simple terms, the energy operator for the strong interaction gives the same result when an up quark and an otherwise identical down quark are swapped around.
785:
748:, but the Hamiltonian of the strong interaction is isospin invariant. As a consequence the nuclear forces are charge independent. Properties like the stability of
1982:
3957:
2789:
Ignoring the massless problem, as Yang and Mills did, the theory makes a firm prediction: the vector particle should couple to all particles of a given isospin
809:
624:
1332:
representation acts. Note that this vector space has nothing to do with the physical space, except similar mathematical formalism. Isospin is described by two
1787:
1555:
flavour symmetry, which would hold if all six quarks were identical. However, the very much larger masses of the charm, bottom, and top quarks means that
814:
298:
2808:
in 1960 predicted that there should be a massive vector boson which is coupled to isospin, and predicted that it would show universal couplings. The
329:
629:
536:
1891:
1452:
1563:, isospin symmetry is often treated as exact for the three light quarks (uds), while the three heavy quarks (cbt) must be treated separately.
4329:
Bando, M.; Kugo, T.; Uehara, S.; Yamawaki, K.; Yanagida, T. (1985). "Is the ρ Meson a
Dynamical Gauge Boson of Hidden Local Symmetry?".
1281:
has a symmetry, that symmetry manifests itself through a set of states that have the same energy (the states are described as being
2024:
used
Heisenberg's concept in his 1937 paper where he introduced the term "isotopic spin" to indicate how the concept is similar to
293:
3883:
2121:. By assuming that isospin was conserved by nuclear interactions, the new mesons were more easily accommodated by nuclear theory.
752:
can be predicted based on isospin analysis. However, this invariance is not exact and the quark model gives more precise results.
4425:(2 ed.). Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo: Springer.
4540:
4514:
4430:
4273:
4130:
4055:
2782:
of electromagnetism. Unlike the photon, the SU(2) gauge theory would contain self-interacting gauge bosons. The condition of
322:
1528:
Pauli matrices only act within the
Hilbert space of isospin, not that of spin, and therefore is common to denote them with
3568:
4610:
626:
for the proton and zero for the neutron. For a system of n nucleons, the charge operator depends upon the mass number A:
3540:
1113:
4102:
2884:, made it clear that the concept of isospin symmetry could be broadened to an even larger symmetry group, now called
315:
303:
4261:
3873:
1278:
928:
3508:
3476:
2893:
1253:
2908:. To better understand the origin of this symmetry, Gell-Mann proposed the existence of up, down and strange
1727:
1693:
4524:
1653:
a single up or down quark together with an additional quark of higher flavour – strange (
4292:(1937). "On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei".
1259:
22:
4020:
are related to the same symmetry but for different forces. Weak isospin is the gauge symmetry of the
1679:
396:
392:
4447:
4217:
708:
439:
4600:
2763:
2448: – were grouped together because they all have nearly the same mass (approximately
1668:
a single up or down quark together with two additional quarks of higher flavour –
4331:
2897:
2869:
2845:
1283:
4094:
507:
2814:
1540:
1379:
60:
1764:
one up quark and one down quark, with an additional quark of higher flavour –
1608:
Particles of total isospin 1 can be made from two up quarks, two down quarks, or one of each:
4556:
2817:, ideas which led to successful theoretical pictures of GeV-scale photon-nucleus scattering.
2775:
1605:
and can be made by a combination of any three up or down quarks (but only up or down quarks).
412:
4532:
4459:
4387:
4340:
4303:
4226:
4168:
3992:
3962:
3596:
763:
4266:
Festi-Val: Festschrift for Val
Telegdi; essays in physics in honour of his 65th birthday;
1378:), to which the "3" subscript refers, is chosen due to notational conventions that relate
8:
4147:
4026:
3319:
3248:
3047:
2976:
1961:
4463:
4391:
4344:
4307:
4230:
4172:
4499:
4242:
4194:
4087:
3942:
2758:
Attempts have been made to promote isospin from a global to a local symmetry. In 1954,
2750:
respectively); yet, they can also be thought of as the excited states of the nucleons.
1881:{\displaystyle c_{1}(\mathrm {u{\bar {u}}+d{\bar {d}}} )+c_{2}(\mathrm {s{\bar {s}}} )}
1291:
794:
745:
609:
4375:
4536:
4510:
4475:
4426:
4403:
4399:
4356:
4269:
4246:
4212:
4198:
4159:
4126:
4098:
4051:
2125:
2001:
1356:
1274:
364:
related to the up- and down quark content of the particle. Isospin is also known as
2710:); the difference in charge being difference in the charges of up and down quarks (+
1003:{\displaystyle {\frac {1}{2}}Y={\frac {1}{2}}(Q_{\textrm {min}}+Q_{\textrm {max}}).}
4595:
4590:
4467:
4395:
4348:
4311:
4234:
4184:
4180:
4176:
4118:
4046:
Povh, Bogdan; Klaus, Rith; Scholz, Christoph; Zetsche, Frank (2008) . "Chapter 2".
4021:
3877:
2912:
which would belong to the fundamental representation of the SU(3) flavor symmetry.
2901:
2783:
2768:
1204:
For example, a strange quark can be combined with an up and a down quark to form a
1011:
702:
373:
347:
225:
27:
705:, nuclei with the same mass number like K and Ar, only differ in the value of the
4605:
4294:
3869:
2885:
2017:
343:
142:
4352:
4151:
2451:
391:
because its quantum mechanical description is mathematically similar to that of
4082:
2830:
2759:
2430:
2025:
1765:
1411:
1333:
433:
407:
isospin symmetry ultimately led directly to the discovery and understanding of
400:
361:
35:
4471:
2804:
When Yang and Mills proposed the theory, there was no candidate vector boson.
2771:
would then describe how to transform isospin along a path between two points.
2012:(symbol n). His model resembled the bonding model for molecule Hydrogen ion, H
1674:
an up quark, a down quark, and either an up or a down quark –
1030:) is defined as a vector quantity in which up and down quarks have a value of
4584:
4479:
4407:
4289:
2923:
2904:, and was promptly recognized to correspond to the adjoint representation of
2805:
2021:
1627:
117:
108:
4360:
4315:
4017:
3863:
2801:
would be the same as the self-coupling of the vector bosons to themselves.
