726:
1176:
doublets in nature the predicted value of the quasi-fixed point comes into agreement with experiment. Even if there are two Higgs doublets, the fixed point for the top mass is reduced, 170~200 GeV. Some theorists believed this was supporting evidence for the
Supersymmetric Standard Model, however no other signs of supersymmetry have emerged at the
483:
283:
1175:
factor in the equation, and any Higgs mixing angle effects. Since the observed top quark mass of 174 GeV is slightly lower than the standard model prediction by about 20%, this suggests there may be more Higgs doublets beyond the single standard model Higgs boson. If there are many additional Higgs
1047:
This is known as a (infrared) quasi-fixed point of the renormalization group equation for the Yukawa coupling. No matter what the initial starting value of the coupling is, if it is sufficiently large at high energies to begin with, it will reach this quasi-fixed point value, and the corresponding
38:
is a set of coupling constants, or other parameters, that evolve from arbitrary initial values at very high energies (short distance) to fixed, stable values, usually predictable, at low energies (large distance). This usually involves the use of the
721:{\displaystyle \ \mu \ {\frac {\ \partial }{\partial \mu }}\ y_{\mathrm {t} }\approx {\frac {\ y_{\text{t}}\ }{16\ \pi ^{2}}}\left({\frac {\ 9\ }{2}}y_{\mathrm {t} }^{2}-8g_{3}^{2}-{\frac {\ 9\ }{4}}g_{2}^{2}-{\frac {\ 17\ }{20}}g_{1}^{2}\right)\ ,}
126:
1215:
The name "infrared" is metaphorical, since the effect is seen as energy decreases, by analogy with descent to light with lower energy than visible light. Effects which appear with rising energy are metaphorically called
74:, the physical system approaches an infrared fixed point that is independent of the initial short distance dynamics that defines the material. This determines the properties of the phase transition at the
817:
937:
1157:
1095:
444:
1099:
The renormalization group equation for large values of the top Yukawa coupling was first considered in 1981 by
Pendleton & Ross, and the "infrared quasi-fixed point" was proposed by
1009:
974:
855:
1045:
888:
389:
319:
473:
352:
1107:
theories of electroweak symmetry breaking in which the Higgs boson is composite at extremely short distance scales, composed of a pair of top and anti-top quarks.
278:{\displaystyle \ \mu \ {\frac {\partial }{\partial \mu }}\ y_{q}\approx {\frac {y_{q}}{\ 16\pi ^{2}\ }}\left({\frac {\ 9\ }{2}}y_{q}^{2}-8g_{3}^{2}\right)\ ,}
110:'s Yukawa coupling. Yukawa couplings are not constants and their properties change depending on the energy scale at which they are measured, this is known as
1192:
in which the coupling constant of a Yang–Mills theory evolves to a fixed value. The beta-function vanishes, and the theory possesses a symmetry known as
54:. The fixed points are generally independent of the initial values of the parameters over a large range of the initial values. This is known as
1103:. The prevailing view at the time was that the top quark mass would lie in a range of 15 to 26 GeV. The quasi-infrared fixed point emerged in
117:
1641:
1429:
Bardeen, William A.; Hill, Christopher T. & Lindner, Manfred (1990). "Minimal dynamical symmetry breaking of the standard model".
55:
1636:
79:
1631:
1626:
769:
893:
106:
which determine the masses of the particles. Most of the quarks' and leptons' Yukawa couplings are small compared to the
762:
The Yukawa couplings of the up, down, charm, strange and bottom quarks, are small at the extremely high energy scale of
1113:
1051:
1189:
394:
1585:
Banks, Tom; A., Zaks (1982). "On the Phase
Structure of Vector-Like Gauge Theories with Massless Fermions".
1276:
51:
1104:
979:
976:
cause the expression on the right side to quickly approach zero as we descend in energy scale, which stops
944:
86:
usually depend only upon dimension of space, and are independent of the atomic or molecular constituents.
