2019:) or beauty, and a light anti-quark (either up, down or strange), can be viewed as systems in which the light quark is "tethered" by the gluonic force to the fixed heavy quark, like a ball tethered to a pole. These systems give us a view of the chiral symmetry breaking in its simplest form, that of a single light-quark state.
77:, which is a solvable theory of composite bosons that exhibits dynamical spontaneous chiral symmetry when a 4-fermion coupling constant becomes sufficiently large. Nambu was awarded the 2008 Nobel prize in physics "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics".
100:
Massless fermions in 4 dimensions are described by either left or right-handed spinors that each have 2 complex components. These have spin either aligned (right-handed chirality), or counter-aligned (left-handed chirality), with their momenta. In this case the chirality is a conserved quantum number
924:
271:
In QCD, the gauge theory of strong interactions, the lowest mass quarks are nearly massless and an approximate chiral symmetry is present. In this case the left- and right-handed quarks are interchangeable in bound states of mesons and baryons, so an exact chiral symmetry of the quarks would imply
562:
symmetry. Under spontaneous symmetry breaking, the chiral symmetry is spontaneously broken to the "diagonal flavor SU(3) subgroup", generating low mass Nambu–Goldstone bosons. These are identified with the pseudoscalar mesons seen in the spectrum, and form an octet representation of the diagonal
605:, have masses much larger than the scale of the strong interactions, thus they do not display the features of spontaneous chiral symmetry breaking. However bound states consisting of a heavy quark and a light quark (or two heavies and one light) still display a universal behavior, where the
1001:
that defines QCD as a Yang-Mills gauge theory and leads to the gluonic force that binds quarks into baryons and meson. In this article we will not focus on the binding dynamics of QCD where quarks are confined within the baryon and meson particles that are observed in the laboratory (see
1920:
1691:
One of the most spectacular aspects of spontaneous symmetry breaking, in general, is the phenomenon of the Nambu–Goldstone bosons. In QCD these appear as approximately massless particles. corresponding to the eight broken generators of the original
2523:
1110:
146:
A Dirac mass term explicitly breaks the chiral symmetry. In quantum electrodynamics (QED) the electron mass unites left and right handed spinors forming a 4 component Dirac spinor. In the absence of mass and quantum loops, QED would have a
2334:
2990:
1793:, simultaneously. These two types of symmetry breaking typically occur separately, and at different energy scales, and are not predicated on each other. The properties of these pNGB's can be calculated from chiral Lagrangians, using
2006:
1768:
1346:
799:
234:
symmetry that allows a common phase rotation of left and right together, which is the gauge symmetry of electrodynamics. (At the quantum loop level, the chiral symmetry is broken, even for massless electrons, by the
1777:
These states have small masses due to the explicit masses of the underlying quarks and as such are referred to as "pseudo-Nambu-Goldstone bosons" or "pNGB's". pNGB's are a general phenomenon and arise in any
556:
2581:
782:
2234:
which would be zero if the chiral symmetry breaking was turned off. The excited states of non-strange, heavy-light mesons are usually short-lived resonances due to the principal strong decay mode
2651:
2232:
735:
2398:
1392:
1807:
1517:
366:) are much lighter than any of the other particles in the spectrum. The low masses of the pseudoscalar mesons, as compared to the heavier states, is also quite striking. The next heavier
2704:). Bardeen, Eichten and Hill predicted, using the chiral Lagrangian, numerous observable decay modes which have been confirmed by experiments. Similar phenomena should be seen in the
203:
2702:
2616:
999:
1215:
1174:
141:
1473:
1429:
958:
2403:
2165:
2078:
695:
649:
2782:
2119:
2188:
1028:
2237:
101:
of the given fermion, and the left and right handed spinors can be independently phase transformed. More generally they can form multiplets under some symmetry group
2729:
1247:
457:
430:
399:
354:
324:
297:
266:
232:
2857:
1131:
919:{\displaystyle \mathrm {SU} (3)_{\mathsf {L}}\times \mathrm {SU} (3)_{\mathsf {R}}\times \mathrm {U} (1)_{\mathsf {V}}\times \mathrm {U} (1)_{\mathsf {A}}~.}
1933:
1695:
1273:
3449:
2837:
Chiral symmetry breaking in QCD is furthermore intimately associated with quantum effects, arising at the
Feynman diagram loop level, generating the
490:. If we assume the light quarks are ideally massless (and ignore electromagnetic and weak interactions), then the theory has an exact global
2850:
The resulting generic formula for the mass of pseudogoldstone bosons in the presence of an explicit breaking perturbation is often called
272:"parity doubling", and every state should appear in a pair of equal mass particles, called "parity partners". In the notation, (spin), a
466:
of chiral symmetry in the strong interactions. In QCD, the fundamental fermion sector consists of three "flavors" of light mass quarks,
3071:
3227:
3046:
493:
2030:
studied the properties of these systems implementing both the heavy quark symmetry and the chiral symmetries of light quarks in a
3526:
2539:
740:
578:
where the masses of the pseudoscalar mesons are determined by the quark masses, and various quantum effects can be computed in
3116:
Procura, M.; Musch, B.; Wollenweber, T.; Hemmert, T.; Weise, W. (2006). "Nucleon mass: From lattice QCD to the chiral limit".
1542:
account for approximately 99% of the mass of a proton or neutron, and these effects thus account for most of the mass of all
3473:
Bernstein, J.; Gell-Mann, M.; Michel, L. (1960). "On the renormalization of the axial vector coupling constant in β-decay".
1673:. QCD then leads to the baryon bound states, which each contain combinations of three quarks (such as the proton (uud) and
3531:
3521:
2621:
1786:
463:
62:
2197:
2191:
2031:
700:
74:
1915:{\displaystyle ~(\mathrm {SU} (3)_{\mathsf {L}}\times \mathrm {SU} (3)_{\mathsf {R}})/\mathrm {SU} (3)_{\mathsf {V}}~.}
2336:
and are therefore hard to observe. Though the results were approximate, they implied the charm-strange excited mesons
1923:
2339:
1797:, which expands around the exactly symmetric zero-quark mass theory. In particular, the computed mass must be small.