2426:
2037:
1602:
1298:
1015:
760:
The charge operator can be expressed in terms of the projection of isospin
126:
4189:
1951:{\displaystyle {\frac {1}{\sqrt {2}}}(\mathrm {u{\bar {u}}-d{\bar {d}}} )}
1514:{\displaystyle \tau _{3}={\begin{pmatrix}1&0\\0&-1\end{pmatrix}}.}
4506:
3987:
2413:
1560:
1328:, which are coordinates in the same 3-dimensional vector space where the
788:
171:
69:
2825:
931:. The hypercharge is the center of splitting for the isospin multiplet:
4238:
3534:
2793:. The coupling to the nucleon would be the same as the coupling to the
1544:
1360:
1270:
1185:
In any combination of quarks, the 3rd component of the isospin vector (
151:
87:
2813:
current led to the prediction of rho-photon mixing and the concept of
1258:
Isospin is regarded as a symmetry of the strong interaction under the
4573:
2853:
2809:
1759:
1669:
1620:
1371:
1263:
749:
415:. Isospin symmetry remains an important concept in particle physics.
268:
2876:
The discovery and subsequent analysis of additional particles, both
2128:
according to the number of different charge states seen: 2 doublets
741:
eigenvalue. For this reason isospin is also called "isobaric spin".
3502:
1675:
1524:
While the forms of these matrices are isomorphic to those of spin,
920:{\displaystyle Q={\frac {1}{2}}Y+T_{3},\ \ \ \ T_{3}=T,T-1,...,-T.}
2857:
Combinations of three u, d or s-quarks forming baryons with spin-
2009:
1662:
1658:
1548:
1193:
428:
78:
2786:
suggests that they have zero mass, just as in electromagnetism.
2042:
These considerations would also prove useful in the analysis of
1244:) have different experimentally detected masses and half-lives.
2881:
2779:
2005:
1612:
1576:
1572:
1205:
424:
377:
2124:
As further particles were discovered, they were assigned into
3851:
2909:
2905:
2877:
2043:
2004:
introduced a new (unnamed) concept to explain binding of the
1678:. Note that three identical quarks would be forbidden by the
1626:
with an additional quark of higher flavour –
1615: – further differentiated by total spin into
1556:
1552:
1266:
408:
381:
2829:
Combinations of three u, d or s-quarks forming baryons with
744:
The internal structure of these nucleons is governed by the
695:{\displaystyle {\hat {Q}}=e({\hat {T}}_{3}+{\frac {1}{2}}A)}
3624:
2889:
2798:
2794:
2151:
2047:
1654:
1616:
599:{\displaystyle {\hat {Q}}=e({\hat {T}}_{3}+{\frac {1}{2}})}
4421:
Greiner, Walter; Müller, Berndt; Greiner, Walter (1996).
4029:(left and right) and is a global (not a gauge) symmetry.
2926:, in terms of quark-flavour eigenstates, is described by
1093: = 0. Therefore, for hadrons in general, where
4328:
4152:"Review of Particle Physics: Naming scheme for hadrons"
4045:
3712:
3400:
3128:
1474:
3995:
3965:
3945:
3886:
3635:
3599:
3571:
3543:
3511:
3479:
3206:
2934:
1964:
1894:
1790:
1730:
1696:
1455:
1116:
937:
817:
797:
766:
711:
632:
612:
539:
510:
442:
4420:
3586:{\displaystyle \left\vert \downarrow \right\rangle }
1107:
are the numbers of up and down quarks respectively,
4498:
4264:. In Winter, Klaus; Telegdi, Valentine L. (eds.).
4086:
4008:
3978:
3951:
3931:
3840:
3612:
3585:
3558:{\displaystyle \left\vert \uparrow \right\rangle }
3557:
3525:
3493:
3463:
3188:
2560:). Thus, all the Deltas were said to have isospin
1976:
1950:
1880:
1750:
1716:
1682:due to requirement of anti-symmetric wave function
1513:
1175:{\displaystyle I_{3}={\frac {1}{2}}(n_{u}-n_{d}).}
1174:
1002:
919:
803:
779:
733:
694:
618:
598:
525:
464:
2046:-nucleon interactions after the discovery of the
436:angular momentum. The component of the operator,
4582:
4139:
2104:) could be assigned to an isospin triplet with
3876:for charge to isospin would also apply to the
2778:describes interacting vector bosons, like the
1784:The flavour wave-function must be of the form
1687:Particles of total isospin 0 can be made from
16:Quantum number related to the weak interaction
4496:
4081:
3959:is related to the projection of weak isospin
2820:
1089:for down quarks, while all other quarks have
323:
3932:{\displaystyle Q=T_{3}+{\frac {1}{2}}Y_{w}.}
3828:
3810:
3797:
3784:
3772:
3754:
3748:
3730:
3701:
3688:
3681:
3663:
3653:
3640:
3519:
3513:
3487:
3481:
3303:
3289:
3284:
3270:
3265:
3251:
3218:
3207:
3031:
3017:
3012:
2998:
2993:
2979:
2946:
2935:
2915:In the quark model, the isospin projection (
2420:
1770:anything not involving any up or down quarks
1390:representation spaces. Namely, for the spin-
1290:Like the case for regular spin, the isospin
1021:
2582:, and each individual charge had different
4448:"Relation Between Strong and Weak Isospin"
4211:
4123:An Introductory Course of Particle Physics
3526:{\displaystyle \mathrm {\vert d\rangle } }
3494:{\displaystyle \mathrm {\vert u\rangle } }
2753:
1370:state specifies certain flavor state of a
1340: – the total isospin, and
1273:being the up flavour and down flavour. In
755:
387:The name of the concept contains the term
330:
316:
4523:
4452:International Journal of Modern Physics E
4376:"Partial-symmetries of weak interactions"
4282:
4268:. Amsterdam: North-Holland Physics Publ.
4188:
4077:
4075:
4073:
4071:
4069:
4067:
3872:proposed that as relation similar to the
1581:Hadron nomenclature is based on isospin.
376:seen more broadly in the interactions of
4574:Nuclear Structure and Decay Data - IAEA
4253:
2852:
2824:
2425:For example, the particles known as the
1347: – an eigenvalue of the
504:; it is related to the charge operator,
4373:
3623:Similarly, the isospin symmetry of the
2458:) and interact in nearly the same way.
1551:could lead to further expansions up to
1247:
472:, for this coordinate has eigenvalues +
4583:
4445:
4288:
4215:(1932). "Über den Bau der Atomkerne".
