1603:
1623:
For the low-energy solar neutrinos, on the other hand, the matter effect is negligible, and the formalism of oscillations in vacuum is valid. The size of the source (i.e. the solar core) is significantly larger than the oscillation length, therefore, averaging over the oscillation factor, one obtains
1606:
Survival probability of solar neutrinos as predicted by the MSW theory. The continuous line is for neutrinos that are detected in the day, the dotted one for neutrinos that are detected in the night and that pass through the Earth, experiencing "regeneration". The 4 vertical strips indicate the
1842:
carry away about 99% of the gravitational energy of the supernova and are considered strongest source of cosmic neutrinos in the MeV range. As such, scientists have attempted to simulate and mathematically characterize the action of MSW dynamics on SN neutrinos.
627:) has an opposite sign. If the electron density of matter changes along the path of neutrinos, the mixing of neutrinos grows to maximum at some value of the density, and then turns back; it leads to resonant conversion of one type of neutrinos to another one.
1366:
1792:
The transition between the low energy regime (the MSW effect is negligible) and the high energy regime (the oscillation probability is determined by matter effects) lies in the region of about 2 MeV for the solar neutrinos.
791:
1706:
967:
878:
458:
1139:
1934:
589:
1546:
1452:
1217:
1888:
1583:(SNO), which has resolved the solar neutrino problem. SNO measured the flux of solar electron neutrinos to be ~34% of the total neutrino flux (the electron neutrino flux measured via the
50:– the analysis is more complicated, as shown by Mikheyev, Smirnov and Wolfenstein. It leads to a wide admixture of emanating neutrino flavors, which provides a compelling solution to the
2279:
1599:
measured a mixture of charged current and neutral current reactions, that also support the occurrence of the MSW effect with a similar suppression, but with less confidence.
161:
1037:
285:
1168:
1733:
1573:
616:
488:
1485:
1402:
1253:
1073:
1000:
700:
670:
339:
1988:
1961:
239:
212:
1836:
2211:
460:. Since neutrino oscillations depend upon the squared mass difference of the neutrinos, neutrino oscillations experience different dynamics than they did in vacuum.
515:
366:
2128:
Lunardini, C.; Smirnov, A. Yu. (7 March 2001). "Neutrinos from SN 1987A, Earth matter effects, and the large mixing angle solution of the solar neutrino problem".
1258:
386:
185:
39:
of varying density. The MSW effect is broadly analogous to the differential retardation of sound waves in density-variable media, however it also involves the
672:, and remain as such as the density of solar material changes. Thus, the neutrinos of high energy leaving the Sun are in a vacuum propagation eigenstate,
705:
1627:
883:
1995:
1782:
alone verify the MSW pattern; however all these experiments are consistent with each other and provide us strong evidence of the MSW effect.
1755:
808:
46:
In free space, the separate rates of neutrino eigenstates lead to standard neutrino flavor oscillation. Within matter – such as within the
391:
1080:
2104:
2277:
Mikheyev, S. P.; Smirnov, A. Yu. (1985). "Resonance enhancement of oscillations in matter and solar neutrino spectroscopy".
2192:
2002:
within the Earth, the MSW effect can partially explain the difference of the
Kamiokande and IMB energy spectrum of events.
1893:
621:
With antineutrinos, the conceptual point is the same but the effective charge that the weak interaction couples to (called
490:
describes the change of flavors of the eigenstates. In matter, the mixing angle depends on the number density of electrons
2241:
1796:
The MSW effect can also modify neutrino oscillations in the Earth, and future search for new oscillations and/or leptonic
520:
1219:
that is, the eigenfrequency for a system of mixed neutrinos becomes approximately equal to the eigenfrequency of medium.
2269:
2049:, but it happens that this probability is negligibly small—this is sometimes called propagation in the adiabatic regime.
1498:
1407:
1173:
1789:, that is uniquely able to measure the parameters of oscillation that are also consistent with all other measurements.
2200:
77:
predicted that a slow decrease of the density of matter can resonantly enhance the neutrino mixing. Later in 1986,
2060:
1853:
114:
2516:
2460:"Mikheyev-Smirnov-Wolfenstein enhancement of oscillations as a possible solution to the solar-neutrino problem"
98:
388:
change, which means that the neutrinos in matter now have a different effective mass than they did in vacuum:
1742: ≈ 60%. This is consistent with the experimental observations of low energy solar neutrinos by the
1751:
1580:
635:
1999:
1487:
itself fluctuates – the interval between its maximum and minimum values is called the resonance layer.