1351:
2653:
within a few percent of the model prediction (also the more recently confirmed heavy quark spin-symmetry partner,
1794:
1790:
1482:
587:
579:
559:
3460:
1479:
which was the original successful classification scheme of the elementary particles including strangeness. The
459:
vector mesons are heavier still, appearing as short-lived resonances far (in mass) from their parity partners.
54:
1677:(udd)). The baryons then acquire masses given, approximately, by the sums of their constituent quark masses.
150:
1476:
2656:
2590:
1003:
963:
356:
91:
42:
1179:
1138:
104:
2518:{\displaystyle ~\mathrm {D_{s}} (0^{+},1^{+})\rightarrow \mathrm {K} +\mathrm {D_{u,d}} (0^{-},1^{-})~,}
1441:
1397:
960:
symmetries, called "flavor-chiral" symmetries, should not be confused with the quark "color" symmetry,
1538:, since no degenerate parity partners of the nucleon appear. Chiral symmetry breaking and the quantum
929:
3484:
3456:
3423:
3380:
3312:
3259:
3184:
3135:
3090:
2803:
1779:
1627:
For the light quarks the chiral symmetry breaking condensate can be viewed as inducing the so-called
46:
3358:
3290:
2124:
2037:
2027:
1250:
654:
608:
20:
2734:
3536:
3500:
3439:
3396:
3370:
3354:
3336:
3302:
3286:
3200:
3151:
3125:
2023:
1927:
1267:
1105:{\displaystyle \langle {\bar {q}}_{\mathsf {R}}^{a}\,q_{\mathsf {L}}^{b}\rangle =v\,\delta ^{ab}}
1022:
50:
3038:
3032:
2329:{\displaystyle \mathrm {D} (0^{+},1^{+})\rightarrow \mathrm {\pi } +\mathrm {D} (0^{-},1^{-})~,}
586:
computations, which show that the pseudoscalar masses vary with the quark masses as dictated by
2083:
3328:
3223:
3067:
3042:
2838:
2793:
2170:
1539:
1010:
66:
1926:
is not a group, and consists of the eight axial generators, corresponding to the eight light
3492:
3475:
3431:
3414:
3388:
3320:
3293:(1994). "Chiral dynamics and heavy quark symmetry in a solvable toy field theoretic model".
3267:
3192:
3175:
3170:
3143:
3098:
2985:{\displaystyle ~m_{\mathrm {\pi } }^{2}f_{\mathrm {\pi } }^{2}=-\langle 0|~\,]~|0\rangle ~.}
1575:
26:
2707:
1220:
435:
408:
377:
332:
302:
275:
2825:
2034:
approximation. They showed that chiral symmetry breaking causes the s-wave ground states
1543:
1531:
242:
208:
34:
3244:
792:
If the three light quark masses of QCD are set to zero, we then have a
Lagrangian with a
3488:
3427:
3384:
3316:
3263:
3188:
3139:
3094:
1116:
793:
236:
70:
58:
3515:
3504:
3443:
3204:
3012:
Dynamical Model of
Elementary Particles Based on an Analogy with Superconductivity. I
2001:{\displaystyle \mathrm {SU} (3)_{\mathsf {L}}\times \mathrm {SU} (3)_{\mathsf {R}}~.}
1763:{\displaystyle \mathrm {SU} (3)_{\mathsf {L}}\times \mathrm {SU} (3)_{\mathsf {R}}~.}
1341:{\displaystyle ~\mathrm {SU} (3)_{\mathsf {L}}\times \mathrm {SU} (3)_{\mathsf {R}}~}
367:
3400:
3155:
3340:
2798:
1686:
598:
483:
371:
38:
69:
in condensed matter physics. The basic idea was introduced to particle physics by
2587:
collaboration, and was seen to be surprisingly narrow, with a mass gap above the
594:
583:
479:
3392:
3147:
1800:
Technically, the spontaneously broken chiral symmetry generators comprise the
1599:
1524:
1520:
1475:
constitutes the original pre-quark idea of Gell-Mann and Ne'eman known as the
1263:
may be viewed as the measure of the strength of the chiral symmetry breaking.
1018:
95:
3271:
1013:
can form, composed of bilinear operators involving the quantum fields of the
3324:
602:
487:
402:
205:
chiral symmetry, but the Dirac mass of the electron breaks this to a single
3332:
3412:
Gell-Mann, M.; Lévy, M. (1960). "The axial vector current in beta decay".
1581:
1559:
268:
gauge symmetry is preserved, which is essential for consistency of QED.)
3130:
2400:
could be abnormally narrow (long-lived) since the principal decay mode,
3496:
3435:
3375:
3307:
3196:
2016:
1674:
1555:
1551:
1535:
1433:
53:, and it also occurs through the Brout-Englert-Higgs mechanism in the
3102:
1563:
1547:
37:
associated with massless fermions. This is usually associated with a
2584:
1801:
1771:
1438:
which acts upon the up and down quarks). The unbroken subgroup of
1014:
567:
359:
2526:
363:
784:) due to the light quark chiral symmetry breaking (see below).
329:
Experimentally, however, it is observed that the masses of the
574:
break the chiral symmetry as well. This can be described by a
3173:; Lévy, M. (1960). "The axial vector current in beta decay".
566:
Beyond the idealization of massless quarks, the actual small
551:{\displaystyle SU(3)_{\mathsf {L}}\times SU(3)_{\mathsf {R}}}
299:
meson would therefore have the same mass as a parity partner
33:
generally refers to the dynamical spontaneous breaking of a
3081:
Wilczek, F. (1999). "Mass without mass I: Most of matter".
1112:
driven by quantum loop effects of quarks and gluons, with
2576:{\displaystyle \;\mathrm {D} _{\mathrm {s} }^{*}(2317)\;}
777:{\displaystyle \;\mathrm {D} _{\mathrm {s} }^{*}(2317)\;}
2121:) to be split from p-wave parity partner excited states
1519:
symmetry is anomalous, broken by gluon effects known as
590:, (effectively as the square-root of the quark masses).