4145:
4064:
1751:{\displaystyle \mathrm {d{\bar {d}}} }
1717:{\displaystyle \mathrm {u{\bar {u}}} }
1566:
372:. Isospin symmetry is a subset of the
4259:
418:
4529:Introduction to Elementary Particles
2487:is required (giving the projections
1995:
1026:In the modern formulation, isospin (
4497:Itzykson, C.; Zuber, J.-B. (1980).
4262:"Remarks on the history of isospin"
4117:
2031:
1010:This relation has an analog in the
13:
4490:
4374:Glashow, Sheldon L. (1961-02-01).
4093:(2nd ed.). Springer. p.
3819:
3814:
3763:
3758:
3739:
3734:
3672:
3667:
3516:
3484:
3299:
3296:
3293:
3280:
3277:
3274:
3261:
3258:
3255:
3211:
3027:
3024:
3021:
3008:
3005:
3002:
2989:
2986:
2983:
2939:
1935:
1929:
1917:
1911:
1865:
1859:
1829:
1823:
1811:
1805:
1738:
1732:
1704:
1698:
14:
4622:
4565:
4423:Gauge theory of weak interactions
1888:for an isospin-0 combination, as
1301:-valued: it has three components
1690:a neutral quark-antiquark pair:
4439:
4414:
4367:
3857:
1226:) and the isospin-0 state (the
4322:
4205:
4181:10.1016/j.physletb.2008.07.018
4111:
4039:
3850:Although the discovery of the
3576:
3548:
3442:
3425:
3408:
3215:
3170:
3153:
3136:
2943:
2429: – baryons of
2008:and the then newly discovered
1945:
1938:
1920:
1907:
1875:
1868:
1855:
1839:
1832:
1814:
1801:
1778:
1741:
1707:
1254:Representation theory of SU(2)
1201: axis of flavour space).
1166:
1140:
994:
964:
734:{\displaystyle {\hat {T}}_{3}}
719:
689:
661:
651:
639:
593:
568:
558:
546:
517:
465:{\displaystyle {\hat {T}}_{3}}
450:
395:(in particular, in the way it
1:
4089:Quantum Mechanics: Symmetries
4032:
3198:and the (spin-up) neutron by
4400:10.1016/0029-5582(61)90469-2
3822:
3766:
3742:
3675:
1359:for which flavor states are
423:To a good approximation the
7:
4550:
4353:10.1103/PhysRevLett.54.1215
3874:Gell-Mann–Nishijima formula
3443:↑ ↑ ↓
3426:↑ ↓ ↑
3409:↓ ↑ ↑
3171:↑ ↑ ↓
3154:↑ ↓ ↑
3137:↓ ↑ ↑
1634:Particles of total isospin
1585:Particles of total isospin
929:Gell-Mann–Nishijima formula
10:
4627:
4611:Flavour (particle physics)
4446:Robson, B. A. (Oct 2004).
4125:. CRC Press. p. 226.
3861:
3537:flavour eigenstate, while
2821:The introduction of quarks
2050:in 1947. The three pions (
2035:
1990:
1570:
1251:
1050:, with the 3rd-component (
526:{\displaystyle {\hat {Q}}}
411:and to the development of
4472:10.1142/S0218301304002521
4146:Amsler, C.; et al. (
2421:An example: Delta baryons
1680:Pauli exclusion principle
1022:Quark content and isospin
4050:. Springer. p. 21.
3505:flavour eigenstate, and
1619:(total spin 0) and
1374:. The third coordinate (
4332:Physical Review Letters
3593:are the eigenstates of
2754:Gauged isospin symmetry
1363:. In other words, each
756:Relation to hypercharge
304:Flavour complementarity
101:Related quantum numbers
4316:10.1103/PhysRev.51.106
4218:Zeitschrift für Physik
4010:
3980:
3953:
3933:
3842:
3614:
3587:
3559:
3527:
3495:
3465:
3190:
2892:and their property of
2873:
2850:
2815:vector meson dominance
2797:. The coupling to the
1978:
1952:
1882:
1752:
1718:
1515:
1176:
1004:
921:
805:
781:
735:
696:
620:
606:which has eigenvalues
600:
527:
466:
4533:John Wiley & Sons
4085:; Müller, B. (1994).
4011:
4009:{\displaystyle Y_{w}}
3981:
3979:{\displaystyle T_{3}}
3954:
3934:
3843:
3615:
3613:{\displaystyle S_{z}}
3588:
3560:
3528:
3496:
3466:
3191:
2856:
2828:
1979:
1953:
1883:
1753:
1719:
1516:
1414:divided by 2, and so
1177:
1005:
927:This is known as the
922:
806:
782:
780:{\displaystyle T_{3}}
736:
697:
621:
601:
528:
467:
4501:Quantum Field Theory
4260:Brown, L.M. (1988).
4048:Particles and Nuclei
3993:
3963:
3943:
3884:
3633:
3597:
3569:
3541:
3509:
3477:
3204:
2932:
2609:was associated with
1962:
1892:
1788:
1728:
1694:
1536:to avoid confusion.
1453:
1406:case, components of
1248:Isospin and symmetry
1114:
1073:for up quarks, and −
935:
815:
795:
764:
709:
630:
610:
537:
508:
440:
4464:2004IJMPE..13..999R
4392:1961NucPh..22..579G
4345:1985PhRvL..54.1215B
4308:1937PhRv...51..106W
4231:1932ZPhy...77....1H
4173:2008PhLB..667....1A
4148:Particle Data Group
1977:{\displaystyle I=1}
1758: –
1567:Hadron nomenclature
4239:10.1007/BF01342433
4006:
3976:
3949:
3929:
3838:
3836:
3723:
3610:
3583:
3555:
3523:
3491:
3461:
3452:
3389:
3308:
3186:
3180:
3117:
3036:
2874:
2851:
2235:of Sigma baryons (
2126:isospin multiplets
1974:
1948:
1878:
1748:
1714:
1650:can be made from:
1511:
1502:
1172:
1000:
917:
801:
777:
746:strong interaction
731:
692:
616:
596:
523:
462:
419:Isospin invariance
4577:Nuclides' Isospin
4557:Chan–Paton factor
4542:978-0-471-60386-3
4516:978-0-07-032071-0
4432:978-3-540-60227-9
4339:(12): 1215–1218.
