1115:
1251:
59:. The simplest version, "Type 1", extends the Standard Model by assuming two or more additional right-handed neutrino fields inert under the electroweak interaction, and the existence of a very large mass scale. This allows the mass scale to be identifiable with the postulated scale of grand unification.
979:
1535:
1621:
1134:
2099:(1979). "Horizontal gauge symmetry and masses of neutrinos", Proceedings: Workshop on the Unified Theories and the Baryon Number in the Universe: published in KEK Japan, February 13-14, 1979, Conf. Proc. C7902131, p.95- 99.
1856:
325:
235:
141:
1427:
1951:
925:
2000:
663:
495:
1726:
can be formed using these doublet components – only a nonrenormalizable, dimension 5 term is allowed. This is the origin of the pattern and hierarchy of scales of the mass matrix
1110:{\displaystyle {\tfrac {1}{2}}\,B'\,\chi ^{\alpha }\chi _{\alpha }\,,\quad {\frac {1}{2}}\,B\,\eta ^{\alpha }\eta _{\alpha }\,,\quad \mathrm {or} \quad M\,\eta ^{\alpha }\chi _{\alpha }\,,}
1898:
1455:
584:
771:
426:
398:
365:
1654:
1246:{\displaystyle {\frac {1}{2}}\,{\begin{pmatrix}\chi &\eta \end{pmatrix}}{\begin{pmatrix}B'&M\\M&B\end{pmatrix}}{\begin{pmatrix}\chi \\\eta \end{pmatrix}}.}
2231:(1980). Lévy, Maurice; Basdevant, Jean-Louis; Speiser, David; Weyers, Jacques; Gastmans, Raymond; Jacob, Maurice (eds.). "The future of elementary particle physics".
1712:
1680:
871:
835:
1541:
1333:
952:
1785:
607:
548:
1744:
730:
702:
525:
2033:
It is possible to generate two low-mass neutrinos with only one right-handed neutrino, but the resulting mass spectra are generally not viable.
1790:
246:
156:
780:, which is in qualitative accord with experiments—sometimes regarded as supportive evidence for the framework of Grand Unified Theories.
2378:
84:
1357:
1903:
878:
1683:
1956:
615:
2252:
434:
67:
This model produces a light neutrino, for each of the three known neutrino flavors, and a corresponding very heavy
1865:
2168:
1859:
1272:
500:
Thus, if one of the eigenvalues goes up, the other goes down, and vice versa. This is the point of the name "
1530:{\displaystyle \quad v\;\approx \;\mathrm {246\;GeV} ,\qquad \qquad |\langle H\rangle |\;=\;v/{\sqrt {2}}}
36:
is a generic model used to understand the relative sizes of observed neutrino masses, of the order of
553:
743:
403:
370:
337:
1754:
1449:
1437:
74:
The simple mathematical principle behind the seesaw mechanism is the following property of any 2×2
1268:
1633:
1256:
Since the right-handed neutrino spinor is uncharged under all standard model gauge symmetries,
1616:{\displaystyle M_{t}={\mathcal {O}}\left(v/{\sqrt {2}}\right)\;\approx \;\mathrm {174\;GeV} ,}
2352:
1659:
853:
817:
2323:
2284:
2200:
2122:
2071:
1318:
937:
75:
29:
17:
8:
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2327:
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2288:
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2126:
2075:
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589:
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2373:
2268:
1729:
1627:
1344:
970:
715:
687:
510:
2248:
2164:
2083:
1953:
A huge scale has thus induced a dramatically small neutrino mass for the eigenvector
1121:
733:
48:, which are millions of times heavier. The name of the seesaw mechanism was given by
2110:
2331:
2292:
2240:
2208:
2184:
2148:
2130:
2096:
2079:
1719:
963:
801:
49:
21:
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2156:
2052:
1276:
681:
2296:
1715:
1125:
931:
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331:
56:
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2367:
2335:
2152:
2134:
955:
847:
1758:
1723:
1336:
1290:
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844:
797:
776:
709:
37:
1851:{\displaystyle B\approx M_{\mathsf {GUT}}\approx \mathrm {10^{15}~GeV} ,}
1441:
1348:
1309:
812:
677:
429:
2213:
2188:
147:
1279:, like the Dirac masses of the charged leptons. In particular, since
1260:
is a free parameter which can in principle take any arbitrary value.
