20:
515:
69:
309:
510:{\displaystyle {\begin{pmatrix}\gamma ~\\{\textsf {Z}}^{0}\end{pmatrix}}={\begin{pmatrix}\quad \cos \theta _{\textsf {w}}&\sin \theta _{\textsf {w}}\\-\sin \theta _{\textsf {w}}&\cos \theta _{\textsf {w}}\end{pmatrix}}{\begin{pmatrix}{\textsf {B}}^{0}\\{\textsf {W}}^{0}\end{pmatrix}}.}
1349:
875:
766:
997:
620:
104:, along the Weinberg angle. The neutral Higgs field (upper left, circled) breaks the electroweak symmetry and interacts with other particles to give them mass. Three components of the Higgs field become part of the massive
213:. Its measured value is slightly below 30°, but also varies, very slightly increasing, depending on how high the relative momentum of the particles involved in the interaction is that the angle is used for.
1231:
771:
673:
916:
Because the value of the mixing angle is currently determined empirically, in the absence of any superseding theoretical derivation it is mathematically defined as
922:
552:
1026:', is a key prediction of the electroweak theory. The most precise measurements have been carried out in electron–positron collider experiments at a value of
1704:
Aaij, R.; Adeva, B.; Adinolfi, M.; Affolder, A.; Ajaltouni, Z.; Akar, S.; et al. (2015-11-27). "Measurement of the forward-backward asymmetry in
1189:, establishing experimentally the so-called 'running' of the weak mixing angle. These values correspond to a Weinberg angle varying between 28.7° and
1799:
1796:
Q-weak: A precision test of the
Standard Model and determination of the weak charges of the quarks through parity-violating electron scattering
1654:
1611:
1344:{\displaystyle \sin ^{2}\theta _{\textsf {w}}=1-\left({\frac {\ m_{\textsf {W}}\ }{m_{\textsf {Z}}}}\right)^{2}=0.22305(23)~.}
1688:
1627:
1830:
1222:
for this measurement is determined by the partonic collision energy, which is close to the Z boson mass.
146:
1835:
1820:
1783:
1103:
19:
870:{\displaystyle \quad \sin \theta _{\textsf {w}}={\frac {\quad g'~}{\ {\sqrt {g^{2}+g'^{\ 2}~}}\ }}~.}
1123:, which is an average over measurements made in different processes, at different detectors. Atomic
1680:
1533:
is an open, free parameter, although it is constrained and predicted through other measurements of
761:{\displaystyle \cos \theta _{\textsf {w}}={\frac {\quad g~}{\ {\sqrt {g^{2}+g'^{\ 2}~}}\ }}\quad }
1768:
1619:
129:
1023:
1803:
1581:
992:{\displaystyle \cos \theta _{\textsf {w}}={\frac {\ m_{\textsf {W}}\ }{m_{\textsf {Z}}}}~.}
1153:
615:{\displaystyle m_{\textsf {Z}}={\frac {m_{\textsf {W}}}{\,\cos \theta _{\textsf {w}}}}\,.}
8:
1787:
1764:
1585:
1747:
1477:
is distinct from the similar-appearing symbol occasionally used for momentum-transfer
1751:
1739:
1684:
1623:
1593:
1012:
643:
1729:
1721:
1646:
1589:
1149:
1124:
656:
86:
149:
121:
1725:
1148:, but with much lower precision. In 2005 results were published from a study of
1825:
1534:
1521:
525:
133:
105:
1814:
1743:
1572:
Glashow, Sheldon (February 1961). "Partial-symmetries of weak interactions".
1197:
measured in 7 and 8 TeV proton–proton collisions an effective angle of
1780:
E158: A precision measurement of the weak mixing angle in Møller scattering
647:
257:
188:
73:
1500:
Note that at present, there is no generally accepted theory that explains
1779:
1734:
125:
1357:
282:
210:
1712:
decays and determination of the effective weak mixing angle".
98:, of the known elementary particles, showing electric charge,
68:
1795:
1194:
1703:
260:(i.e. 'mixing') that simultaneously produces the massive
1491:, but upper case is common and may occur in some graphs.