4275:978-0-444-87099-5
4160:Physics Letters B
4132:978-1-4822-1698-1
4119:Pal, Palash Baran
4057:978-3-540-79367-0
3952:{\displaystyle Q}
3914:
3825:
3769:
3745:
3722:
3721:
3678:
3241:
3238:
2969:
2966:
2776:Yang–Mills theory
2002:Werner Heisenberg
1996:Origin of isospin
1941:
1923:
1905:
1904:
1871:
1835:
1817:
1744:
1710:
1275:quantum mechanics
1138:
990:
975:
962:
946:
864:
861:
858:
855:
832:
804:{\displaystyle Y}
722:
684:
664:
642:
619:{\displaystyle e}
591:
571:
549:
520:
453:
413:Yang–Mills theory
340:
339:
4618:
4546:
4520:
4504:
4484:
4483:
4443:
4437:
4436:
4418:
4412:
4411:
4371:
4365:
4364:
4326:
4320:
4319:
4286:
4280:
4279:
4257:
4251:
4250:
4209:
4203:
4202:
4192:
4156:
4143:
4137:
4136:
4121:(29 July 2014).
4115:
4109:
4108:
4092:
4079:
4062:
4061:
4043:
4022:weak interaction
4015:
4013:
4012:
4007:
4005:
4004:
3985:
3983:
3982:
3977:
3975:
3974:
3958:
3956:
3955:
3950:
3939:Here the charge
3938:
3936:
3935:
3930:
3925:
3924:
3915:
3907:
3902:
3901:
3878:weak interaction
3847:
3845:
3844:
3839:
3837:
3827:
3826:
3818:
3796:
3795:
3779:
3775:
3771:
3770:
3762:
3747:
3746:
3738:
3724:
3717:
3713:
3700:
3699:
3680:
3679:
3671:
3652:
3651:
3619:
3617:
3616:
3611:
3609:
3608:
3592:
3590:
3589:
3584:
3582:
3564:
3562:
3561:
3556:
3554:
3532:
3530:
3529:
3524:
3522:
3500:
3498:
3497:
3492:
3490:
3470:
3468:
3467:
3462:
3457:
3453:
3449:
3445:
3432:
3428:
3415:
3411:
3394:
3390:
3313:
3309:
3302:
3283:
3264:
3242:
3240:
3239:
3234:
3225:
3214:
3195:
3193:
3192:
3187:
3185:
3181:
3177:
3173:
3160:
3156:
3143:
3139:
3122:
3118:
3041:
3037:
3030:
3011:
2992:
2970:
2968:
2967:
2962:
2953:
2942:
2902:Murray Gell-Mann
2866:
2865:
2861:
2842:
2841:
2837:
2784:gauge invariance
2769:gauge connection
2745:
2743:
2742:
2739:
2736:
2725:
2723:
2722:
2719:
2716:
2709:
2708:
2707:
2700:
2699:
2691:
2690:
2689:
2682:
2681:
2673:
2672:
2671:
2664:
2663:
2655:
2654:
2653:
2646:
2645:
2633:
2632:
2630:
2629:
2626:
2623:
2608:
2607:
2606:
2599:
2598:
2590:
2581:
2580:
2578:
2577:
2574:
2571:
2559:
2558:
2556:
2555:
2552:
2549:
2542:
2540:
2539:
2536:
2533:
2526:
2524:
2523:
2520:
2517:
2510:
2508:
2507:
2504:
2501:
2486:
2484:
2483:
2480:
2477:
2470:
2457:
2447:
2445:
2444:
2441:
2438:
2407:
2406:
2405:
2398:
2397:
2389:
2388:
2387:
2380:
2379:
2371:
2370:
2369:
2362:
2361:
2353:
2352:
2351:
2344:
2343:
2335:
2334:
2332:
2331:
2328:
2325:
2313:
2312:
2311:
2304:
2303:
2295:
2288:
2287:
2286:
2279:
2278:
2270:
2269:
2268:
2261:
2260:
2252:
2251:
2250:
2243:
2242:
2234:
2227:
2226:
2225:
2218:
2217:
2209:
2208:
2207:
2200:
2199:
2191:
2190:
2189:
2183:
2180:
2179:
2171:
2170:
2169:
2162:
2161:
2149:
2148:
2146:
2145:
2142:
2139:
2120:
2110:
2103:
2102:
2101:
2094:
2093:
2085:
2084:
2083:
2076:
2075:
2067:
2066:
2065:
2058:
2057:
2032:The particle zoo
1984:
1983:
1981:
1980:
1975:
1957:
1955:
1954:
1949:
1944:
1943:
1942:
1934:
1925:
1924:
1916:
1906:
1900:
1896:
1887:
1885:
1884:
1879:
1874:
1873:
1872:
1864:
1854:
1853:
1838:
1837:
1836:
1828:
1819:
1818:
1810:
1800:
1799:
1782:
1757:
1755:
1754:
1749:
1747:
1746:
1745:
1737:
1723:
1721:
1720:
1715:
1713:
1712:
1711:
1703:
1649:
1647:
1646:
1643:
1640:
1600:
1598:
1597:
1594:
1591:
1520:
1518:
1517:
1512:
1507:
1506:
1465:
1464:
1442:
1438:
1436:
1435:
1432:
1429:
1405:
1403:
1402:
1399:
1396:
1377:
1366:
1343:
1339:
1243:
1242:
1241:
1234:
1233:
1225:
1224:
1223:
1216:
1215:
1200:
1188:
1181:
1179:
1178:
1173:
1165:
1164:
1152:
1151:
1139:
1131:
1126:
1125:
1103:
1096:
1092:
1088:
1086:
1085:
1082:
1079:
1072:
1070:
1069:
1066:
1063:
1053:
1049:
1047:
1046:
1043:
1040:
1033:
1029:
1012:weak interaction
1009:
1007:
1006:
1001:
993:
992:
991:
988:
978:
977:
976:
973:
963:
955:
947:
939:
926:
924:
923:
918:
874:
873:
862:
859:
856:
853:
849:
848:
833:
825:
810:
808:
807:
802:
786:
784:
783:
778:
776:
775:
740:
738:
737:
732:
730:
729:
724:
723:
715:
701:
699:
698:
693:
685:
677:
672:
671:
666:
665:
657:
644:
643:
635:
625:
623:
622:
617:
605:
603:
602:
597:
592:
584:
579:
578:
573:
572:
564:
551:
550:
542:
532:
530:
529:
524:
522:
521:
513:
503:
501:
500:
497:
494:
487:
485:
484:
481:
478:
471:
469:
468:
463:
461:
460:
455:
454:
446:
393:angular momentum
374:flavour symmetry
348:particle physics
332:
325:
318:
226:Weak hypercharge
28:particle physics
19:
18:
4626:
4625:
4621:
4620:
4619:
4617:
4616:
4615:
4601:Nuclear physics
4581:
4580:
4568:
4562:
4553:
4543:
4517:
4493:
4491:Further reading
4488:
4487:
4458:(5): 999–1018.