705:
320:{\displaystyle \lambda _{(-)}={\frac {B-{\sqrt {B^{2}+4M^{2}}}}{2}}.}
230:{\displaystyle \lambda _{(+)}={\frac {B+{\sqrt {B^{2}+4M^{2}}}}{2}},}
804:, and the corresponding charges of the lepton- and neutrino fields.
808:
669:
68:
25:
2275:(1980). "Neutrino mass and spontaneous parity non-conservation".
2010:
1787:
in the unbroken phase, but generate a large, non-vanishing value
136:{\displaystyle A={\begin{pmatrix}0&M\\M&B\end{pmatrix}}.}
1422:{\displaystyle {\mathcal {L}}_{yuk}=y\,\eta L\epsilon H^{*}+...}
2015:
841:
501:
45:
1946:{\displaystyle \lambda _{(-)}\;\approx \;\mathrm {0.01\;eV} .}
954:
be a postulated right-handed neutrino Weyl spinor which is a
920:{\displaystyle L={\begin{pmatrix}\chi \\\ell \end{pmatrix}},}
41:
1656:. It can be chosen smaller consistently, but extreme values
962:– i.e. a neutrino that fails to interact weakly, such as a
1995:{\displaystyle \nu \approx \chi -{\frac {\;M\;}{B}}\eta .}
2261:
773:
then leads to a very small neutrino mass, comparable to
658:{\displaystyle \lambda _{-}\approx -{\frac {M^{2}}{B}}.}
796:
by considering the most general mass matrix allowed by
609:
while the smaller eigenvalue is approximately equal to
2147:
2062:
at a rate of one out of 1 billion muon decays?".
1219:
1178:
1154:
984:
893:
99:
55:
There are several types of models, each extending the
2177:
2045:
1959:
1906:
1868:
1793:
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1137:
982:
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746:
718:
690:
618:
592:
556:
533:
513:
490:{\displaystyle \lambda _{(+)}\;\lambda _{(-)}=-M^{2}}
437:
406:
373:
340:
249:
159:
87:
2314:(1980). "Neutrino masses in SU(2) ⊗ U(1) theories".
2159:(1979). Freedman, D.; van Nieuwenhuizen, P. (eds.).
2303:
2267:
850:; the other part is the left-handed charged lepton
708:and violates lepton number conservation; while the
2163:. Amsterdam, NL: North Holland. pp. 315–321.
1994:
1945:
1892:
1850:
1779:
1738:
1706:
1674:
1648:
1615:
1529:
1421:
1327:
1271:, and can only appear after the symmetry has been
1245:
1109:
946:
919:
865:
829:
765:
724:
696:
657:
601:
578:
542:
519:
489:
420:
392:
359:
319:
229:
135:
2111:"Horizontal symmetry and mass of the $ t$ quark"
2365:
2221:
71:for each flavor, which has yet to be observed.
2309:
1351:, in the conventional standard model fashion,
2189:"Horizontal symmetry and masses of neutrinos"
2141:
1893:{\displaystyle M\approx \mathrm {100\;GeV} }
1499:
1493:
1746:within the "Type 1" seesaw mechanism.
1979:
1975:
1932:
1927:
1923:
1879:
1714:on the other hand, is forbidden, since no
1599:
1594:
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1511:
1507:
1472:
1467:
1463:
454:
2212:
2051:
1387:
1148:
1103:
1082:
1065:
1044:
1040:
1025:
1004:
995:
668:This mechanism serves to explain why the
2183:
2108:
2227:
2366:
1812:
1809:
1806:
1761:may be present, which initially force
934:with neutrino masses omitted, and let
792:arises in a natural manner within the
507:In applying this model to neutrinos,
24:, and, in particular, in theories of
1753:can be motivated in the context of
13:
1936:
1933:
1886:
1883:
1880:
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1606:
1603:
1600:
1560:
1479:
1476:
1473:
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14:
2390:
2379:Physics beyond the Standard Model
2345:
1436:is naturally of the order of the
969:There are now three ways to form
732:are of order of the much smaller
2109:Yanagida, Tsutomu (1979-12-01).
930:as it is present in the minimal
672:masses are so small. The matrix
527:is taken to be much larger than
62:
2193:Progress of Theoretical Physics
1487:
1486:
1459:
1078:
1069:
1029:
579:{\displaystyle \lambda _{(+)},}
52:in a Tokyo conference in 1981.