1141:
which is when the neutrino system experiences resonance and the mixing becomes maximal. For very small
805:
and becomes maximal under certain conditions of the relationship between the vacuum oscillation length
74:
65:
led to understanding that the oscillation parameters of neutrinos are changed in matter. In 1985, the
2046:
139:
1009:
244:
1144:
2421:
2364:
1767:
1711:
1608:
1551:
594:
466:
302:
In the presence of matter, the
Hamiltonian of the system changes with respect to the potential:
1576:
1495:
For high-energy solar neutrinos the MSW effect is important, and leads to the expectation that
1457:
1371:
1225:
1046:
1003:
972:
675:
645:
305:
128:). This coherent forward scattering is analogous to the electromagnetic process leading to the
51:
2186:
1966:
1939:
217:
190:
2011:
1990:
oscillated inside the Earth. Due to the differences in the distance traveled by neutrinos to
1814:
32:
1361:{\displaystyle \ n_{r}={\frac {\Delta m^{2}}{\ 2{\sqrt {2\ }}E\ G_{f}\ }}\ \cos(2\theta )\ }
2473:
2430:
2383:
2342:
2311:
2288:
2225:
2147:
1743:
493:
344:
8:
1839:
62:
2477:
2434:
2387:
2346:
2315:
2292:
2229:
2151:
2511:
2407:
2373:
2163:
2137:
2110:
2082:
634:
where electron neutrinos are produced. The high-energy neutrinos seen, for example, in
371:
368:
is the
Hamiltonian in vacuum. Correspondingly, the mass eigenstates and eigenvalues of
170:
164:
90:
70:
2362:
Parke, S. J. (1986). "Nonadiabatic level crossing in resonant neutrino oscillations".
2489:
2464:
2446:
2399:
2333:
2302:
2256:
Brooijmans, Gustaaf (28 July 1998). Neutrino oscillations in matter: The MSW effect.
2196:
2167:
2114:
2100:
288:
125:
2411:
1779:
2481:
2438:
2391:
2350:
2319:
2233:
2212:"Antineutrinos From Distant Reactors Simulate the Disappearance of Solar Neutrinos"
2155:
2092:
1607:
values of the energies at which the survival probability was measured, by means of
1596:
786:{\displaystyle \nu _{\text{e}}=\nu _{1m}\cos \theta _{m}+\nu _{2m}\sin \theta _{m}}
639:
133:
129:
40:
28:
1701:{\displaystyle P_{\text{ee}}=1-{\tfrac {1}{2}}\sin ^{2}\left(2\theta _{s}\right)}
1588:
1584:
121:
2442:
2395:
2096:
2061:"Neutrinos from type-II supernovae and the neutrino-driven supernova mechanism1"
2159:
94:
2505:
2354:
2323:
2216:
1602:
1040:
292:
78:
58:
2485:
962:{\displaystyle \ \ell _{0}={\frac {{\sqrt {2\ }}\pi }{\ G_{f}\ n_{e}\ }}\ ,}
2450:
2403:
1797:
623:
296:
66:
2493:
2419:
Bethe, H. A. (1986). "Possible explanation of the solar-neutrino puzzle".
1454:
the resonance density goes to zero. In a medium with fluctuating density,
1746:(the first experiment to reveal the solar neutrino problem), followed by
117:
2142:
1991:
1592:
1591:
reaction). The SNO results agree well with the expectations. Earlier,
86:
2331:
Wolfenstein, L. (1979). "Neutrino oscillations and stellar collapse".
2237:
1808:
1771:
1612:
873:{\displaystyle \ \ell _{\nu }={\frac {\ 4\pi \ E\ }{\Delta m^{2}}}\ }
802:
2459:
630:
The effect is important at the very large electron densities of the
2378:
2087:
1847:
1763:
110:
82:
1846:
Some effect of MSW flavor conversion has already been observed in
132:
of light in a medium and can be described either as the classical
1786:
1759:
453:{\displaystyle \nu _{1},\nu _{2}\rightarrow \nu _{1m},\nu _{2m}}
1747:
1735: = 34° this corresponds to a survival probability of
124:'s elastic forward scattering of the electron neutrinos (i.e.,
36:
1785:
These results are further supported by the reactor experiment
642:, are produced mainly as the higher mass eigenstate in matter
43:
of three separate quantum fields which experience distortion.