50:
Conversely, if the length-scale decreases and the physical parameters approach fixed values, then we have
1254:
1177:
112:
40:
1594:
1551:
1496:
1438:
1403:
1363:
1326:
1285:
890:
is increased slightly at the low energy scales at which the quark masses are generated by the Higgs,
763:
75:
44:
1530:
Hill, Christopher T.; Machado, Pedro; Thomsen, Anders; Turner, Jessica (2019). "Scalar democracy".
1472:
1389:
1100:
822:
67:
1354:
Pendleton, B.; Ross, G.G. (1981). "Mass and mixing angle predictions from infrared fixed points".
857:
term can be neglected in the above equation for all but the top quark. Solving, we then find that
1567:
1541:
1512:
1486:
1193:
941:
On the other hand, solutions to this equation for large initial values typical for the top quark
355:
99:
83:
1475:; Machado, Pedro; Thomsen, Anders; Turner, Jessica (2019). "Where are the next Higgs bosons?".
1014:
860:
361:
291:
1454:
449:
331:
1602:
1559:
1504:
1446:
1411:
1371:
1334:
1293:
1234:
71:
1532:
1477:
1394:
1268:
1159:
if there is more than one Higgs doublet, the value will be reduced by an increase in the
1598:
1555:
1500:
1442:
1407:
1367:
1330:
1289:
95:
1110:
While the value of the quasi-fixed point is determined in the
Standard Model of about
1620:
1606:
1571:
1516:
1375:
477:
A more complete version of the same formula is more appropriate for the top quark:
325:
322:
1563:
1508:
1298:
103:
745:
is the weak hypercharge gauge coupling. For small or near constant values of
17:
1450:
1415:
1339:
1229:
107:
1458:
1392:(1981). "Quark and lepton masses from renormalization group fixed points".
446:
This equation describes how the Yukawa coupling changes with energy scale
116:
of the constants. The dynamics of Yukawa couplings are determined by the
43:, which specifically details the way parameters in a physical system (a
31:
1314:
1546:
1491:
1269:"Reliable perturbative results for strong interactions?"
1116:
1054:
1017:
982:
947:
896:
863:
825:
812:{\displaystyle \ \mu \approx 10^{15}\mathrm {GeV} ~.}
772:
486:
452:
397:
364:
334:
294:
129:
932:{\displaystyle \ \mu \approx 125\ \mathrm {GeV} ~.}
1188:Another example of an infrared fixed point is the
1151:
1089:
1039:
1003:
968:
931:
882:
849:
811:
720:
467:
438:
383:
346:
313:
277:
1152:{\displaystyle \ m\approx 220\ \mathrm {GeV} ~,}
1090:{\displaystyle \ m\approx 220\ \mathrm {GeV} ~.}
1011:from changing and locks it to the QCD coupling
439:{\displaystyle \ q\in \{\mathrm {u,b,t} \}~.}
8:
427:
407:
47:) depend on the energy scale being probed.
1545:
1490:
1338:
1297:
1132:
1115:
1070:
1053:
1025:
1016:
991:
990:
981:
956:
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912:
895:
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862:
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833:
824:
792:
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629:
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372:
363:
333:
302:
293:
258:
253:
237:
232:
210:
193:
176:
170:
161:
139:
128:
1315:"Asymptotically free gauge theories. 1"
1246:
1208:
738:is the weak isospin gauge coupling and
759:the qualitative behavior is the same.
391:is the Yukawa coupling for the quark
7:
1048:quark mass is predicted to be about
1004:{\displaystyle \ y_{\mathrm {t} }\ }
969:{\displaystyle \ y_{\mathrm {t} }\ }
1139:
1136:
1133:
1077:
1074:
1071:
992:
957:
919:
916:
913:
799:
796:
793:
603:
525:
507:
502:
423:
417:
411:
328:coupling (which is a function of
145:
141:
25:
1313:Gross, D.J.; Wilczek, F. (1973).