2102:
2090:
2027:
1918:
1912:
1503:
1489:
766:{\displaystyle \lambda _{(-)}}
758:
752:
740:below. The smaller eigenvalue
568:
562:
466:
460:
449:
443:
421:{\displaystyle \left|M\right|}
393:{\displaystyle \lambda _{(-)}}
385:
379:
360:{\displaystyle \lambda _{(+)}}
352:
346:
261:
255:
171:
165:
1:
2039:
1860:spontaneous symmetry breaking
783:
2084:10.1016/0370-2693(77)90435-X
2021:
1124:, which can be written as a
550:Then the larger eigenvalue,
7:
2004:
1757:. In such models, enlarged
18:theory of grand unification
10:
2395:
2353:"Seesaw Mechanism details"
2297:10.1103/PhysRevLett.44.912
1858:around the scale of their
1649:{\displaystyle y\approx 1}
1269:electroweak gauge symmetry
973:mass terms, giving either
586:is approximately equal to
2245:10.1007/978-1-4684-7197-7
2336:10.1103/PhysRevD.22.2227
2135:10.1103/PhysRevD.20.2986
1450:vacuum expectation value
1438:vacuum expectation value
738:vacuum expectation value
40:, compared to those of
2357:quantumfieldtheory.info
680:for the neutrinos. The
1996:
1947:
1894:
1852:
1781:
1740:
1708:
1676:
1675:{\displaystyle y\gg 1}
1650:
1617:
1531:
1440:of the standard model
1423:
1343:can be generated from
1339:0, the mass parameter
1329:
1247:
1111:
948:
921:
867:
866:{\displaystyle \ell ,}
831:
830:{\displaystyle \chi ,}
800:of the standard model
767:
726:
698:
659:
603:
580:
544:
521:
491:
422:
394:
361:
321:
231:
137:
1997:
1948:
1895:
1853:
1782:
1741:
1709:
1677:
1651:
1626:if the dimensionless
1618:
1532:
1424:
1330:
1328:{\displaystyle \eta }
1248:
1112:
949:
947:{\displaystyle \eta }
922:
868:
832:
768:
727:
704:is comparable to the
699:
660:
604:
581:
545:
522:
492:
423:
395:
362:
322:
232:
138:
1957:
1904:
1866:
1791:
1765:
1730:
1693:
1660:
1634:
1542:
1456:
1358:
1319:
1273:spontaneously broken
1135:
980:
938:
879:
854:
818:
744:
736:, called the VEV or
716:
688:
616:
590:
554:
531:
511:
504:" of the mechanism.
435:
404:
371:
338:
247:
157:
85:
30:neutrino oscillation
2328:1980PhRvD..22.2227S
2289:1980PhRvL..44..912M
2214:10.1143/PTP.64.1103
2205:1980PThPh..64.1103Y
2127:1979PhRvD..20.2986Y
2076:1977PhLB...67..421M
1780:{\displaystyle B=0}
1682:can make the model
1345:Yukawa interactions
676:is essentially the
1992:
1943:
1890:
1862:. So given a mass
1848:
1777:
1749:The large size of
1736:
1707:{\displaystyle B'}
1704:
1672:
1646:
1613:
1527:
1419:
1325:
1243:
1234:
1208:
1167:
1122:complex conjugates
1107:
993:
944:
917:
908:
863:
827:
763:
722:
694:
655:
602:{\displaystyle B,}
599:
576:
543:{\displaystyle M.}
540:
517:
487:
418:
390:
357:
317:
227:
133:
124:
2254:978-1-4684-7199-1
2121:(11): 2986–2988.
2115:Physical Review D
2064:Physics Letters B
1984:
1834:
1755:grand unification
1739:{\displaystyle A}
1583:
1525:
1146:
1038:
992:
971:Lorentz covariant
734:electroweak scale
725:{\displaystyle M}
697:{\displaystyle B}
650:
520:{\displaystyle B}
312:
306:
222:
216:
2386:
2360:
2340:
2339:
2322:(9): 2227–2235.
2307:
2301:
2300:
2265:
2259:
2258:
2233:NATO Sci. Ser. B
2225:
2219:
2218:
2216:
2199:(3): 1103–1105.