1775:
1616:
591:. As the neutrinos propagate through density-variant matter,
2300:
Wolfenstein, L. (1978). "Neutrino oscillations in matter".
2045:
the neutrinos have the maximal probability to change their
2077:
Janka, H.-Th (2017). "Neutrino
Emission from Supernovae".
2023:
1803:
631:
47:
1368:
and is directly related the number density of electrons
1134:{\displaystyle \ \ell _{\nu }=\ell _{0}\cos(\theta )\ ,}
702:, that has a reduced overlap with the electron neutrino
287:
induces the evolution of mixed neutrino flavors (either
618:
changes – and with it, the flavors of the eigenstates.
187:. The difference of potentials for different neutrinos
1651:
1969:
1942:
1929:{\displaystyle \nu _{\mu ,\tau }\rightarrow \nu _{2}}
1896:
1856:
1817:
1714:
1630:
1554:
1501:
1490:
1460:
1410:
1374:
1261:
1228:
1176:
1147:
1083:
1049:
1039:
is understood as the distance over which the matter "
1012:
975:
886:
811:
708:
678:
648:
597:
523:
496:
469:
394:
374:
347:
308:
247:
220:
193:
173:
142:
1774: (862 keV), pep (1.44 MeV), and
1762:
radiochemical experiments), and, more recently, the
793:
seen by charged current reactions in the detectors.
584:{\displaystyle \theta _{m}(x)=\theta _{m}(n_{e}(x))}
880:and the matter density-dependent refraction length
1982:
1955:
1928:
1882:
1830:
1727:
1700:
1567:
1541:{\displaystyle P_{\text{ee}}=\sin ^{2}\theta _{s}}
1540:
1479:
1447:{\displaystyle \ \theta ={\frac {\pi }{\ 4\ }}\ ,}
1446:
1396:
1360:
1247:
1212:{\displaystyle \ \ell _{\nu }\approx \ell _{0}\ ,}
1211:
1162:
1133:
1067:
1031:
994:
961:
872:
785:
694:
664:
610:
583:
509:
482:
452:
380:
360:
333:
279:
233:
206:
179:
155:
1850:. In the case of normal neutrino mass hierarchy,
2503:
2127:
1838:neutrinos and antineutrinos of all flavors, and
2276:
1766:experiment, which observed the neutrinos from
796:
2209:
1936:, transitions occurred inside the star, then
1404:If vacuum density reaches the maximal value,
463:Similar to the vacuum case, the mixing angle
101:provided analytic treatments of this effect.
2184:
2029:
1883:{\displaystyle \nu _{e}\rightarrow \nu _{1}}
16:Particle physics process affecting neutrinos
2330:
2299:
1043:" from the coherent scattering is equal to
120:(mass eigenstates) of neutrinos due to the
2255:
2457:
2377:
2141:
2086:
1579:. This was dramatically confirmed in the
1778:(< 15 MeV) separately. The
1601:
1255:is informed by the resonance condition:
1811:are calculated to emit of the order of
2504:
2066:. Max-Planck-Institut für Astrophysik.
1804:Supernova neutrinos and the MSW effect
2418:
2361:
2193:Springer Science & Business Media
2076:
2058:
1587:reaction, and the total flux via the
1077:The resonance condition is given by
113:in matter changes the instantaneous
801:Neutrino flavor mixing experiences
21:Mikheyev–Smirnov–Wolfenstein effect
13:
2458:Rosen, S. P.; Gelb, J. M. (1986).
1491:Solar neutrinos and the MSW effect
1281:
851:
14:
2528:
2280:Soviet Journal of Nuclear Physics
517:and the energy of the neutrinos:
2270:Université catholique de Louvain
1768:pp (< 420 keV)
2177:
1800:may make use of this property.
1619:solar neutrinos, respectively.