3026:
3024:
3245:"Behavior of Current Divergences under SU_{3}×SU_{3}"
2860:
2737:
2710:
2659:
2624:
2593:
2542:
2406:
2342:
2240:
2200:
2173:
2127:
2086:
2040:
1936:
1810:
1698:
1620:
masses only contribute a total of about 9.4 MeV
1485:
1444:
1400:
1354:
1276:
1223:
1182:
1141:
1119:
1031:
966:
932:
802:
743:
703:
657:
611:
496:
438:
411:
380:
335:
305:
278:
245:
211:
153:
107:
2646:{\displaystyle \;\Delta M\approx 348{\text{ MeV ,}}}
1266:
The quark condensate is induced by non-perturbative
3361:(2003). "Chiral multiplets of heavy-light mesons".
2227:{\displaystyle ~\Delta M\approx 338{\text{ MeV,}}~}
730:{\displaystyle ~\Delta M\approx 348{\text{ MeV,}}~}
462:This is a primary consequence of the phenomenon of
2984:
2776:
2723:
2696:
2645:
2610:
2575:
2517:
2392:
2328:
2226:
2182:
2159:
2113:
2072:
2000:
1914:
1762:
1511:
1467:
1423:
1386:
1340:
1241:
1209:
1168:
1135:The condensate is not invariant under independent
1125:
1104:
993:
952:
918:
776:
729:
689:
643:
550:
478: , as well as three flavors of heavy quarks,
451:
424:
393:
348:
318:
291:
260:
226:
197:
135:
3218:Donoghue, J.; Golowich, E.; Holstein, B. (1994).
697:parity partners by a universal mass gap of about
2194:gave an approximate estimate of the mass gap of
2015:Mesons containing a heavy quark, such as charm (
1431:the original symmetry of nuclear physics called
2393:{\displaystyle ~\mathrm {D_{s}} (0^{+},1^{+})~}
1387:{\displaystyle ~\mathrm {SU} (3)_{\mathsf {V}}}
3243:Gell-Mann, M.; Oakes, R.; Renner, B. (1968).
1527:is much heavier than the other light mesons.
1512:{\displaystyle \mathrm {U} (1)_{\mathsf {A}}}
8:
2973:
2904:
1530:Chiral symmetry breaking is apparent in the
1079:
1032:
3064:Gauge Theory of Elementary Particle Physics
3031:Peskin, Michael; Schroeder, Daniel (1995).
2525:would be blocked, owing to the mass of the
582:. This can be confirmed more rigorously by
2625:
2607:
2594:
2572:
2543:
773:
744:
3374:
3306:
3129:
2965:
2958:
2943:
2935:
2926:
2921:
2910:
2892:
2886:
2885:
2875:
2869:
2868:
2859:
2736:
2715:
2709:
2679:
2672:
2664:
2658:
2638:
2623:
2600:
2595:
2592:
2557:
2551:
2550:
2545:
2541:
2500:
2487:
2467:
2462:
2454:
2442:
2429:
2415:
2410:
2405:
2378:
2365:
2351:
2346:
2341:
2311:
2298:
2286:
2278:
2266:
2253:
2241:
2239:
2216:
2199:
2172:
2148:
2135:
2126:
2090:
2085:
2061:
2048:
2039:
1985:
1984:
1966:
1956:
1955:
1937:
1935:
1899:
1898:
1880:
1875:
1865:
1864:
1846:
1836:
1835:
1817:
1809:
1747:
1746:
1728:
1718:
1717:
1699:
1697:
1502:
1501:
1486:
1484:
1448:
1443:
1404:
1399:
1377:
1376:
1358:
1353:
1328:
1327:
1309:
1299:
1298:
1280:
1275:
1222:
1217:rotations, but is invariant under common
1200:
1199:
1181:
1159:
1158:
1140:
1118:
1093:
1088:
1073:
1067:
1066:
1061:
1055:
1049:
1048:
1037:
1036:
1030:
985:
967:
965:
933:
931:
903:
902:
887:
877:
876:
861:
851:
850:
832:
822:
821:
803:
801:
758:
752:
751:
746:
742:
719:
702:
678:
665:
656:
632:
619:
610:
541:
540:
514:
513:
495:
443:
437:
416:
410:
385:
379:
340:
334:
310:
304:
283:
277:
244:
210:
189:
167:
152:
131:
125:
112:
106:
3034:An Introduction to Quantum Field Theory
3003:
2815:
198:{\displaystyle U(1)_{L}\times U(1)_{R}}
1986:
1957:
1900:
1866:
1837:
1748:
1719:
1554:, which form the nuclei of atoms, are
1503:
1378:
1329:
1300:
1201:
1160:
1068:
1050:
904:
878:
852:
823:
542:
515:
3062:Cheng, Ta-Pei; Li, Ling-Fong (1984).
3010:Y. Nambu and G. Jona-Lasinio (1961),
1348:down to the diagonal vector subgroup
7:
2697:{\displaystyle D_{s1^{+}}^{*}(2460)}
2611:{\displaystyle \;\mathrm {D_{s}} \;}
994:{\displaystyle \mathrm {SU} (3)_{c}}
1210:{\displaystyle SU(3)_{\mathsf {R}}}
1169:{\displaystyle SU(3)_{\mathsf {L}}}
136:{\displaystyle G_{L}\times G_{R}{}}
2626:
2601:
2597:
2552:
2546:
2474:
2468:
2464:
2455:
2416:
2412:
2352:
2348:
2287:
2242:
2204:
2174:
1970:
1967:
1941:
1938:
1884:
1881:
1850:
1847:
1821:
1818:
1732:
1729:
1703:
1700:
1631:. Hence, the light up quark, with
1487:
1452:
1449:
1408:
1405:
1362:
1359:
1313:
1310:
1284:
1281:
971:
968:
937:
934:
888:
862:
836:
833:
807:
804:
753:
747:
707:
61:. This phenomenon is analogous to
14:
1468:{\displaystyle ~\mathrm {SU} (3)}
1424:{\displaystyle ~\mathrm {SU} (2)}
651:ground states are split from the
953:{\displaystyle \mathrm {SU} (3)}
788:Light Quarks and Mass Generation
737:(confirmed experimenally by the
570:masses (and electroweak forces)
1770:They include eight mesons, the
1394:; (this contains as a subgroup
3222:. Cambridge University Press.