2181:
2175:
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2138:
2106:
2100:
2094:
2088:
2087:
2061:
2049:
2034:
2031:
2001:
1999:
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1993:
1985:
1980:
1973:
1952:
1950:
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1783:
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1759:gauge symmetries
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1745:
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1737:
1720:weak hypercharge
1713:
1711:
1710:
1705:
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1681:
1679:
1678:
1673:
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1589:
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1536:
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1528:
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1482:
1435:
1432:This means that
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1334:
1332:
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1267:is forbidden by
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1213:
1212:
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1054:
1053:
1039:
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1024:
1023:
1014:
1013:
1003:
994:
985:
964:sterile neutrino
953:
951:
950:
945:
926:
924:
923:
918:
913:
912:
872:
870:
869:
864:
836:
834:
833:
828:
798:gauge invariance
791:
779:
772:
770:
769:
764:
762:
761:
731:
729:
728:
723:
712:mass components
703:
701:
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608:
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582:
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541:
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524:
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470:
469:
453:
452:
427:
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417:
399:
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388:
366:
364:
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326:
324:
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50:Tsutomu Yanagida
34:seesaw mechanism
22:particle physics
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2310:Schechter, J.;
2308:
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2283:(14): 912–915.
2277:Phys. Rev. Lett
2269:Mohapatra, R.N.
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1628:Yukawa coupling
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1277:Higgs mechanism
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1083:
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819:
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789:
788:The 2×2 matrix
786:
774:
751:
747:
745:
742:
741:
717:
714:
713:
689:
686:
685:
684:mass component
673:
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635:
623:
619:
617:
614:
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591:
588:
587:
561:
557:
555:
552:
551:
532:
529:
528:
512:
509:
508:
481:
477:
459:
455:
442:
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436:
433:
432:
407:
405:
402:
401:
378:
374:
372:
369:
368:
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341:
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271:
269:
254:
250:
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245:
244:
210:
206:
194:
190:
188:
181:
179:
164:
160:
158:
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154:
123:
122:
117:
111:
110:
105:
95:
94:
86:
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5:
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2346:External links
2344:
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2273:Senjanovic, G.
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1799:
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1718:singlet under
1716:renormalizable
1702:
1699:
1689:The parameter
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1668:
1665:
1645:
1642:
1639:
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1263:The parameter
1254:
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1231:
1228:
1227:
1224:
1221:
1220:
1218:
1211:
1205:
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1200:
1197:
1196:
1193:
1190:
1187:
1184:
1180:
1179:
1177:
1170:
1164:
1161:
1159:
1156:
1155:
1153:
1145:
1142:
1126:quadratic form
1118:
1117:
1106:
1100:
1096:
1090:
1086:
1081:
1076:
1073:
1068:
1062:
1058:
1052:
1048:
1043:
1037:
1034:
1028:
1022:
1018:
1012:
1008:
1002:
999:
991:
988:
943:
932:standard model
928:
927:
916:
911:
905:
902:
901:
898:
895:
894:
892:
887:
884:
862:
859:
826:
823:
794:standard model
785:
782:
760:
757:
754:
750:
721:
693:
666:
665:
654:
649:
644:
640:
634:
631:
626:
622:
598:
595:
575:
570:
567:
564:
560:
539:
536:
516:
484:
480:
476:
473:
468:
465:
462:
458:
451:
448:
445:
441:
416:
413:
410:
387:
384:
381:
377:
354:
351:
348:
344:
332:geometric mean
328:
327:
316:
311:
303:
299:
295:
292:
287:
283:
277:
274:
268:
263:
260:
257:
253:
238:
237:
226:
221:
213:
209:
205:
202:
197:
193:
187:
184:
178:
173:
170:
167:
163:
144:
143:
132:
127:
121:
118:
116:
113:
112:
109:
106:
104:
101:
100:
98:
93:
90:
64:
61:
57:Standard Model
9:
6:
4:
3:
2:
2391:
2380:
2377:
2375:
2372:
2371:
2369:
2358:
2354:
2350:
2349:
2337:
2333:
2329:
2325:
2321:
2317:
2313:
2306:
2298:
2294:
2290:
2286:
2282:
2278:
2274:
2270:
2264:
2256:
2250:
2246:
2242:
2238:
2234:
2230:
2229:Glashow, S.L.
2224:
2215:
2210:
2206:
2202:
2198:
2194:
2190:
2186:
2180:
2172:
2166:
2162:
2158:
2154:
2150:
2149:Gell-Mann, M.