2121:
2070:
2052:
2041:When neutrinos go through the
2035:
1913:
1867:
1352:
1343:
1122:
1116:
578:
575:
569:
556:
540:
534:
418:
156:{\displaystyle n_{\text{ref}}}
99:Los Alamos National Laboratory
1:
2017:
1032:{\displaystyle \ \ell _{0}\ }
280:{\displaystyle V=V_{1}-V_{2}}
1581:Sudbury Neutrino Observatory
1163:{\displaystyle \ \theta \ ,}
636:Sudbury Neutrino Observatory
7:
2443:10.1103/PhysRevLett.56.1305
2396:10.1103/PhysRevLett.57.1275
2188:The Science of Astrobiology
2097:10.1007/978-3-319-21846-5_4
2005:
1728:{\displaystyle \theta _{s}}
1568:{\displaystyle \theta _{s}}
797:Resonance in the MSW effect
611:{\displaystyle \theta _{m}}
483:{\displaystyle \theta _{m}}
10:
2533:
2210:Schwarzschild, B. (2003).
2160:10.1103/PhysRevD.63.073009
104:
57:Works in 1978 and 1979 by
23:(often referred to as the
2185:Chela-Flores, J. (2011).
1480:{\displaystyle \ n_{r}\ }
1397:{\displaystyle \ n_{e}~.}
1248:{\displaystyle \ n_{r}\ }
1068:{\displaystyle \ 2\pi ~.}
995:{\displaystyle \ G_{f}\ }
695:{\displaystyle \nu _{2m}}
665:{\displaystyle \nu _{2m}}
334:{\displaystyle H=H_{0}+V}
2355:10.1103/PhysRevD.20.2634
2324:10.1103/PhysRevD.17.2369
1983:{\displaystyle \nu _{2}}
1956:{\displaystyle \nu _{1}}
1780:measurements of Borexino
1006:. The refraction length
234:{\displaystyle \nu _{2}}
207:{\displaystyle \nu _{1}}
2486:10.1103/PhysRevD.34.969
2422:Physical Review Letters
2365:Physical Review Letters
1831:{\displaystyle 10^{58}}
1170:this condition becomes
1004:Fermi coupling constant
31:process which modifies
2081:. pp. 1575–1604.
2079:Handbook of Supernovae
1984:
1957:
1930:
1884:
1832:
1729:
1702:
1620:
1569:
1542:
1481:
1448:
1398:
1362:
1249:
1222:The resonance density
1213:
1164:
1135:
1069:
1033:
996:
963:
874:
787:
696:
666:
612:
585:
511:
484:
454:
382:
362:
335:
281:
235:
208:
181:
157:
52:solar neutrino problem
2517:Astroparticle physics
2012:Neutrino oscillations
1985:
1958:
1931:
1885:
1833:
1730:
1703:
1605:
1570:
1543:
1482:
1449:
1399:
1363:
1250:
1214:
1165:
1136:
1070:
1034:
997:
964:
875:
788:
697:
667:
613:
586:
512:
510:{\displaystyle n_{e}}
485:
455:
383:
363:
361:{\displaystyle H_{0}}
336:
282:
236:
209:
182:
158:
33:neutrino oscillations
1967:
1940:
1894:
1854:
1815:
1744:Homestake experiment
1712:
1628:
1552:
1499:
1458:
1408:
1372:
1259:
1226:
1174:
1145:
1081:
1047:
1010:
973:
884:
809:
706:
676:
646:
595:
521:
494:
467:
392:
372:
345:
306:
245:
218:
191:
171:
140:
41:propagation dynamics
2478:1986PhRvD..34..969R
2435:1986PhRvL..56.1305B
2388:1986PhRvL..57.1275P
2347:1979PhRvD..20.2634W
2316:1978PhRvD..17.2369W
2293:1985YaFiz..42.1441M
2230:2003PhT....56c..14S
2152:2001PhRvD..63g3009L
1840:supernova neutrinos
63:Lincoln Wolfenstein
2059:Janka, HT (1996).
1980:
1953:
1926:
1880:
1828:
1725:
1698:
1660:
1621:
1565:
1538:
1477:
1444:
1394:
1358:
1245:
1209:
1160:
1131:
1065:
1029:
992:
959:
870:
783:
692:
662:
608:
581:
507:
480:
450:
378:
358:
331:
277:
231:
204:
177:
165:electric potential
153:
97:and James Gelb of
91:Cornell University
71:Stanislav Mikheyev
2465:Physical Review D
2429:(12): 1305–1308.
2372:(10): 1275–1278.
2341:(10): 2634–2635.