3220:Dynamics of the Standard Model
2966:
2959:
2955:
2936:
2918:
2911:
2691:
2685:
2569:
2563:
2506:
2480:
2451:
2448:
2422:
2384:
2358:
2317:
2291:
2275:
2272:
2246:
2154:
2128:
2067:
2041:
1981:
1974:
1952:
1945:
1895:
1888:
1872:
1861:
1854:
1832:
1825:
1814:
1743:
1736:
1714:
1707:
1498:
1491:
1462:
1456:
1418:
1412:
1373:
1366:
1324:
1317:
1295:
1288:
1236:
1230:
1196:
1189:
1155:
1148:
1042:
982:
975:
947:
941:
899:
892:
873:
866:
847:
840:
818:
811:
770:
764:
684:
658:
638:
612:
537:
530:
510:
503:
255:
249:
221:
215:
186:
179:
164:
157:
16:Phenomenon in particle physics
1:
2784:heavy-heavy-strange baryons.
2160:{\displaystyle (0^{+},1^{+})}
2073:{\displaystyle (0^{-},1^{-})}
1270:and spontaneously breaks the
690:{\displaystyle (0^{+},1^{+})}
644:{\displaystyle (0^{-},1^{-})}
464:spontaneous symmetry breaking
2777:{\displaystyle ccs,bcs,bbs,}
1025:. This takes the form :
593:The three heavy quarks: the
3037:. Westview Press. pp.
2167:by a universal "mass gap",
1774:, kaons and the eta meson.
1616:. Naively, the light quark
3553:
3393:10.1103/PhysRevD.68.054024
3148:10.1103/PhysRevD.73.114510
1930:, the nondiagonal part of
1795:chiral perturbation theory
1791:explicit symmetry breaking
1684:
588:chiral perturbation theory
580:chiral perturbation theory
89:
18:
2114:{\displaystyle ^{parity}}
3272:10.1103/PhysRev.175.2195
2192:Nambu–Jona-Lasinio model
2183:{\displaystyle \Delta M}
2032:Nambu–Jona-Lasinio model
1661:constituent quark masses
1629:constituent quark masses
75:Nambu–Jona-Lasinio model
73:, in particular, in the
55:electroweak interactions
31:chiral symmetry breaking
3455:. High Energy Physics.
3325:10.1103/PhysRevD.49.409
3527:Quantum chromodynamics
3363:Physical Review D
3295:Physical Review D
2986:
2841:and quark confinement.
2778:
2725:
2698:
2647:
2612:
2583:was discovered by the
2577:
2519:
2394:
2330:
2228:
2184:
2161:
2115:
2074:
2002:
1916:
1764:
1681:Nambu-Goldstone bosons
1624:to the proton's mass.
1513:
1469:
1425:
1388:
1342:
1243:
1211:
1170:
1127:
1106:
1004:Quantum chromodynamics
995:
954:
920:
778:
731:
691:
645:
552:
453:
426:
395:
350:
320:
293:
262:
228:
199:
137:
92:Quantum chromodynamics
86:Quantum chromodynamics
43:quantum chromodynamics
2987:
2779:
2726:
2724:{\displaystyle B_{s}}
2699:
2648:
2613:
2578:
2520:
2395:
2331:
2229:
2185:
2162:
2116:
2075:
2003:
1917:
1765:
1514:
1470:
1426:
1389:
1343:
1244:
1242:{\displaystyle SU(3)}
1212:
1171:
1128:
1107:
996:
955:
921:
779:
732:
692:
646:
553:
454:
452:{\displaystyle 1^{+}}
427:
425:{\displaystyle 0^{+}}
396:
394:{\displaystyle 1^{-}}
351:
349:{\displaystyle 0^{-}}
321:
319:{\displaystyle 0^{-}}
294:
292:{\displaystyle 0^{+}}
263:
229:
200:
138:
3532:Mathematical physics
3522:Quantum field theory
3457:Princeton University
2858:
2804:Top Quark Condensate
2735:
2708:
2657:
2622:
2591:
2540:
2404:
2340:
2238:
2198:
2171:
2125:
2084:
2038:
1934:
1808:
1780:quantum field theory
1696:
1645:and down quark with
1562:). For example, the
1483:
1442:
1398:
1352:
1274:
1221:
1180:
1139:
1133:≈ −(250 MeV)³ .
1117:
1029:
964:
930:
800:
741:
701:
655:
609:
563:SU(3) flavor group.