880:
The electric charge is then expressible in terms of it,
1651:
The NIST reference on constants, units, and uncertainty
524:
also gives the relationship between the masses of the
461:
361:
318:
1234:
925:
774:
676:
555:
312:
1079:is more frequently used. The 2004 best estimate of
1343:
991:
869:
760:
614:
509:
16:Angle characterizing electroweak symmetry breaking
1559:Particle Physics and Introduction to Field Theory
221:The algebraic formula for the combination of the
1812:
1605:
1603:
1022:, at which it is measured. This variation, or '
136:of particle physics, and is usually denoted as
1655:National Institute of Standards and Technology
1762:
1600:
1516:should be what it is. The specific value is
1616:Gauge Theory of Elementary Particle Physics
1376:) couples to the unbroken electric charge,
625:The angle can be expressed in terms of the
1733:
1433: boson couples to the broken charge
1302:
1286:
1254:
975:
959:
938:
788:
689:
608:
599:
586:
579:
562:
485:
467:
442:
422:
397:
377:
334:
67:
18:
1609:
1571:
1813:
1641:
1639:
1763:Erler, J.; Freitas, A.; et al. (
1674:
1800:Jefferson National Accelerator Lab.
1636:
1556:
1039:, corresponding to the mass of the
13:
14:
1847:
191:plane, producing as a result the
32:, and relation between couplings
1681:North-Holland Physics Publishing
800:
775:
757:
701:
364:
1714:Journal of High Energy Physics
1697:
1668:
1565:
1550:
1494:
1465:
1332:
1326:
303:) is expressed by the formula
1:
1544:
1225:CODATA 2022 gives the value
1127:experiments yield values for
147:spontaneous symmetry breaking
1769:Review of the Standard Model
1594:10.1016/0029-5582(61)90469-2
1458:
1011:varies as a function of the
7:
1784:Stanford Linear Accelerator
145:. It is the angle by which
10:
1852:
1069:In practice, the quantity
216:
64:. Adapted from Lee (1981).
1726:10.1007/JHEP11(2015)190
1620:Oxford University Press
913:(refer to the figure).
130:electroweak interaction
1345:
1215:, though the value of
1144:, below 0.01 GeV/
993:
871:
762:
616:
511:
120:is a parameter in the
109:
65:
1831:Dimensionless numbers
1653:. 2022 CODATA value.
1524:: The Weinberg angle
1354:The massless photon (
1346:
1137:at smaller values of
994:
872:
763:
617:
512:
209: boson, and the
71:
22:
1804:Department of Energy
1622:. pp. 349–355.
1484:. This article uses
1471:The electric charge
1232:
1156:in which a value of
923:
772:
674:
553:
310:
1788:Stanford University
1765:Particle Data Group
1675:Okun, L.B. (1982).
1647:"Weak mixing angle"
1586:1961NucPh..22..579G
1504:the measured value
1836:Physical constants
1821:Electroweak theory
1677:Leptons and Quarks
1557:Lee, T.D. (1981).
1341:
989:
867:
758:
612:
507:
498:
450:
347:
110:
66:
1786:(SLAC) (Report).
1520:predicted by the
1337:
1308:
1304:
1294:
1288:
1279:
1256:
1154:Møller scattering
1013:momentum transfer
985:
981:
977:
967:
961:
952:
940:
863:
859:
857:
853:
852:
843:
816:
811:
790:
755:
753:
749:
748:
739:
712:
707:
691:
667:, respectively),
606:
601:
581:
564:
522:weak mixing angle
487:
469:
444:
424:
399:
379:
336:
326:
281:and the massless
114:weak mixing angle
1843:
1807:
1791:
1775:
1773:
1767:(PDG)) (2019) .
1756:
1755:
1737:
1711:
1709:
1701:
1695:
1694:
1672:
1666:
1665:
1663:
1662:
1643:
1634:
1633:
1607:
1598:
1597:
1569:
1563:
1562:
1554:
1538:
1529:
1515:
1510:
1498:
1492:
1490:
1483:
1476:
1469:
1454:
1450:
1432:
1431:
1430:
1423:
1422:
1414:
1410:
1406:
1405:
1403:
1402:
1399:
1396:
1375:
1374:
1372:
1371:
1364:
1363:
1350:
1348:
1347:
1342:
1335:
1319:
1318:
1313:
1309:
1307:
1306:
1305:
1295:
1292:
1291:
1290:
1289:
1277:
1275:
1259:
1258:
1257:
1244:
1243:
1221:
1214:
1212:
1211:
1204:
1192:
1188:
1183:
1176:was obtained at
1175:
1174:
1172:
1163:
1150:parity violation
1143:
1133:
1125:parity violation
1122:
1121:
1117:
1114:
1106:
1101:
1096:
1085:
1075:
1062:
1056:
1055:
1054:
1047:
1046:
1038:
1033:
1021:
1007:
998:
996:
995:
990:
983:
982:
980:
979:
978:
968:
965:
964:
963:
962:
950:
948:
943:
942:
941:
909:
903:
893:
876:
874:
873:
868:
861:
860:
858:
855:
854:
850:
849:
848:
847:
841:
828:
827:
818:
814:
812:
809:
808:
798:
793:
792:
791:
767:
765:
764:
759:
756:
754:
751:
750:
746:
745:
744:
743:
737:
724:
723:
714:
710:
708:
705:
699:
694:
693:
692:
666:
664:
657:weak hypercharge
654:
642:
633:
621:
619:
618:
613:
607:
605:
604:
603:
602:
584:
583:
582:
572:
567:
566:
565:
542:
533:
516:
514:
513:
508:
503:
502:
495:
494:
489:
488:
477:
476:
471:
470:
455:
454:
447:
446:
445:
427:
426:
425:
402:
401:
400:
382:
381:
380:
352:
351:
344:
343:
338:
337:
324:
302:
301:
300:
293:
292:
280:
278:
277:
276:
269:
268:
256:
255:
254:
247:
246:
238:
237:
236:
229:
228:
208:
207:
206:
199:
198:
187:
186:
185:
178:
177:
169:
168:
167:
160:
159:
141:
103:
94:
87:weak hypercharge
84:
60:
46:
44:
37:
28:
1851:
1850:
1846:
1845:
1844:
1842:
1841:
1840:
1811:
1810:
1802:(Report). U.S.