2334:Physical Review D
2303:Physical Review D
2238:10.1063/1.1570758
2130:Physical Review D
2106:978-3-319-21845-8
2030:Chela-Flores 2011
1659:
1638:
1509:
1476:
1463:
1440:
1436:
1434:
1428:
1413:
1390:
1377:
1357:
1336:
1332:
1330:
1317:
1310:
1309:
1298:
1264:
1244:
1231:
1205:
1179:
1156:
1150:
1127:
1086:
1061:
1052:
1028:
1015:
991:
978:
955:
951:
949:
936:
923:
914:
913:
889:
869:
865:
848:
842:
833:
814:
716:
381:{\displaystyle H}
180:{\displaystyle V}
150:
126:weak interactions
2524:
2497:
2454:
2415:
2381:
2358:
2327:
2310:(9): 2369–2374.
2296:
2273:
2258:A New Limit on ν
2252:
2250:
2249:
2240:. Archived from
2206:
2172:
2171:
2145:
2125:
2119:
2118:
2090:
2074:
2068:
2067:
2065:
2056:
2050:
2039:
2033:
2027:
1989:
1987:
1986:
1981:
1979:
1978:
1962:
1960:
1959:
1954:
1952:
1951:
1935:
1933:
1932:
1927:
1925:
1924:
1912:
1911:
1889:
1887:
1886:
1881:
1879:
1878:
1866:
1865:
1837:
1835:
1834:
1829:
1827:
1826:
1734:
1732:
1731:
1726:
1724:
1723:
1707:
1705:
1704:
1699:
1697:
1693:
1692:
1691:
1671:
1670:
1661:
1652:
1640:
1639:
1636:
1597:Super-Kamiokande
1574:
1572:
1571:
1566:
1564:
1563:
1547:
1545:
1544:
1539:
1537:
1536:
1524:
1523:
1511:
1510:
1507:
1486:
1484:
1483:
1478:
1474:
1473:
1472:
1461:
1453:
1451:
1450:
1445:
1438:
1437:
1435:
1432:
1426:
1421:
1411:
1403:
1401:
1400:
1395:
1388:
1387:
1386:
1375:
1367:
1365:
1364:
1359:
1355:
1334:
1333:
1331:
1328:
1327:
1326:
1315:
1311:
1307:
1303:
1296:
1294:
1293:
1292:
1279:
1274:
1273:
1262:
1254:
1252:
1251:
1246:
1242:
1241:
1240:
1229:
1218:
1216:
1215:
1210:
1203:
1202:
1201:
1189:
1188:
1177:
1169:
1167:
1166:
1161:
1154:
1148:
1140:
1138:
1137:
1132:
1125:
1109:
1108:
1096:
1095:
1084:
1074:
1072:
1071:
1066:
1059:
1050:
1038:
1036:
1035:
1030:
1026:
1025:
1024:
1013:
1001:
999:
998:
993:
989:
988:
987:
976:
968:
966:
965:
960:
953:
952:
950:
947:
946:
945:
934:
933:
932:
921:
919:
915:
911:
907:
904:
899:
898:
887:
879:
877:
876:
871:
867:
866:
864:
863:
862:
849:
846:
840:
831:
829:
824:
823:
812:
792:
790:
789:
784:
782:
781:
766:
765:
750:
749:
734:
733:
718:
717:
714:
701:
699:
698:
693:
691:
690:
671:
669:
668:
663:
661:
660:
640:Super-Kamiokande
617:
615:
614:
609:
607:
606:
590:
588:
587:
582:
568:
567:
555:
554:
533:
532:
516:
514:
513:
508:
506:
505:
489:
487:
486:
481:
479:
478:
459:
457:
456:
451:
449:
448:
433:
432:
417:
416:
404:
403:
387:
385:
384:
379:
367:
365:
364:
359:
357:
356:
340:
338:
337:
332:
324:
323:
286:
284:
283:
278:
276:
275:
263:
262:
240:
238:
237:
232:
230:
229:
213:
211:
210:
205:
203:
202:
186:
184:
183:
178:
162:
160:
159:
154:
152:
151:
148:
134:refractive index
130:refractive index
109:The presence of
29:particle physics
2532:
2531:
2527:
2526:
2525:
2523:
2522:
2521:
2502:
2501:
2500:
2265:
2261:
2247:
2245:
2203:
2180:
2175:
2126:
2122:
2107:
2075:
2071:
2063:
2057:
2053:
2040:
2036:
2028:
2024:
2020:
2008:
1974:
1970:
1968:
1965:
1964:
1947:
1943:
1941:
1938:
1937:
1920:
1916:
1901:
1897:
1895:
1892:
1891:
1874:
1870:
1861:
1857:
1855:
1852:
1851:
1822:
1818:
1816:
1813:
1812:
1806:
1758:(collectively,
1741:
1719:
1715:
1713:
1710:
1709:
1687:
1683:
1679:
1675:
1666:
1662:
1650:
1635:
1631:
1629:
1626:
1625:
1589:neutral current
1585:charged current
1559:
1555:
1553:
1550:
1549:
1532:
1528:
1519:
1515:
1506:
1502:
1500:
1497:
1496:
1493:
1468:
1464:
1459:
1456:
1455:
1425:
1420:
1409:
1406:
1405:
1382:
1378:
1373:
1370:
1369:
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1318:
1302:
1295:
1288:
1284:
1280:
1278:
1269:
1265:
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1256:
1236:
1232:
1227:
1224:
1223:
1197:
1193:
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1175:
1172:
1171:
1146:
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1142:
1104:
1100:
1091:
1087:
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1045:
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1016:
1011:
1008:
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983:
979:
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970:
941:
937:
928:
924:
920:
906:
905:
903:
894:
890:
885:
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881:
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850:
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819:
815:
810:
807:
806:
799:
777:
773:
758:
754:
745:
741:
726:
722:
713:
709:
707:
704:
703:
683:
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677:
674:
673:
653:
649:
647:
644:
643:
602:
598:
596:
593:
592:
563:
559:
550:
546:
528:
524:
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519:
518:
501:
497:
495:
492:
491:
474:
470:
468:
465:
464:
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425:
421:
412:
408:
399:
395:
393:
390:
389:
373:
370:
369:
352:
348:
346:
343:
342:
319:
315:
307:
304:
303:
271:
267:
258:
254:
246:
243:
242:
225:
221:
219:
216:
215:
198:
194:
192:
189:
188:
172:
169:
168:
147:
143:
141:
138:
137:
122:charged current
107:
17:
12:
11:
5:
2530:
2520:
2519:
2514:
2499:
2498:
2472:(4): 969–979.
2455:
2416:
2359:
2328:
2297:
2287:(6): 913–917.
2274:
2263:
2259:
2253:
2207:
2201:
2181:
2179:
2176:
2174:
2173:
2143:hep-ph/0009356
2120:
2105:
2069:
2051:
2034:
2032:, p. 305.
2021:
2019:
2016:
2015:
2014:
2007:
2004:
1977:
1973:
1950:
1946:
1923:
1919:
1915:
1910:
1907:
1904:
1900:
1877:
1873:
1869:
1864:
1860:
1825:
1821:
1805:
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1739:
1722:
1718:
1696:
1690:
1686:
1682:
1678:
1674:
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1634:
1562:
1558:
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1471:
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1424:
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958:
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322:
318:
314:
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274:
270:
266:
261:
257:
253:
250:
228:
224:
201:
197:
176:
146:
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103:
95:S. Peter Rosen
75:Alexei Smirnov
15:
9:
6:
4:
3:
2:
2529:
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2313:
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2294:
2290:
2286:
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2272:. p. 40.
2271:
2267:
2254:
2244:on 2007-07-10
2243:
2239:
2235:
2231:
2227:
2223:
2219:
2218:
2217:Physics Today
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2208:
2204:
2202:9789400716278
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2189:
2183:
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2161:
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2136:(7): 073009.
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2102:
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2084:
2080:
2073:
2062:
2055:
2048:
2044:
2043:MSW resonance
2038:
2031:
2026:
2022:
2013:
2010:
2009:
2003:
2001:
1997:
1993:
1975:
1971:
1948:
1944:
1921:
1917:
1908:
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1898:
1875:
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1849:
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1610:
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1600:
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1578:
1575:is the solar
1560:
1556:
1533:
1529:
1525:
1520:
1516:
1512:
1503:
1488:
1469:
1465:
1441:
1429:
1422:
1417:
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1391:
1383:
1379:
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1340:
1337:
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816:
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735:
730:
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684:
680:
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638:(SNO) and in
637:
633:
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625:
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603:
599:
572:
564:
560:
551:
547:
543:
537:
529:
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434:
429:
426:
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400:
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375:
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316:
312:
309:
300:
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294:
290:
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268:
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248:
226:
222:
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195:
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131:
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102:
100:
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92:
88:
84:
80:
79:Stephen Parke
76:
72:
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53:
49:
44:
42:
38:
34:
30:
26:
25:matter effect
22:
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2426:
2420:
2369:
2363:
2338:
2332:
2307:
2301:
2284:
2278:
2266:Oscillations
2257:
2246:. Retrieved
2242:the original
2224:(3): 14–16.