494:
436:
409:
378:
333:
303:
276:
261:{\displaystyle U(1)}
243:
227:{\displaystyle U(1)}
209:
151:
105:
47:quantum field theory
3489:1960NCim...16..560B
3428:1960NCim...16..705G
3385:2003PhRvD..68e4024B
3317:1994PhRvD..49..409B
3264:1968PhRv..175.2195G
3189:1960NCim...16..705G
3140:2006PhRvD..73k4510P
3095:1999PhT....52k..11W
2897:
2880:
2684:
2562:
2028:Christopher T. Hill
1928:pseudoscalar mesons
1525:corresponding meson
1268:strong interactions
1251:pion decay constant
1078:
1060:
763:
432:scalars mesons and
21:Chirality (physics)
3497:10.1007/BF02731920
3436:10.1007/BF02859738
3357:; Eichten, Estia;
3197:10.1007/BF02859738
2982:
2881:
2864:
2774:
2721:
2694:
2660:
2643:
2608:
2573:
2544:
2515:
2390:
2326:
2224:
2180:
2157:
2111:
2070:
2024:William A. Bardeen
2011:Heavy-light mesons
1998:
1912:
1760:
1509:
1465:
1421:
1384:
1338:
1239:
1207:
1166:
1123:
1102:
1062:
1035:
1023:fermion condensate
991:
950:
916:
774:
745:
727:
687:
641:
548:
449:
422:
391:
346:
316:
289:
258:
224:
195:
133:
51:strong interaction
3118:Physical Review D
2978:
2964:
2917:
2863:
2839:conformal anomaly
2794:Conformal anomaly
2641:
2511:
2409:
2389:
2345:
2322:
2223:
2219:
2203:
1994:
1908:
1813:
1756:
1540:conformal anomaly
1447:
1403:
1357:
1337:
1279:
1126:{\displaystyle v}
1045:
1011:vacuum condensate
912:
726:
722:
706:
576:chiral Lagrangian
67:superconductivity
3544:
3508:
3476:Il Nuovo Cimento
3467:
3465:
3459:. Archived from
3454:
3447:
3415:Il Nuovo Cimento
3405:
3404:
3378:
3351:
3345:
3344:
3310:
3283:
3277:
3275:
3249:
3240:
3234:
3233:
3215:
3209:
3208:
3176:Il Nuovo Cimento
3167:
3161:
3159:
3133:
3113:
3107:
3106:
3103:10.1063/1.882879
3077:
3059:
3053:
3052:
3028:
3019:
3008:
2992:
2991:
2989:
2988:
2983:
2976:
2969:
2962:
2948:
2947:
2931:
2930:
2915:
2914:
2896:
2891:
2890:
2879:
2874:
2873:
2861:
2852:Dashen's formula
2848:
2842:
2835:
2829:
2820:
2783:
2781:
2780:
2775:
2730:
2728:
2727:
2722:
2720:
2719:
2703:
2701:
2700:
2695:
2683:
2678:
2677:
2676:
2652:
2650:
2649:
2644:
2642:
2639:
2617:
2615:
2614:
2609:
2606:
2605:
2604:
2582:
2580:
2579:
2574:
2561:
2556:
2555:
2549:
2532:
2524:
2522:
2521:
2516:
2509:
2505:
2504:
2492:
2491:
2479:
2478:
2477:
2458:
2447:
2446:
2434:
2433:
2421:
2420:
2419:
2407:
2399:
2397:
2396:
2391:
2387:
2383:
2382:
2370:
2369:
2357:
2356:
2355:
2343:
2335:
2333:
2332:
2327:
2320:
2316:
2315:
2303:
2302:
2290:
2282:
2271:
2270:
2258:
2257:
2245:
2233:
2231:
2230:
2225:
2221:
2220:
2217:
2201:
2189:
2187:
2186:
2181:
2166:
2164:
2163:
2158:
2153:
2152:
2140:
2139:
2120:
2118:
2117:
2112:
2110:
2109:
2079:
2077:
2076:
2071:
2066:
2065:
2053:
2052:
2007:
2005:
2004:
1999:
1992:
1991:
1990:
1989:
1973:
1962:
1961:
1960:
1944:
1921:
1919:
1918:
1913:
1906:
1905:
1904:
1903:
1887:
1879:
1871:
1870:
1869:
1853:
1842:
1841:
1840:
1824:
1811:
1769:
1767:
1766:
1761:
1754:
1753:
1752:
1751:
1735:
1724:
1723:
1722:
1706:
1672:
1667:
1658:
1657:≈ 4.8 MeV ,
1653:
1644:
1643:≈ 2.3 MeV ,
1639:
1623:
1615:
1610:
1597:
1596:≈ 2.3 MeV ,
1592:
1579:
1570:
1518:
1516:
1515:
1510:
1508:
1507:
1506:
1490:
1474:
1472:
1471:
1466:
1455:
1445:
1430:
1428:
1427:
1422:
1411:
1401:
1393:
1391:
1390:
1385:
1383:
1382:
1381:
1365:
1355:
1347:
1345:
1344:
1339:
1335:
1334:
1333:
1332:
1316:
1305:
1304:
1303:
1287:
1277:
1262:
1260:
1248:
1246:
1245:
1240:
1216:
1214:
1213:
1208:
1206:
1205:
1204:
1175:
1173:
1172:
1167:
1165:
1164:
1163:
1134:
1132:
1130:
1129:
1124:
1111:
1109:
1108:
1103:
1101:
1100:
1077:
1072:
1071:
1059:
1054:
1053:
1047:
1046:
1038:
1000:
998:
997:
992:
990:
989:
974:
959:
957:
956:
951:
940:
926:Note that these
925:
923:
922:
917:
910:
909:
908:
907:
891:
883:
882:
881:
865:
857:
856:
855:
839:
828:
827:
826:
810:
783:
781:
780:
775:
762:
757:
756:
750:
736:
734:
733:
728:
724:
723:
720:
704:
696:
694:
693:
688:
683:
682:
670:
669:
650:
648:
647:
642:
637:
636:
624:
623:
557:
555:
554:
549:
547:
546:
545:
520:
519:
518:
477:
473:
469:
458:
456:
455:
450:
448:
447:
431:
429:
428:
423:
421:
420:
400:
398:
397:
392:
390:
389:
355:
353:
352:
347:
345:
344:
325:
323:
322:
317:
315:
314:
298:
296:
295:
290:
288:
287:
267:
265:
264:
259:
233:
231:
230:
225:
204:
202:
201:
196:
194:
193:
172:
171:
142:
140:
139:
134:
132:
130:
129:
117:
116:
27:particle physics
3552:
3551:
3547:
3546:
3545:
3543:
3542:
3541:
3512:
3511:
3472:
3463:
3452:
3448:
3411:
3408:
3353:
3352:
3348:
3285:
3284:
3280:
3252:Physical Review
3247:
3242:
3241:
3237:
3230:
3217:
3216:
3212:
3169:
3168:
3164:
3131:hep-lat/0603001
3115:
3114:
3110:
3080:
3079:
3074:
3061:
3060:
3056:
3049:
3030:
3029:
3022:
3009:
3005:
3001:
2996:
2995:
2939:
2922:
2856:
2855:
2849:
2845:
2836:
2832:
2826:Current algebra
2821:
2817:
2812:
2790:
2733:
2732:
2711:
2706:
2705:
2668:
2655:
2654:
2620:
2619:
2596:
2589:
2588:
2538:
2537:
2530:
2496:
2483:
2463:
2438:
2425:
2411:
2402:
2401:
2374:
2361:
2347:
2338:
2337:
2307:
2294:
2262:
2249:
2236:
2235:
2196:
2195:
2169:
2168:
2144:
2131:
2123:
2122:
2087:
2082:
2081:
2057:
2044:
2036:
2035:
2013:
1980:
1951:
1932:
1931:
1894:
1860:
1831:
1806:
1805:
1742:
1713:
1694:
1693:
1689:
1683:
1670:
1665:
1664:
1656:
1651:
1650:
1642:
1637:
1636:
1621:
1613:
1608:
1607:
1595:
1590:
1589:
1573:
1568:
1567:
1532:mass generation
1497:
1481:
1480:
1477:"Eightfold Way"
1440:
1439:
1396:
1395:
1372:
1350:
1349:
1323:
1294:
1272:
1271:
1261:≈ 93 MeV ,
1259:
1255:
1254:
1249:rotations. The
1219:
1218:
1195:
1178:
1177:
1154:
1137:
1136:
1115:
1114:
1113:
1089:
1027:
1026:
981:
962:
961:
928:
927:
898:
872:
846:
817:
798:
797:
790:
739:
738:
699:
698:
674:
661:
653:
652:
628:
615:
607:
606:
536:
509:
492:
491:
475:
471:
467:
439:
434:
433:
412:
407:
406:
381:
376:
375:
336:
331:
330:
306:
301:
300:
279:
274:
273:
241:
240:
207:
206:
185:
163:
149:
148:
121:
108:
103:
102:
98:
90:Main articles:
88:
83:
35:chiral symmetry
23:
17:
12:
11:
5:
3550:
3548:
3540:
3539:
3534:
3529:
3524:
3514:
3513:
3510:
3509:
3483:(3): 560–568.