4444:
4440:
4433:
4419:
4415:
4380:Nuclear Physics
4372:
4368:
4327:
4323:
4295:Physical Review
4287:
4283:
4276:
4258:
4254:
4210:
4206:
4154:
4144:
4140:
4133:
4116:
4112:
4105:
4080:
4065:
4058:
4044:
4040:
4035:
4000:
3996:
3994:
3991:
3990:
3970:
3966:
3964:
3961:
3960:
3944:
3941:
3940:
3920:
3916:
3906:
3897:
3893:
3885:
3882:
3881:
3870:Sheldon Glashow
3866:
3860:
3835:
3834:
3817:
3813:
3800:
3791:
3787:
3781:
3780:
3761:
3757:
3737:
3733:
3729:
3725:
3711:
3704:
3695:
3691:
3685:
3684:
3670:
3666:
3656:
3647:
3643:
3636:
3634:
3631:
3630:
3604:
3600:
3598:
3595:
3594:
3572:
3570:
3567:
3566:
3544:
3542:
3539:
3538:
3512:
3510:
3507:
3506:
3480:
3478:
3475:
3474:
3451:
3450:
3441:
3437:
3434:
3433:
3424:
3420:
3417:
3416:
3407:
3403:
3399:
3395:
3388:
3387:
3382:
3374:
3365:
3364:
3356:
3351:
3342:
3341:
3333:
3325:
3318:
3314:
3307:
3306:
3292:
3287:
3273:
3268:
3254:
3247:
3243:
3233:
3229:
3224:
3210:
3205:
3202:
3201:
3179:
3178:
3169:
3165:
3162:
3161:
3152:
3148:
3145:
3144:
3135:
3131:
3127:
3123:
3116:
3115:
3110:
3102:
3093:
3092:
3084:
3079:
3070:
3069:
3061:
3053:
3046:
3042:
3035:
3034:
3020:
3015:
3001:
2996:
2982:
2975:
2971:
2961:
2957:
2952:
2938:
2933:
2930:
2929:
2921:
2886:flavor symmetry
2863:
2859:
2858:
2846:baryon decuplet
2839:
2835:
2834:
2823:
2756:
2740:
2737:
2734:
2733:
2731:
2720:
2717:
2714:
2713:
2711:
2706:
2704:
2703:
2702:
2698:
2696:
2695:
2694:
2693:
2688:
2686:
2685:
2684:
2680:
2678:
2677:
2676:
2675:
2670:
2668:
2667:
2666:
2662:
2660:
2659:
2658:
2657:
2652:
2650:
2649:
2648:
2644:
2642:
2641:
2640:
2639:
2627:
2624:
2621:
2620:
2618:
2616:
2610:
2605:
2603:
2602:
2601:
2597:
2595:
2594:
2593:
2592:
2589:
2583:
2575:
2572:
2569:
2568:
2566:
2561:
2553:
2550:
2547:
2546:
2544:
2537:
2534:
2531:
2530:
2528:
2521:
2518:
2515:
2514:
2512:
2505:
2502:
2499:
2498:
2496:
2494:
2488:
2481:
2478:
2475:
2474:
2472:
2469:
2463:
2449:
2442:
2439:
2436:
2435:
2433:
2423:
2404:
2402:
2401:
2400:
2396:
2394:
2393:
2392:
2391:
2386:
2384:
2383:
2382:
2378:
2376:
2375:
2374:
2373:
2368:
2366:
2365:
2364:
2360:
2358:
2357:
2356:
2355:
2350:
2348:
2347:
2346:
2342:
2340:
2339:
2338:
2337:
2336:Delta baryons (
2329:
2326:
2323:
2322:
2320:
2315:
2310:
2308:
2307:
2306:
2302:
2300:
2299:
2298:
2297:
2296:Lambda baryon (
2290:
2285:
2283:
2282:
2281:
2277:
2275:
2274:
2273:
2272:
2267:
2265:
2264:
2263:
2259:
2257:
2256:
2255:
2254:
2249:
2247:
2246:
2245:
2241:
2239:
2238:
2237:
2236:
2229:
2224:
2222:
2221:
2220:
2216:
2214:
2213:
2212:
2211:
2206:
2204:
2203:
2202:
2198:
2196:
2195:
2194:
2193:
2188:
2186:
2185:
2184:
2181:
2178:
2176:
2175:
2174:
2173:
2168:
2166:
2165:
2164:
2160:
2158:
2157:
2156:
2155:
2143:
2140:
2137:
2136:
2134:
2129:
2118:
2112:
2105:
2100:
2098:
2097:
2096:
2092:
2090:
2089:
2088:
2087:
2082:
2080:
2079:
2078:
2074:
2072:
2071:
2070:
2069:
2064:
2062:
2061:
2060:
2056:
2054:
2053:
2052:
2051:
2040:
2034:
2018:alpha particles
2015:
1998:
1993:
1988:
1987:
1963:
1960:
1959:
1933:
1932:
1915:
1914:
1910:
1895:
1893:
1890:
1889:
1863:
1862:
1858:
1849:
1845:
1827:
1826:
1809:
1808:
1804:
1795:
1791:
1789:
1786:
1785:
1783:
1779:
1760:eta mesons
1736:
1735:
1731:
1729:
1726:
1725:
1702:
1701:
1697:
1695:
1692:
1691:
1644:
1641:
1638:
1637:
1635:
1595:
1592:
1589:
1588:
1586:
1579:
1571:Main articles:
1569:
1501:
1500:
1492:
1486:
1485:
1480:
1470:
1469:
1460:
1456:
1454:
1451:
1450:
1445:
1440:
1433:
1430:
1427:
1426:
1424:
1422:
1400:
1397:
1394:
1393:
1391:
1375:
1369:
1364:
1355:
1346:
1341:
1337:
1334:quantum numbers
1327:
1318:
1309:
1256:
1250:
1240:
1238:
1237:
1236:
1232:
1230:
1229:
1228:
1227:
1222:
1220:
1219:
1218:
1214:
1212:
1211:
1210:
1209:
1198:
1191:
1186:
1160:
1156:
1147:
1143:
1130:
1121:
1117:
1115:
1112:
1111:
1106:
1101:
1099:
1094:
1090:
1083:
1080:
1077:
1076:
1074:
1067:
1064:
1061:
1060:
1058:
1056:
1051:
1044:
1041:
1038:
1037:
1035:
1031:
1027:
1024:
1014:where T is the
987:
986:
982:
972:
971:
967:
954:
938:
936:
933:
932:
869:
865:
844:
840:
824:
816:
813:
812:
796:
793:
792:
771:
767:
765:
762:
761:
758:
725:
714:
713:
712:
710:
707:
706:
676:
667:
656:
655:
654:
634:
633:
631:
628:
627:
611:
608:
607:
583:
574:
563:
562:
561:
541:
540:
538:
535:
534:
512:
511:
509:
506:
505:
498:
495:
492:
491:
489:
482:
479:
476:
475:
473:
456:
445:
444:
443:
441:
438:
437:
421:
344:nuclear physics
336:
266:
253:
242:
234:
219:
143:Electric charge
139:
57:
36:quantum numbers
26:
17:
12:
11:
5:
4624:
4614:
4613:
4608:
4603:
4598:
4593:
4579:
4578:
4567:
4566:External links
4564:
4560:
4559:
4552:
4549:
4548:
4547:
4541:
4521:
4515:
4492:
4489:
4486:
4485:
4438:
4431:
4413:
4386:(4): 579–588.