118:renormalization group equation
1:
850:{\displaystyle \ y_{q}^{2}\ }
1607:10.1016/0550-3213(82)90035-9
1376:10.1016/0370-2693(81)90017-4
1564:10.1103/PhysRevD.100.015015
1509:10.1103/PhysRevD.100.015051
1299:10.1103/PhysRevLett.30.1346
1267:Politzer, H. David (1973).
98:, quarks and leptons have "
1658:
1642:Fixed points (mathematics)
1040:{\displaystyle \ g_{3}~.}
883:{\displaystyle \ y_{q}\ }
384:{\displaystyle \ y_{q}\ }
314:{\displaystyle \ g_{3}\ }
1451:10.1103/PhysRevD.41.1647
1257:and references therein.
468:{\displaystyle \ \mu ~.}
347:{\displaystyle \ \mu \ }
52:ultraviolet fixed points
1416:10.1103/PhysRevD.24.691
1340:10.1103/PhysRevD.8.3633
1277:Physical Review Letters
82:. Observables, such as
1637:Conformal field theory
1190:Banks–Zaks fixed point
1184:Banks–Zaks fixed point
1153:
1105:top quark condensation
1091:
1041:
1005:
970:
933:
884:
851:
813:
722:
469:
440:
385:
348:
315:
279:
27:Low energy fixed point
1632:Statistical mechanics
1627:Renormalization group
1255:renormalization group
1178:Large Hadron Collider
1154:
1092:
1042:
1006:
971:
934:
885:
852:
814:
723:
470:
441:
386:
349:
316:
280:
41:renormalization group
1473:Hill, Christopher T.
1114:
1052:
1015:
980:
945:
894:
861:
823:
770:
484:
450:
395:
362:
354:and associated with
332:
292:
127:
76:critical temperature
45:quantum field theory
36:infrared fixed point
1599:1982NuPhB.196..189B
1556:2019PhRvD.100a5015H
1501:2019PhRvD.100a5051H
1443:1990PhRvD..41.1647B
1408:1981PhRvD..24..691H
1368:1981PhLB...98..291P
1331:1973PhRvD...8.3633G
1290:1973PhRvL..30.1346P
843:
706:
670:
634:
613:
263:
242:
68:statistical physics
62:Statistical physics
1194:conformal symmetry
1149:
1087:
1037:
1001:
966:
929:
880:
847:
829:
809:
718:
692:
656:
620:
597:
465:
436:
381:
356:asymptotic freedom
344:
311:
275:
249:
228:
84:critical exponents
1431:Physical Review D
1325:(10): 3633–3652.
1319:Physical Review D
1284:(26): 1346–1349.
1145:
1131:
1119:
1083:
1069:
1057:
1033:
1020:
1000:
985:
965:
950:
925:
911:
899:
879:
866:
846:
828:
805:
775:
764:grand unification
714:
690:
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185:
156:
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132:
72:phase transitions
16:(Redirected from
1649:
1611:
1610:
1582:
1576:
1575:
1549:
1527:
1521:
1520:
1494:
1469:
1463:
1462:
1437:(5): 1647–1660.
1426:
1420:
1419:
1386:
1380:
1379:
1351:
1345:
1344:
1342:
1310:
1304:
1303:
1301:
1273:
1264:
1258:
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1235:Cutoff (physics)
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853:
848:
844:
842:
837:
826:
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815:
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803:
802:
791:
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773:
755:
748:
741:
734:
727:
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724:
719:
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365:
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199:
198:
197:
183:
181:
180:
171:
166:
165:
154:
153:
151:
140:
136:
130:
100:Yukawa couplings
70:of second order
21:
1657:
1656:
1652:
1651:
1650:
1648:
1647:
1646:
1617:
1616:
1615:
1614:
1593:(2): 189--204.