1794:
1778:
1771:
1759:
1707:
1705:
1702:
1698:
1691:
1683:. p. 214.
1673:
1669:
1660:
1658:
1645:
1644:
1637:
1630:
1608:
1601:
1574:Nuclear Physics
1570:
1566:
1555:
1551:
1547:
1542:
1541:
1532:
1525:
1513:
1506:
1505:
1499:
1495:
1485:
1478:
1472:
1470:
1466:
1461:
1453:
1441:
1435:
1434:
1429:
1427:
1426:
1425:
1421:
1419:
1418:
1417:
1416:
1413:
1400:
1397:
1394:
1393:
1391:
1390:
1388:
1378:
1377:
1370:
1368:
1367:
1366:
1362:
1360:
1359:
1358:
1356:
1355:
1314:
1301:
1300:
1296:
1285:
1284:
1280:
1276:
1274:
1270:
1269:
1253:
1252:
1248:
1239:
1235:
1233:
1230:
1229:
1216:
1210:
1207:
1206:
1205:
1199:
1198:
1190:
1178:
1177:
1170:
1168:
1166:
1158:
1157:
1138:
1136:
1128:
1119:
1115:
1112:
1110:
1104:
1091:
1090:
1088:
1080:
1078:
1070:
1065:
1058:
1053:
1051:
1050:
1049:
1045:
1043:
1042:
1041:
1040:
1028:
1027:
1016:
1010:
1003:
974:
973:
969:
958:
957:
953:
949:
947:
937:
936:
932:
924:
921:
920:
912:
901:
897:
896:
881:
840:
836:
832:
823:
819:
817:
813:
801:
799:
797:
787:
786:
782:
773:
770:
769:
736:
732:
728:
719:
715:
713:
709:
700:
698:
688:
687:
683:
675:
672:
671:
662:
659:
650:
641:
635:
632:
626:
598:
597:
593:
585:
578:
577:
573:
571:
561:
560:
556:
554:
551:
550:
545:
538:
536:
529:
497:
496:
490:
484:
483:
482:
479:
478:
472:
466:
465:
464:
457:
456:
449:
448:
441:
440:
436:
428:
421:
420:
416:
404:
403:
396:
395:
391:
383:
376:
375:
371:
357:
356:
346:
345:
339:
333:
332:
331:
328:
327:
314:
313:
311:
308:
307:
299:
297:
296:
295:
291:
289:
288:
287:
286:
275:
273:
272:
271:
267:
265:
264:
263:
262:
261:
253:
251:
250:
249:
245:
243:
242:
241:
240:
235:
233:
232:
231:
227:
225:
224:
223:
222:
219:
205:
203:
202:
201:
197:
195:
194:
193:
192:
184:
182:
181:
180:
176:
174:
173:
172:
171:
166:
164:
163:
162:
158:
156:
155:
154:
153:
144:
137:
99:
97:
90:
83:
77:
72:The pattern of
63:
48:
42:
39:
33:
31:
24:
23:Weinberg angle
17:
12:
11:
5:
1849:
1839:
1838:
1833:
1828:
1823:
1809:
1808:
1792:
1776:
1758:
1757:
1696:
1689:
1667:
1635:
1628:
1599:
1580:(4): 579–588.