4366:
4321:
4302:(2): 106–119.
4281:
4274:
4252:
4213:Heisenberg, W.
4204:
4190:1854/LU-685594
4138:
4131:
4110:
4104:978-3540580805
4103:
4063:
4056:
4037:
4036:
4034:
4031:
4016:. Isospin and
4003:
3999:
3973:
3969:
3948:
3928:
3923:
3919:
3913:
3910:
3905:
3900:
3896:
3892:
3889:
3862:Main article:
3859:
3856:
3833:
3830:
3824:
3821:
3816:
3812:
3809:
3806:
3803:
3801:
3799:
3794:
3790:
3786:
3783:
3782:
3778:
3774:
3768:
3765:
3760:
3756:
3753:
3750:
3744:
3741:
3736:
3732:
3728:
3720:
3716:
3710:
3707:
3705:
3703:
3698:
3694:
3690:
3687:
3686:
3683:
3677:
3674:
3669:
3665:
3662:
3659:
3657:
3655:
3650:
3646:
3642:
3639:
3638:
3627:are given by:
3607:
3603:
3581:
3578:
3575:
3553:
3550:
3547:
3521:
3518:
3515:
3489:
3486:
3483:
3460:
3456:
3448:
3444:
3440:
3436:
3435:
3431:
3427:
3423:
3419:
3418:
3414:
3410:
3406:
3402:
3401:
3398:
3393:
3386:
3383:
3381:
3378:
3375:
3373:
3370:
3367:
3366:
3363:
3360:
3357:
3355:
3352:
3350:
3347:
3344:
3343:
3340:
3337:
3334:
3332:
3329:
3326:
3324:
3321:
3320:
3317:
3312:
3305:
3301:
3298:
3295:
3291:
3288:
3286:
3282:
3279:
3276:
3272:
3269:
3267:
3263:
3260:
3257:
3253:
3250:
3249:
3246:
3237:
3232:
3228:
3223:
3220:
3217:
3213:
3209:
3184:
3176:
3172:
3168:
3164:
3163:
3159:
3155:
3151:
3147:
3146:
3142:
3138:
3134:
3130:
3129:
3126:
3121:
3114:
3111:
3109:
3106:
3103:
3101:
3098:
3095:
3094:
3091:
3088:
3085:
3083:
3080:
3078:
3075:
3072:
3071:
3068:
3065:
3062:
3060:
3057:
3054:
3052:
3049:
3048:
3045:
3040:
3033:
3029:
3026:
3023:
3019:
3016:
3014:
3010:
3007:
3004:
3000:
2997:
2995:
2991:
2988:
2985:
2981:
2978:
2977:
2974:
2965:
2960:
2956:
2951:
2948:
2945:
2941:
2937:
2919:
2822:
2819:
2760:Chen Ning Yang
2755:
2752:
2705:
2697:
2687:
2679:
2669:
2661:
2651:
2643:
2614:
2604:
2596:
2587:
2492:
2467:
2422:
2419:
2408:), and so on.
2403:
2395:
2385:
2377:
2367:
2359:
2349:
2341:
2309:
2301:
2284:
2276:
2266:
2258:
2248:
2240:
2223:
2215:
2205:
2197:
2187:
2177:
2167:
2159:
2116:
2099:
2091:
2081:
2073:
2063:
2055:
2036:Main article:
2033:
2030:
2013:
1997:
1994:
1992:
1989:
1986:
1985:
1973:
1970:
1967:
1947:
1940:
1937:
1931:
1928:
1922:
1919:
1913:
1909:
1903:
1899:
1877:
1870:
1867:
1861:
1857:
1852:
1848:
1844:
1841:
1834:
1831:
1825:
1822:
1816:
1813:
1807:
1803:
1798:
1794:
1776:
1775:
1774:
1773:
1772:
1771:
1768:
1766:Lambda baryons
1762:
1743:
1740:
1734:
1709:
1706:
1700:
1685:
1684:
1683:
1672:
1670:Xi baryon
1666:
1661:), or bottom (
1632:
1631:
1630:
1624:
1623:(total spin 1)
1606:
1568:
1565:
1522:
1521:
1510:
1505:
1499:
1496:
1493:
1491:
1488:
1487:
1484:
1481:
1479:
1476:
1475:
1473:
1468:
1463:
1459:
1443:
1418:
1412:Pauli matrices
1367:
1351:
1344:
1323:
1314:
1305:
1249:
1246:
1239:
1231:
1221:
1213:
1189:
1183:
1182:
1171:
1168:
1163:
1159:
1155:
1150:
1146:
1142:
1137:
1134:
1129:
1124:
1120:
1104:
1097:
1054:
1023:
1020:
999:
996:
985:
981:
970:
966:
961:
958:
953:
950:
945:
942:
916:
913:
910:
907:
904:
901:
898:
895:
892:
889:
886:
883:
880:
877:
872:
868:
852:
847:
843:
839:
836:
831:
828:
823:
820:
800:
774:
770:
757:
754:
728:
721:
718:
691:
688:
683:
680:
675:
670:
663:
660:
653:
650:
647:
641:
638:
615:
595:
590:
587:
582:
577:
570:
567:
560:
557:
554:
548:
545:
519:
516:
459:
452:
449:
434:intrinsic spin
420:
417:
362:quantum number
338:
337:
335:
334:
327:
320:
312:
309:
308:
307:
306:
301:
296:
288:
287:
286:Flavour mixing
283:
282:
281:
280:
279:
278:
264:
255:
251:
240:
232:
223:
222:
221:
217:
204:
166:
165:
161:
160:
159:
158:
149:
140:
137:
124:
115:
103:
102:
98:
97:
96:
95:
85:
76:
67:
58:
55:
39:
38:
31:
30:
15:
9:
6:
4:
3:
2:
4623:
4612:
4609:
4607:
4604:
4602:
4599:
4597:
4594:
4592:
4589:
4588:
4586:
4576:
4575:
4570:
4569:
4563:
4558:
4555:
4554:
4544:
4538:
4534:
4530:
4526:
4525:Griffiths, D.