3469:
3468:
3466:on 2016-03-06.
3422:(4): 705–726.
3407:
3406:
3376:hep-ph/0305049
3346:
3308:hep-ph/9304265
3301:(1): 409–425.
3278:
3235:
3228:
3210:
3183:(4): 705–726.
3162:
3124:(11): 114510.
3108:
3073:978-0198519614
3072:
3066:. Oxford U.P.
3054:
3047:
3020:
3002:
3000:
2997:
2994:
2993:
2981:
2975:
2972:
2968:
2961:
2957:
2954:
2951:
2946:
2942:
2938:
2934:
2929:
2925:
2920:
2913:
2909:
2906:
2903:
2900:
2895:
2889:
2884:
2878:
2872:
2867:
2843:
2830:
2814:
2813:
2811:
2808:
2807:
2806:
2801:
2796:
2789:
2786:
2773:
2770:
2767:
2764:
2761:
2758:
2755:
2752:
2749:
2746:
2743:
2740:
2718:
2714:
2693:
2690:
2687:
2682:
2675:
2671:
2667:
2663:
2637:
2634:
2631:
2628:
2603:
2599:
2571:
2568:
2565:
2560:
2554:
2548:
2514:
2508:
2503:
2499:
2495:
2490:
2486:
2482:
2476:
2473:
2470:
2466:
2461:
2457:
2453:
2450:
2445:
2441:
2437:
2432:
2428:
2424:
2418:
2414:
2386:
2381:
2377:
2373:
2368:
2364:
2360:
2354:
2350:
2325:
2319:
2314:
2310:
2306:
2301:
2297:
2293:
2289:
2285:
2281:
2277:
2274:
2269:
2265:
2261:
2256:
2252:
2248:
2244:
2215:
2212:
2209:
2206:
2179:
2176:
2156:
2151:
2147:
2143:
2138:
2134:
2130:
2108:
2105:
2102:
2099:
2096:
2093:
2089:
2069:
2064:
2060:
2056:
2051:
2047:
2043:
2012:
2009:
1997:
1988:
1983:
1979:
1976:
1972:
1969:
1965:
1959:
1954:
1950:
1947:
1943:
1940:
1911:
1902:
1897:
1893:
1890:
1886:
1883:
1878:
1874:
1868:
1863:
1859:
1856:
1852:
1849:
1845:
1839:
1834:
1830:
1827:
1823:
1820:
1816:
1759:
1750:
1745:
1741:
1738:
1734:
1731:
1727:
1721:
1716:
1712:
1709:
1705:
1702:
1685:Main article:
1682:
1679:
1671:≈ 300 MeV
1668:
1654:
1640:
1614:≈ 4.8 MeV
1611:
1593:
1571:
1544:visible matter
1505:
1500:
1496:
1493:
1489:
1464:
1461:
1458:
1454:
1451:
1420:
1417:
1414:
1410:
1407:
1380:
1375:
1371:
1368:
1364:
1361:
1331:
1326:
1322:
1319:
1315:
1312:
1308:
1302:
1297:
1293:
1290:
1286:
1283:
1257:
1238:
1235:
1232:
1229:
1226:
1203:
1198:
1194:
1191:
1188:
1185:
1162:
1157:
1153:
1150:
1147:
1144:
1122:
1099:
1096:
1092:
1087:
1084:
1081:
1076:
1070:
1065:
1058:
1052:
1044:
1041:
1034:
988:
984:
980:
977:
973:
970:
949:
946:
943:
939:
936:
915:
906:
901:
897:
894:
890:
886:
880:
875:
871:
868:
864:
860:
854:
849:
845:
842:
838:
835:
831:
825:
820:
816:
813:
809:
806:
794:symmetry group
789:
786:
772:
769:
766:
761:
755:
749:
718:
715:
712:
709:
686:
681:
677:
673:
668:
664:
660:
640:
635:
631:
627:
622:
618:
614:
544:
539:
535:
532:
529:
526:
523:
517:
512:
508:
505:
502:
499:
446:
442:
419:
415:
388:
384:
343:
339:
313:
309:
286:
282:
257:
254:
251:
248:
237:chiral anomaly
223:
220:
217:
214:
192:
188:
184:
181:
178:
175:
170:
166:
162:
159:
156:
128:
124:
120:
115:
111:
87:
84:
82:
79:
71:Yoichiro Nambu
59:standard model
19:Main article:
15:
13:
10:
9:
6:
4:
3:
2:
3549:
3538:
3535:
3533:
3530:
3528:
3525:
3523:
3520:
3519:
3517:
3506:
3502:
3498:
3494:
3490:
3486:
3482:
3478:
3477:
3471:
3470:
3462:
3458:
3451:
3450:"online copy"
3445:
3441:
3437:
3433:
3429:
3425:
3421:
3417:
3416:
3410:
3409:
3402:
3398:
3394:
3390:
3386:
3382:
3377:
3372:
3369:(5): 054024.