1564:
1548:
1546:
1543:
1540:
1539:
1535:Standard Model
1530:
1522:Standard Model
1511:
1493:
1463:
1462:
1460:
1457:
1451:
1439:
1428:
1420:
1411:
1386:
1369:
1361:
1352:
1351:
1340:
1334:
1331:
1328:
1325:
1322:
1317:
1312:
1299:
1283:
1273:
1268:
1265:
1262:
1251:
1247:
1242:
1238:
1208:
1164:
1134:
1086:
1076:
1063:
1052:
1044:
1008:
1000:
999:
988:
972:
956:
946:
935:
931:
928:
910:
894:
878:
877:
866:
846:
839:
835:
831:
826:
822:
807:
804:
796:
785:
781:
778:
742:
735:
731:
727:
722:
718:
704:
697:
686:
682:
679:
637:
628:
623:
622:
611:
596:
592:
589:
576:
570:
559:
543:
534:
526:W and Z bosons
518:
517:
506:
501:
493:
481:
480:
475:
463:
462:
460:
453:
439:
435:
432:
429:
419:
415:
412:
409:
406:
405:
394:
390:
387:
384:
374:
370:
367:
363:
362:
360:
355:
350:
342:
330:
329:
323:
320:
319:
317:
298:
290:
274:
266:
252:
244:
234:
226:
218:
215:
204:
196:
183:
175:
165:
157:
142:
134:Standard Model
132:, part of the
128:theory of the
118:Weinberg angle
106:W and Z bosons
95:
81:
61:
29:
15:
9:
6:
4:
3:
2:
1848:
1837:
1834:
1832:
1829:
1827:
1824:
1822:
1819:
1818:
1816:
1805:
1801:
1797:
1793:
1789:
1785:
1781:
1777:
1770:
1766:
1761:
1760:
1753:
1749:
1745:
1741:
1736:
1735:1721.1/116170
1731:
1727:
1723:
1719:
1715:
1700:
1692:
1690:0-444-86924-7
1686:
1682:
1678:
1671:
1657:. 30 May 2024
1656:
1652:
1648:
1642:
1640:
1631:
1629:0-19-851961-3
1625:
1621:
1617:
1613:
1610:Cheng, T.P.;
1606:
1604:
1595:
1591:
1587:
1583:
1579:
1575:
1568:
1560:
1553:
1549:
1536:
1528:
1523:
1519:
1509:
1503:
1497:
1489:
1482:
1475:
1468:
1464:
1456:
1449:
1445:
1438:
1415:, while the
1409:
1385:
1381:
1373:
1338:
1329:
1323:
1320:
1315:
1310:
1297:
1281:
1271:
1266:
1263:
1260:
1249:
1245:
1240:
1236:
1228:
1227:
1226:
1223:
1220:
1203:
1196:
1187:
1182:
1162:
1155:
1151:
1147:
1142:
1132:
1126:
1108:
1100:
1095:
1084:
1074:
1067:
1061:
1057: boson,
1037:
1032:
1025:
1020:
1014:
1006:
1002:The value of
986:
970:
954:
944:
933:
929:
926:
919:
918:
917:
914:
908:
904:
892:
888:
884:
864:
844:
837:
833:
829:
824:
820:
805:
802:
794:
783:
779:
776:
740:
733:
729:
725:
720:
716:
702:
695:
684:
680:
677:
670:
669:
668:
665:
658:
653:
649:
645:
640:
631:
609:
594:
590:
587:
574:
568:
557:
549:
548:
547:
541:
532:
527:
523:
504:
499:
491:
473:
458:
451:
437:
433:
430:
417:
413:
410:
407:
392:
388:
385:
372:
368:
365:
358:
353:
348:
340:
321:
315:
306:
305:
304:
284:
259:
258:vector bosons
214:
212:
190:
152:the original
151:
148:
140:
135:
131:
127:
123:
119:
115:
107:
102:
93:
88:
80:
75:
70:
59:
55:
51:
45:
36:
27:
21:
1717:
1713:
1699:
1676:
1670:
1659:. Retrieved
1650:
1615:
1577:
1573:
1567:
1558:
1552:
1526:
1517:
1507:
1501:
1496:
1487:
1480:
1473:
1467:
1447:
1443:
1436:
1407:
1383:
1379:
1353:
1224:
1218:
1201:
1185:
1180:
1160:
1145:
1140:
1130:
1098:
1093:
1082:
1072:
1068:
1059:
1035:
1030:
1018:
1004:
1001:
915:
906:
899:
890:
886:
882:
879:
660:
651:
648:weak isospin
638:
629:
624:
539:
530:
528:(denoted as
521:
519:
220:
189:vector boson
138:
117:
113:
111:
100:
91:
78:
74:weak isospin
57:
53:
49:
40:
34:
25:
1720:(11): 190.