2221:
2215:
2187:
2178:Bibliography
2133:
2129:
2123:
2078:
2072:
2054:
2042:
2037:
2025:
1845:
1807:
1798:CP violation
1795:
1791:
1784:
1736:
1622:
1577:mixing angle
1494:
1221:
1076:
800:
629:
624:weak isospin
622:
620:
462:
301:
108:
56:
45:
24:
20:
18:
1615:, pep, and
118:eigenstates
115:Hamiltonian
69:physicists
2506:Categories
2379:2212.06978
2268:(Report).
2248:2010-04-24
2088:1702.08713
2018:References
1992:Kamiokande
1809:Supernovae
1593:Kamiokande
87:Hans Bethe
61:physicist
2512:Neutrinos
2168:119066653
2115:119070646
1972:ν
1945:ν
1918:ν
1914:→
1909:τ
1903:μ
1899:ν
1872:ν
1868:→
1859:ν
1717:θ
1685:θ
1673:
1648:−
1557:θ
1530:θ
1526:
1423:π
1415:θ
1350:θ
1341:
1282:Δ
1195:ℓ
1191:≈
1186:ν
1182:ℓ
1152:θ
1120:θ
1114:
1102:ℓ
1093:ν
1089:ℓ
1057:π
1018:ℓ
917:π
892:ℓ
852:Δ
838:π
821:ν
817:ℓ
803:resonance
775:θ
771:
756:ν
743:θ
739:
724:ν
711:ν
681:ν
651:ν
600:θ
548:θ
526:θ
472:θ
439:ν
423:ν
419:→
410:ν
397:ν
265:−
223:ν
196:ν
111:electrons
2451:10032627
2412:26129285
2404:10033402
2006:See also
1848:SN 1987A
1764:Borexino
1548:, where
341:, where
289:electron
83:Fermilab
59:American
2494:9957237
2474:Bibcode
2431:Bibcode
2384:Bibcode
2343:Bibcode
2312:Bibcode
2289:Bibcode
2226:Bibcode
2148:Bibcode
1787:KamLAND
1760:gallium
1002:is the
163:or the
105:Summary
27:) is a
2492:
2449:
2410:
2402:
2199:
2166:
2113:
2103:
2047:flavor
2000:Baksan
1754:, and
1748:GALLEX
1708:. For
1475:
1462:
1439:
1433:
1427:
1412:
1389:
1376:
1356:
1335:
1329:
1316:
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1297:
1263:
1243:
1230:
1204:
1178:
1155:
1149:
1126:
1085:
1060:
1051:
1027:
1014:
990:
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969:where
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922:
912:
888:
868:
847:
841:
832:
813:
93:, and
67:Soviet
37:matter
2408:S2CID
2374:arXiv
2164:S2CID
2138:arXiv
2111:S2CID
2083:arXiv
2064:(PDF)
1041:phase
295:, or
2490:PMID
2447:PMID
2400:PMID
2197:ISBN
2101:ISBN
1998:and
1963:and
1890:and
1756:SAGE
1595:and
293:muon
214:and
73:and
19:The
2482:doi
2439:doi
2392:doi
2351:doi
2320:doi
2262:→ ν
2234:doi
2156:doi
2093:doi
1996:IMB
1752:GNO
1664:sin
1517:sin
1338:cos
1111:cos
768:sin
736:cos
632:Sun
299:).
297:tau
149:ref
89:of
81:of
48:Sun
35:in
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2480:.
2470:34
2468:.
2462:.
2445:.
2437:.
2427:56
2425:.
2406:.
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2382:.
2370:57
2368:.
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2308:17
2306:.
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2214:.
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2191:.
2162:.
2154:.
2146:.
2134:63
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2099:.
2091:.
1994:,
1824:58
1820:10
1772:Be
1770:,
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2326:.
2322::
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2291::
2264:τ
2260:μ
2251:.
2236::
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2205:.
2170:.
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2117:.
2095::
2085::
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354:0
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326:+
321:0
317:H
313:=
310:H
273:2
269:V
260:1
256:V
252:=
249:V
227:2
200:1
175:V
145:n
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