2144:
2136:
2132:
2128:
2124:
2120:
2116:
2112:
2105:
2098:
2093:
2085:
2081:
2077:
2073:
2069:
2065:
2060:
2054:
2053:Minkowski, P.
2048:
2044:
2030:
2026:
2017:
2014:
2012:
2009:
2008:
2002:
1989:
1986:
1981:
1976:
1969:
1966:
1963:
1960:
1940:
1929:
1924:
1915:
1908:
1876:
1872:
1869:
1861:
1845:
1827:
1823:
1818:
1801:
1797:
1794:
1774:
1771:
1768:
1760:
1756:
1747:
1733:
1725:
1721:
1717:
1700:
1697:
1687:
1685:
1669:
1666:
1663:
1643:
1640:
1637:
1629:
1610:
1596:
1591:
1586:
1580:
1574:
1570:
1566:
1555:
1550:
1546:
1538:
1522:
1516:
1512:
1508:
1496:
1483:
1469:
1464:
1460:
1451:
1447:
1446:
1445:
1443:
1439:
1416:
1413:
1410:
1407:
1402:
1398:
1394:
1391:
1388:
1384:
1381:
1376:
1373:
1370:
1354:
1353:
1352:
1350:
1346:
1338:
1322:
1311:
1292:
1278:
1274:
1270:
1261:
1240:
1235:
1229:
1222:
1216:
1209:
1203:
1198:
1191:
1185:
1182:
1175:
1168:
1162:
1157:
1151:
1143:
1140:
1131:
1130:
1129:
1127:
1123:
1104:
1098:
1094:
1088:
1084:
1079:
1066:
1060:
1056:
1050:
1046:
1041:
1035:
1032:
1026:
1020:
1016:
1010:
1006:
1000:
997:
989:
986:
976:
975:
974:
972:
967:
965:
961:
957:
941:
933:
914:
909:
903:
896:
890:
885:
882:
875:
874:
873:
860:
857:
849:
846:
843:
840:
824:
821:
814:
810:
805:
803:
799:
795:
781:
778:
755:
748:
739:
735:
719:
711:
707:
691:
683:
679:
671:
652:
647:
642:
638:
632:
629:
624:
620:
612:
611:
610:
596:
593:
573:
565:
558:
537:
534:
514:
505:
503:
498:
482:
478:
474:
471:
463:
456:
446:
439:
431:
414:
411:
408:
382:
375:
349:
342:
333:
314:
309:
301:
297:
293:
290:
285:
281:
275:
272:
266:
258:
251:
243:
242:
241:
224:
219:
211:
207:
203:
200:
195:
191:
185:
182:
176:
168:
161:
153:
152:
151:
149:
130:
125:
119:
114:
107:
102:
96:
91:
88:
81:
80:
79:
77:
72:
70:
63:Type 1 seesaw
60:
58:
53:
51:
47:
43:
39:
35:
31:
27:
23:
19:
2356:
2319:
2315:
2305:
2280:
2276:
2263:
2236:
2232:
2223:
2196:
2192:
2185:Yanagida, T.
2179:
2161:Supergravity
2160:
2143:
2118:
2114:
2104:
2097:Yanagida, T.
2092:
2067:
2063:
2058:
2047:
2029:
1748:
1688:
1630:is of order
1625:
1431:
1337:weak isospin
1291:weak isospin
1262:
1255:
1119:
968:
960:weak isospin
929:
845:weak isospin
837:a part of a
806:
787:
737:
667:
506:
499:
428:, since the
329:
239:
145:
78:of the form
73:
66:
54:
44:and charged
33:
15:
2157:Slansky, R.
1442:Higgs field
1349:Higgs field
1310:Higgs field
839:left-handed
813:Weyl spinor
678:mass matrix
430:determinant
148:eigenvalues
146:It has two
28:masses and
2368:Categories
2170:044485438X
2153:Ramond, P.
2070:(4): 421.
2040:References
1120:and their
811:part of a
784:Background
2374:Neutrinos
2316:Phys. Rev
2312:Valle, J.