1537:quantities.
1191:29.3° ≈ 30°
1184:= 0.16 GeV/
1097:= 91.2 GeV/
1815:Categories
1661:2024-05-30
1545:References
1034:= 91.2 GeV
1774:(Report).
1752:118478870
1744:1029-8479
1459:Footnotes
1267:−
1250:θ
1246:
1213:= 0.23142
1102:, in the
934:θ
930:
784:θ
780:
685:θ
681:
644:couplings
595:θ
591:
438:θ
434:
418:θ
414:
408:−
393:θ
389:
373:θ
369:
322:γ
1614:(2006).
1612:Li, L.F.
898: =
838:′
806:′
734:′
122:Weinberg
1582:Bibcode
1404:
1392:
1324:0.22305
1024:running
217:Details
150:rotates
1750:
1742:
1687:
1626:
1365:γ
1336:
1293:
1278:
1173:0.0013
1169:0.2397
1107:scheme
984:
966:
951:
862:
856:
851:
842:
815:
810:
752:
747:
738:
711:
706:
325:
294:γ
283:photon
211:photon
85:, and
47:, and
1826:Angle
1772:(PDF)
1748:S2CID
1514:≈ 29°
1118:0.000
1111:0.231
1089:, at
627:SU(2)
279:boson
126:Salam
1740:ISSN
1718:2015
1710:→ μμ
1685:ISBN
1624:ISBN
1446:sin
1200:sin
1195:LHCb
1159:sin
1129:sin
1081:sin
1071:sin
905:cos
889:sin
768:and
655:and
636:U(1)
634:and
537:and
520:The
239:and
170:and
112:The
56:sin
1730:hdl
1722:doi
1590:doi
1518:not
1502:why
1237:sin
1152:in
1109:is
927:cos
777:sin
678:cos
588:cos
546:),
431:cos
411:sin
386:sin
366:cos
116:or
1817::
1798:.
1782:.
1746:.
1738:.
1728:.
1716:.
1706:Z/
1679:.
1649:.
1638:^
1618:.
1602:^
1588:.
1578:22
1576:.
1455:.
1442:−
1401:2
1395:1
1389:+
1382:=
1330:23
1193:.
1167:=
1120:15
1113:20
1105:MS
1066:.
1036:/c
1015:,
885:=
89:,
76:,
52:=
38:,
1806:.
1790:.
1754:.
1732::
1724::
1708:γ
1693:.
1664:.
1632:.
1596:.
1592::
1584::
1561:.
1531:w
1527:θ
1512:w
1508:θ
1488:q
1486:∆
1481:Q
1479:∆
1474:Q
1452:w
1448:θ
1444:Q
1440:3
1437:T
1424:Z
1412:w
1408:Y
1398:/
1387:3
1384:T
1380:Q
1339:.
1333:)
1327:(
1321:=
1316:2
1311:)
1303:Z
1298:m
1287:W
1282:m
1272:(
1264:1
1261:=
1255:w
1241:2
1219:q
1217:∆
1209:w
1202:θ
1186:c
1181:q
1179:∆
1171:±
1165:w
1161:θ
1146:c
1141:q
1139:∆
1135:w
1131:θ
1116:±
1099:c
1094:q
1092:∆
1087:w
1083:θ
1077:w
1073:θ
1064:Z
1060:m
1048:Z
1031:q
1029:∆
1019:q
1017:∆
1009:w
1005:θ
987:.
976:Z
971:m
960:W
955:m
945:=
939:w
911:w
907:θ
902:′
900:g
895:w
891:θ
887:g
883:e
865:.
845:2
834:g
830:+
825:2
821:g
803:g
795:=
789:w
741:2
730:g
726:+
721:2
717:g
703:g
696:=
690:w
663:′
661:g
652:g
646:(
639:Y
630:L
610:.
600:w
580:W
575:m
569:=
563:Z
558:m
544:Z
540:m
535:W
531:m
505:.
500:)
492:0
486:W
474:0
468:B
459:(
452:)
443:w
423:w
398:w
378:w
359:(
354:=
349:)
341:0
335:Z
316:(
285:(
270:Z
248:B
230:W
200:Z
179:B
161:W
143:W
139:θ
124:–
108:.
101:Q
96:W
92:Y
82:3
79:T
62:W
58:θ
54:g
50:e
43:′
41:g
35:g
30:W
26:θ
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