3368:
3364:
3360:
3356:
3355:Bardeen, W.A.
3350:
3347:
3342:
3338:
3334:
3330:
3326:
3322:
3318:
3314:
3309:
3304:
3300:
3296:
3292:
3288:
3287:Bardeen, W.A.
3282:
3279:
3273:
3269:
3265:
3261:
3257:
3253:
3246:
3239:
3236:
3231:
3229:9780521476522
3225:
3221:
3214:
3211:
3206:
3202:
3198:
3194:
3190:
3186:
3182:
3178:
3177:
3172:
3171:Gell-Mann, M.
3166:
3163:
3157:
3153:
3149:
3145:
3141:
3137:
3132:
3127:
3123:
3119:
3112:
3109:
3104:
3100:
3096:
3092:
3089:(11): 11–13.
3088:
3084:
3083:Physics Today
3075:
3069:
3065:
3058:
3055:
3050:
3048:0-201-50397-2
3044:
3040:
3036:
3035:
3027:
3025:
3021:
3017:
3014:, Phys. Rev.
3013:
3007:
3004:
2998:
2979:
2970:
2952:
2949:
2944:
2940:
2932:
2927:
2923:
2907:
2901:
2898:
2893:
2887:
2882:
2876:
2870:
2865:
2853:
2847:
2844:
2840:
2834:
2831:
2827:
2824:
2819:
2816:
2809:
2805:
2802:
2800:
2797:
2795:
2792:
2791:
2787:
2785:
2771:
2768:
2765:
2762:
2759:
2756:
2753:
2750:
2747:
2744:
2741:
2738:
2716:
2712:
2688:
2680:
2673:
2669:
2665:
2661:
2635:
2632:
2629:
2586:
2566:
2558:
2534:
2528:
2512:
2501:
2497:
2493:
2488:
2484:
2471:
2459:
2443:
2439:
2435:
2430:
2426:
2379:
2375:
2371:
2366:
2362:
2323:
2312:
2308:
2304:
2299:
2295:
2283:
2279:
2267:
2263:
2259:
2254:
2250:
2213:
2210:
2207:
2193:
2177:
2149:
2145:
2141:
2136:
2132:
2106:
2103:
2100:
2097:
2094:
2091:
2088:
2062:
2058:
2054:
2049:
2045:
2033:
2029:
2025:
2020:
2018:
2010:
2008:
1995:
1977:
1963:
1948:
1929:
1925:
1909:
1891:
1876:
1857:
1843:
1828:
1803:
1798:
1796:
1792:
1788:
1785:
1781:
1775:
1773:
1757:
1739:
1725:
1710:
1688:
1680:
1678:
1676:
1662:
1648:
1634:
1630:
1625:
1619:
1605:
1601:
1587:
1583:
1580:contains two
1577:
1565:
1561:
1557:
1553:
1549:
1545:
1541:
1537:
1533:
1528:
1526:
1522:
1494:
1478:
1459:
1437:
1435:
1415:
1369:
1320:
1306:
1291:
1269:
1264:
1252:
1233:
1227:
1224:
1192:
1186:
1183:
1151:
1145:
1142:
1120:
1097:
1094:
1090:
1085:
1082:
1074:
1063:
1056:
1039:
1024:
1021:, known as a
1020:
1016:
1012:
1007:
1005:
986:
978:
944:
913:
895:
884:
869:
858:
843:
829:
814:
795:
787:
785:
767:
759:
716:
713:
710:
679:
675:
671:
666:
662:
633:
629:
625:
620:
616:
604:
600:
596:
591:
589:
585:
581:
577:
573:
569:
564:
561:
533:
527:
524:
521:
506:
500:
497:
489:
485:
481:
465:
460:
444:
440:
417:
413:
404:
386:
382:
373:
372:vector mesons
369:
365:
362:(such as the
361:
358:
341:
337:
327:
311:
307:
284:
280:
269:
252:
246:
238:
218:
212:
190:
182:
176:
173:
168:
160:
154:
144:
126:
122:
118:
113:
109:
97:
93:
85:
80:
78:
76:
72:
68:
64:
63:magnetization
60:
56:
52:
48:
44:
40:
36:
32:
28:
22:
3480:
3474:
3461:the original
3419:
3413:
3366:
3362:
3349:
3298:
3294:
3281:
3255:
3251:
3238:
3219:
3213:
3180:
3174:
3165:
3121:
3117:
3111:
3086:
3082:
3063:
3057:
3033:
3015:
3011:
3006:
2851:
2846:
2833:
2822:
2818:
2799:Little Higgs
2731:mesons and
2536:In 2003 the
2535:
2021:
2014:
1799:
1783:
1776:
1690:
1687:Chiral model
1660:
1659:now acquire
1646:
1632:
1628:
1626:
1617:
1603:
1585:
1584:, each with
1529:
1432:
1265:
1008:
791:
599:bottom quark
592:
575:
571:
565:
484:bottom quark
461:
357:pseudoscalar
328:
270:
145:
99:
39:gauge theory
30:
24:
3258:(5): 2195.
2640: MeV ,
1787:spontaneous
1574:≈ 938
595:charm quark
584:lattice QCD
480:charm quark
3516:Categories
3359:Hill, C.T.
3291:Hill, C.T.
2999:References
2218: MeV,
1600:down quark
1566:, of mass
1521:instantons
1019:QCD vacuum
721: MeV,
572:explicitly
405:, and the
401:, such as
239:, but the
96:QCD vacuum
3537:Asymmetry
3505:119424935
3444:122945049
3205:122945049
3018:, 345-358
2974:⟩
2905:⟨
2902:−
2888:π
2871:π
2810:Footnotes
2681:∗
2633:≈
2627:Δ
2559:∗
2502:−
2489:−
2452:→
2313:−
2300:−
2280:π
2276:→
2211:≈
2205:Δ
2175:Δ
2063:−
2050:−
1964:×
1844:×
1726:×
1663:of about
1582:up quarks
1558:, called
1307:×
1091:δ
1080:⟩
1043:¯
1033:⟨
1009:A static
885:×
859:×
830:×
760:∗
714:≈
708:Δ
634:−
621:−
603:top quark
522:×
488:top quark
403:rho meson
387:−
342:−
312:−
174:×
119:×
3401:10472717
3333:10016779
3156:11301181
2788:See also
2022:In 1994
1647:explicit
1633:explicit
1618:explicit
1604:explicit
1598:and one
1586:explicit
1560:nucleons
1536:nucleons
1523:and the
370:are the
81:Overview
41:such as
3485:Bibcode
3424:Bibcode
3381:Bibcode
3341:1763576
3313:Bibcode
3260:Bibcode
3185:Bibcode
3136:Bibcode
3091:Bibcode
2854:, here
2017:D meson
1675:neutron
1622:(= 1%)
1556:baryons
1552:neutron
1434:isospin
1017:in the
796: :
558:chiral
326:meson.