2055:(1977). "
2022:Footnotes
1987:η
1970:−
1967:χ
1964:≈
1961:ν
1925:≈
1916:−
1909:λ
1873:≈
1819:≈
1798:≈
1667:≫
1641:≈
1592:≈
1500:⟩
1494:⟨
1465:≈
1403:∗
1395:ϵ
1389:η
1347:with the
1323:η
1308:like the
1230:η
1223:χ
1163:η
1158:χ
1099:α
1095:χ
1089:α
1085:η
1061:α
1057:η
1051:α
1047:η
1021:α
1017:χ
1011:α
1007:χ
942:η
904:ℓ
897:χ
858:ℓ
822:χ
807:Call the
756:−
749:λ
706:GUT scale
633:−
630:≈
625:−
621:λ
559:λ
475:−
464:−
457:λ
440:λ
383:−
376:λ
343:λ
276:−
259:−
252:λ
162:λ
2187:(1980).
2005:See also
1900:one has
1701:′
1186:′
1001:′
809:neutrino
682:Majorana
670:neutrino
69:neutrino
26:neutrino
2324:Bibcode
2285:Bibcode
2239:: 687.
2201:Bibcode
2123:Bibcode
2072:Bibcode
2011:Majoron
1724:isospin
1306:
1294:
956:singlet
848:doublet
775:1
400:equals
46:leptons
16:In the
2251:
2167:
2057:μ → e
2016:Spinor
1833:
1315:, and
958:under
842:lepton
802:action
502:seesaw
76:matrix
42:quarks
32:, the
1452:(VEV)
1275:by a
710:Dirac
2249:ISBN
2165:ISBN
1930:0.01
1722:and
1448:the
1335:has
1289:has
367:and
330:The
240:and
2332:doi
2293:doi
2241:doi
2209:doi
2131:doi
2080:doi
1877:100
1597:174
1470:246
1444:,
334:of
20:of
2370::
2355:.
2330:.
2320:22
2318:.
2291:.
2281:44
2279:.
2271:;
2247:.
2237:61
2235:.
2207:.
2197:64
2195:.
2191:.
2155:;
2151:;
2129:.
2119:20
2117:.
2113:.
2078:.
2068:67
2066:.
1828:15
1824:10
1686:.
1284:∈
1128:,
966:.
777:eV
497:.
150::
38:eV
2359:.
2338:.
2334::
2326::
2299:.
2295::
2287::
2257:.
2243::
2217:.
2211::
2203::
2173:.
2137:.
2133::
2125::
2086:.
2082::
2074::
2059:γ
1990:.
1982:B
1977:M
1941:.
1937:V
1934:e
1919:)
1913:(
1887:V
1884:e
1881:G
1870:M
1846:,
1842:V
1839:e
1836:G
1813:T
1810:U
1807:G
1802:M
1795:B
1775:0
1772:=
1769:B
1751:B
1734:A
1698:B
1670:1
1664:y
1644:1
1638:y
1611:,
1607:V
1604:e
1601:G
1587:)
1581:2
1575:/
1571:v
1567:(
1561:O
1556:=
1551:t
1547:M
1523:2
1517:/
1513:v
1509:=
1504:|
1497:H
1490:|
1484:,
1480:V
1477:e
1474:G
1461:v
1434:M
1417:.
1414:.
1411:.
1408:+
1399:H
1392:L
1385:y
1382:=
1377:k
1374:u
1371:y
1365:L
1341:M
1313:H
1303:2
1300:/
1297:1
1286:L
1282:χ
1265:M
1258:B
1241:.
1236:)
1217:(
1210:)
1204:B
1199:M
1192:M
1183:B
1176:(
1169:)
1152:(
1144:2
1141:1
1105:,
1080:M
1075:r
1072:o
1067:,
1042:B
1036:2
1033:1
1027:,
998:B
990:2
987:1
915:,
910:)
891:(
886:=
883:L
861:,
825:,
790:A
759:)
753:(
720:M
692:B
674:A
653:.
648:B
643:2
639:M
597:,
594:B
574:,
569:)
566:+
563:(
538:.
535:M
515:B
483:2
479:M
472:=
467:)
461:(
450:)
447:+
444:(
415:|
412:M
409:|
386:)
380:(
353:)
350:+
347:(
315:.
310:2
302:2
298:M
294:4
291:+
286:2
282:B
273:B
267:=
262:)
256:(
225:,
220:2
212:2
208:M
204:4
201:+
196:2
192:B
186:+
183:B
177:=
172:)
169:+
166:(
131:.
126:)
120:B
115:M
108:M
103:0
97:(
92:=
89:A
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