4522:
4518:
4512:
4508:
4503:
4502:
4495:
4494:
4481:
4477:
4473:
4469:
4465:
4461:
4457:
4453:
4449:
4442:
4434:
4428:
4424:
4417:
4409:
4405:
4401:
4397:
4393:
4389:
4385:
4381:
4377:
4370:
4362:
4358:
4354:
4350:
4346:
4342:
4338:
4334:
4333:
4325:
4317:
4313:
4309:
4305:
4301:
4297:
4296:
4291:
4285:
4277:
4271:
4267:
4263:
4256:
4248:
4244:
4240:
4236:
4232:
4228:
4225:(1–2): 1–11.
4224:
4221:(in German).
4220:
4219:
4214:
4208:
4200:
4196:
4191:
4186:
4182:
4178:
4174:
4170:
4166:
4162:
4161:
4153:
4149:
4142:
4134:
4128:
4124:
4120:
4114:
4106:
4100:
4096:
4091:
4090:
4084:
4078:
4076:
4074:
4072:
4070:
4068:
4059:
4053:
4049:
4042:
4038:
4030:
4028:
4023:
4019:
4001:
3997:
3989:
3986:and the weak
3971:
3967:
3946:
3926:
3921:
3917:
3911:
3908:
3903:
3898:
3894:
3890:
3887:
3879:
3875:
3871:
3865:
3855:
3853:
3848:
3831:
3807:
3804:
3802:
3792:
3788:
3776:
3751:
3726:
3718:
3714:
3708:
3706:
3696:
3692:
3660:
3658:
3648:
3644:
3628:
3626:
3621:
3605:
3601:
3579:
3573:
3551:
3545:
3536:
3504:
3471:
3458:
3454:
3446:
3438:
3429:
3421:
3412:
3404:
3396:
3391:
3384:
3379:
3376:
3371:
3368:
3361:
3358:
3353:
3348:
3345:
3338:
3335:
3330:
3327:
3322:
3315:
3310:
3244:
3235:
3230:
3226:
3221:
3199:
3196:
3182:
3174:
3166:
3157:
3149:
3140:
3132:
3124:
3119:
3112:
3107:
3104:
3099:
3096:
3089:
3086:
3081:
3076:
3073:
3066:
3063:
3058:
3055:
3050:
3043:
3038:
2972:
2963:
2958:
2954:
2949:
2927:
2925:
2924:wave function
2918:
2913:
2911:
2907:
2903:
2899:
2898:Eightfold Way
2895:
2891:
2887:
2883:
2879:
2872:
2871:
2855:
2848:
2847:
2832:
2827:
2818:
2816:
2811:
2807:
2806:J. J. Sakurai
2802:
2800:
2796:
2792:
2787:
2785:
2781:
2777:
2772:
2770:
2765:
2761:
2751:
2749:
2729:
2635:
2613:
2586:
2564:
2491:
2466:
2459:
2456:
2455:
2432:
2428:
2427:Delta baryons
2418:
2415:
2409:
2318:
2314:), a quartet
2293:
2289:), a singlet
2232:
2228:), a triplet
2153:
2132:
2127:
2122:
2119:= +1, 0 or −1
2115:
2108:
2049:
2045:
2039:
2029:
2028:in behavior.
2027:
2023:
2022:Eugene Wigner
2019:
2011:
2007:
2003:
1971:
1968:
1965:
1926:
1901:
1897:
1850:
1846:
1842:
1820:
1796:
1792:
1781:
1777:
1769:
1767:
1763:
1761:
1689:
1688:
1686:
1681:
1677:
1673:
1671:
1667:
1664:
1660:
1656:
1652:
1651:
1633:
1629:
1628:Sigma baryons
1625:
1622:
1618:
1614:
1610:
1609:
1607:
1604:
1603:Delta baryons
1584:
1583:
1582:
1578:
1574:
1564:
1562:
1558:
1554:
1550:
1546:
1542:
1537:
1535:
1531:
1527:
1508:
1503:
1497:
1494:
1489:
1482:
1477:
1471:
1466:
1461:
1457:
1449:
1448:
1447:
1421:
1417:
1413:
1410:are equal to
1409:
1389:
1385:
1381:
1373:
1362:
1358:
1354:
1350:
1335:
1331:
1326:
1322:
1317:
1313:
1308:
1304:
1300:
1296:
1293:
1288:
1286:
1285:
1280:
1276:
1272:
1268:
1265:
1261:
1255:
1245:
1207:
1202:
1195:
1169:
1161:
1157:
1153:
1148:
1144:
1135:
1132:
1127:
1122:
1118:
1110:
1109:
1108:
1034: =
1019:
1017:
1013:
997:
983:
979:
968:
959:
956:
951:
948:
943:
940:
930:
914:
911:
908:
905:
902:
899:
896:
893:
890:
887:
884:
881:
878:
875:
870:
866:
850:
845:
841:
837:
834:
829:
826:
821:
818:
798:
790:
772:
768:
753:
751:
747:
742:
726:
716:
704:
686:
681:
678:
673:
668:
658:
648:
645:
636:
613:
588:
585:
580:
575:
565:
555:
552:
543:
514:
457:
447:
435:
430:
426:
416:
414:
410:
404:
402:
398:
394:
390:
385:
383:
379:
375:
371:
370:isotopic spin
367:
366:isobaric spin
363:
359:
358:
353:
349:
345:
333:
328:
326:
321:
319:
314:
313:
311:
310:
305:
302:
300:
297:
295:
292:
291:
290:
289:
285:
284:
276:
275:
271:
263:
259:
256:
250:
246:
239:
236:
235:
231:
227:
224:
216:
212:
208:
205:
202:
198:
194:
190:
186:
182:
179:
178:
177:
173:
170:
169:
168:
167:
163:
162:
157:
153:
150:
148:
144:
141:
136:
132:
128:
125:
123:
119:
118:Lepton number
116:
114:
110:
109:Baryon number
107:
106:
105:
104:
100:
99:
93:
89:
86:
84:
80:
77:
75:
71:
68:
66:
62:
59:
54:
50:
46:
43:
42:
41:
40:
37:
33:
32:
29:
24:
21:
20:
4572:
4561:
4528:
4500:
4455:
4451:
4441:
4422:
4416:
4383:
4379:
4369:
4336:
4330:
4324:
4299:
4293:
4284:
4265:
4255:
4222:
4216:
4207:
4164:
4158:
4141:
4122:
4113:
4088:
4047:
4041:
4018:weak isospin
3867:
3864:weak isospin
3858:Weak isospin
3849:
3629:
3622:
3472:
3200:
3197:
2928:
2916:
2914:
2875:
2870:baryon octet
2868:
2844:
2803:
2790:
2788:
2773:
2764:Robert Mills
2757:
2747:
2727:
2692:), and ddd (
2636:
2611:
2584:
2562:
2489:
2464:
2460:
2453:
2424:
2410:
2316:
2291:
2230:
2130:
2123:
2113:
2106:
2041:
2038:Particle zoo
1999:
1780:
1663:B meson
1659:D meson
1580:
1538:
1533:
1532:rather than
1529:
1525:
1523:
1419:
1415:
1407:
1387:
1383:
1352:
1348:
1329:
1324:
1320:
1315:
1311:
1306:
1302:
1294:
1289:
1282:
1257:
1203:
1184:
1025:
1016:weak isospin
759:
743:
422:
405:
388:
386:
369:
365:
356:
355:
351:
341:
273:
269:
261:
257:
248:
244:
237:
229:
214:
210:
206:
200:
196:
192:
188:
184:
180:
175:
164:Combinations
155:
146:
134:
130:
127:Weak isospin
121:
112:
91:
82:
73:
64:
52:
48:
44:
4507:McGraw-Hill
4083:Greiner, W.
4027:chiralities
3988:hypercharge
2894:strangeness
2888:. Once the
2791:universally
2414:Lie algebra
1561:lattice QCD
1361:eigenstates
1279:Hamiltonian
789:hypercharge
299:PMNS matrix
172:Hypercharge
70:Strangeness
4585:Categories
4290:Wigner, E.
4167:(1): 1–6.
4150:) (2008).
4033:References
3535:down quark
2810:rho mesons
2591:(e.g. the
2450:1232
1657:), charm (
1621:rho mesons
1601:are named
1545:bottomness
1357:projection
1284:degenerate
1269:, the two
1252:See also:
294:CKM matrix
199:′ +
88:Bottomness
4480:0218-3013
4408:0029-5582
4247:186218053
4199:227119789
3829:⟩
3823:¯
3808:−
3798:⟩
3793:−
3789:π
3773:⟩
3767:¯
3752:−
3749:⟩
3743:¯
3702:⟩
3693:π
3682:⟩
3676:¯
3654:⟩
3645:π
3577:↓
3549:↑
3520:⟩
3488:⟩
3377:−
3369:−
3359:−
3346:−
3336:−
3328:−
3304:⟩
3285:⟩
3266:⟩
3219:⟩
3216:↑
3105:−
3097:−
3087:−
3074:−
3064:−
3056:−
3032:⟩
3013:⟩
2994:⟩
2947:⟩
2944:↑
2867:form the
2843:form the
2000:In 1932,
1939:¯
1927:−
1921:¯
1869:¯
1833:¯
1815:¯
1742:¯
1708:¯
1495:−
1458:τ
1372:multiplet
1277:, when a
1264:Lie group
1154:−
1057:) being +
909:−
888:−
750:deuterium
720:^
662:^
640:^
569:^
547:^
518:^
451:^
4551:See also
4527:(1987).
4361:10030967
3868:In 1961
3580:⟩
3552:⟩
3503:up quark
3447:⟩
3430:⟩
3413:⟩
3175:⟩
3158:⟩
3141:⟩
2674:), udd (
2656:), uud (
2152:K mesons
1676:nucleons
1611:certain
1446:, where
1292:operator
152:X-charge
34:Flavour
4596:Hadrons
4591:Baryons
4460:Bibcode
4388:Bibcode
4341:Bibcode
4304:Bibcode
4227:Bibcode
4169:Bibcode
3533:is the
3501:is the
2882:baryons
2862:⁄
2838:⁄
2746:
2744:
2732:
2726:
2724:
2712:
2631:
2619:
2579:
2567:
2557:
2545:
2541:
2529:
2525:
2513:
2509:
2497:
2485:
2473:
2446:
2434:
2333:
2321:
2147:
2135:
2010:neutron
1991:History
1958:yields
1648:
1636:
1599:
1587:
1549:topness
1437:
1425:
1404:
1392:
1262:of the
1194:Hadrons
1087:
1075:
1071:
1059:
1048:
1036:
703:Isobars
502:
490:
486:
474:
429:neutron
397:couples
378:baryons
360:) is a
352:isospin
94:′
79:Topness
45:Isospin
23:Flavour
4606:Quarks
4539:
4513:
4478:
4429:
4406:
4359:
4272:
4245:
4197:
4129:
4101:
4054:
3852:quarks
3473:Here,
2910:quarks
2878:mesons
2780:photon
2701:Δ
2683:Δ
2665:Δ
2647:Δ
2600:Δ
2399:Δ
2381:Δ
2363:Δ
2345:Δ
2305:Λ
2280:Σ
2262:Σ
2244:Σ
2095:π
2077:π
2059:π
2006:proton
1613:mesons
1577:Mesons
1573:Baryon
1439:
1299:vector
1271:states
1260:action
1235:Λ
1217:Σ
1206:baryon
863:
860:
857:
854:
425:proton
409:quarks
382:mesons
4243:S2CID
4195:S2CID
4155:(PDF)
3625:pions
2906:SU(3)
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