57:of the
49:of the
3503:
3442:
3399:
3339:
3331:
3226:
3203:
3154:
3070:
3045:
2977:
2963:
2916:
2862:
2510:
2408:
2388:
2344:
2321:
2222:
2202:
2190:. The
1993:
1907:
1812:
1804:space
1755:
1564:proton
1548:proton
1446:
1402:
1356:
1336:
1278:
1015:quarks
911:
725:
705:
601:, and
560:flavor
486:, and
474:, and
368:states
360:mesons
45:, the
3501:S2CID
3464:(PDF)
3453:(PDF)
3440:S2CID
3397:S2CID
3371:arXiv
3337:S2CID
3303:arXiv
3248:(PDF)
3201:S2CID
3152:S2CID
3126:arXiv
2585:BaBar
2080:(spin
1924:space
1922:This
1802:coset
1782:with
1772:pions
1649:mass
1635:mass
1606:mass
1602:with
1588:mass
1546:(the
568:quark
3329:PMID
3224:ISBN
3068:ISBN
3043:ISBN
2689:2460
2567:2317
2527:kaon
2026:and
1789:and
1784:both
1550:and
768:2317
364:pion
94:and
65:and
3493:doi
3432:doi
3389:doi
3321:doi
3268:doi
3256:175
3193:doi
3144:doi
3099:doi
3039:670
3016:122
2823:See
2636:348
2618:of
2533:).
2214:338
1669:u,d
1576:MeV
1534:of
1176:or
1006:).
717:348
143:.
25:In
3518::
3499:.
3491:.
3481:16
3479:.
3438:.
3430:.
3420:16
3418:.
3395:.
3387:.
3379:.
3367:68
3365:.
3335:.
3327:.
3319:.
3311:.
3299:49
3297:.
3289:;
3266:.
3254:.
3250:.
3199:.
3191:.
3181:16
3179:.
3150:.
3142:.
3134:.
3122:73
3120:.
3097:.
3087:52
3085:.
3041:.
3023:^
1253:,
597:,
482:,
470:,
374:,
29:,
3507:.
3495::
3487::
3446:.
3434::
3426::
3403:.
3391::
3383::
3373::
3343:.
3323::
3315::
3305::
3276:.
3274:.
3270::
3262::
3232:.
3207:.
3195::
3187::
3160:.
3158:.
3146::
3138::
3128::
3105:.
3101::
3093::
3078:;
3076:.
3051:.
2980:.
2971:0
2967:|
2960:]
2956:]
2953:H
2950:,
2945:5
2941:Q
2937:[
2933:,
2928:5
2924:Q
2919:[
2912:|
2908:0
2899:=
2894:2
2883:f
2877:2
2866:m
2828:.
2772:,
2769:s
2766:b
2763:b
2760:,
2757:s
2754:c
2751:b
2748:,
2745:s
2742:c
2739:c
2717:s
2713:B
2692:)
2686:(
2674:+
2670:1
2666:s
2662:D
2630:M
2602:s
2598:D
2570:)
2564:(
2553:s
2547:D
2531:K
2529:(
2513:,
2507:)
2498:1
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2485:0
2481:(
2475:d
2472:,
2469:u
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2460:+
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2423:(
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2380:+
2376:1
2372:,
2367:+
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2359:(
2353:s
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2324:,
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2309:1
2305:,
2296:0
2292:(
2288:D
2284:+
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2268:+
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2255:+
2251:0
2247:(
2243:D
2208:M
2178:M
2155:)
2150:+
2146:1
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2137:+
2133:0
2129:(
2107:y
2104:t
2101:i
2098:r
2095:a
2092:p
2068:)
2059:1
2055:,
2046:0
2042:(
1996:.
1987:R
1982:)
1978:3
1975:(
1971:U
1968:S
1958:L
1953:)
1949:3
1946:(
1942:U
1939:S
1910:.
1901:V
1896:)
1892:3
1889:(
1885:U
1882:S
1877:/
1873:)
1867:R
1862:)
1858:3
1855:(
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1838:L
1833:)
1829:3
1826:(
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1815:(
1758:.
1749:R
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1740:3
1737:(
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1711:3
1708:(
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1666:m
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1499:)
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1492:(
1488:U
1463:)
1460:3
1457:(
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1419:)
1416:2
1413:(
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1367:(
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1318:(
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1301:L
1296:)
1292:3
1289:(
1285:U
1282:S
1258:π
1256:f
1237:)
1234:3
1231:(
1228:U
1225:S
1202:R
1197:)
1193:3
1190:(
1187:U
1184:S
1161:L
1156:)
1152:3
1149:(
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1121:v
1098:b
1095:a
1086:v
1083:=
1075:b
1069:L
1064:q
1057:a
1051:R
1040:q
987:c
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979:3
976:(
972:U
969:S
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942:(
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914:.
905:A
900:)
896:1
893:(
889:U
879:V
874:)
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867:(
863:U
853:R
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841:(
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815:3
812:(
808:U
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771:)
765:(
754:s
748:D
711:M
685:)
680:+
676:1
672:,
667:+
663:0
659:(
639:)
630:1
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617:0
613:(
543:R
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531:(
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504:(
501:U
498:S
476:s
472:d
468:u
445:+
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418:+
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308:0
285:+
281:0
256:)
253:1
250:(
247:U
222:)
219:1
216:(
213:U
191:R
187:)
183:1
180:(
177:U
169:L
165:)
161:1
158:(
155:U
127:R
123:G
114:L
110:G
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