1584:
1583:
1579:
1533:Physical Review
1529:
1528:
1524:
1478:Physical Review
1471:
1470:
1466:
1428:
1427:
1423:
1395:Physical Review
1388:
1387:
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1348:
1312:
1311:
1307:
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1214:
1210:
1205:
1199:
1186:
1169:
1166:
1163:
1162:
1160:
1112:
1111:
1050:
1049:
1021:
1013:
1012:
986:
978:
977:
951:
943:
942:
892:
891:
867:
859:
858:
821:
820:
819:Therefore, the
782:
768:
767:
758:
753:
751:
746:
744:
739:
737:
732:
676:
640:
581:
578:
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561:
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519:
506:
498:
482:
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447:
393:
392:
368:
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330:
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298:
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289:
212:
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205:
189:
182:
172:
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144:
125:
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92:
64:
28:
23:
22:
15:
12:
11:
5:
1655:
1653:
1645:
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1639:
1634:
1629:
1619:
1618:
1613:
1612:
1577:
1522:
1464:
1421:
1381:
1346:
1305:
1259:
1245:
1244:
1242:
1239:
1238:
1237:
1232:
1225:
1222:
1219:
1218:
1216:"ultraviolet".
1207:
1206:
1204:
1201:
1185:
1182:
1148:
1141:
1138:
1135:
1128:
1125:
1122:
1086:
1079:
1076:
1073:
1066:
1063:
1060:
1036:
1028:
1024:
994:
989:
959:
954:
928:
921:
918:
915:
908:
905:
902:
874:
870:
841:
836:
832:
808:
801:
798:
795:
789:
785:
781:
778:
756:
749:
742:
735:
729:
728:
717:
710:
704:
699:
695:
689:
682:
673:
668:
663:
659:
653:
646:
637:
632:
627:
623:
619:
616:
611:
605:
600:
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568:
564:
557:
543:
533:
527:
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512:
509:
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492:
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458:
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429:
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208:
196:
192:
188:
179:
175:
169:
164:
160:
150:
147:
143:
135:
96:Standard Model
91:
88:
80:critical point
63:
60:
26:
24:
18:IR fixed point
14:
13:
10:
9:
6:
4:
3:
2:
1654:
1643:
1640:
1638:
1635:
1633:
1630:
1628:
1625:
1624:
1622:
1608:
1604:
1600:
1596:
1592:
1588:
1587:Nucl. Phys. B
1581:
1578:
1573:
1569:
1565:
1561:
1557:
1553:
1548:
1543:
1540:(1): 015015.
1539:
1535:
1534:
1526:
1523:
1518:
1514:
1510:
1506:
1502:
1498:
1493:
1488:
1485:(1): 015051.
1484:
1480:
1479:
1474:
1468:
1465:
1460:
1456:
1452:
1448:
1444:
1440:
1436:
1432:
1425:
1422:
1417:
1413:
1409:
1405:
1401:
1397:
1396:
1391:
1385:
1382:
1377:
1373:
1369:
1365:
1361:
1357:
1350:
1347:
1341:
1336:
1332:
1328:
1324:
1320:
1316:
1309:
1306:
1300:
1295:
1291:
1287:
1283:
1279:
1278:
1270:
1263:
1260:
1256:
1250:
1247:
1240:
1236:
1233:
1231:
1228:
1227:
1223:
1212:
1209:
1202:
1200:
1197:
1195:
1191:
1183:
1181:
1179:
1146:
1126:
1123:
1120:
1108:
1106:
1102:
1097:
1084:
1064:
1061:
1058:
1034:
1026:
1022:
987:
952:
939:
926:
906:
903:
900:
872:
868:
839:
834:
830:
806:
787:
783:
779:
776:
765:
760:
715:
708:
702:
697:
693:
687:
680:
671:
666:
661:
657:
651:
644:
635:
630:
625:
621:
617:
614:
609:
598:
592:
585:
575:
566:
562:
555:
541:
531:
520:
510:
490:
480:
479:
478:
475:
462:
456:
433:
420:
414:
404:
401:
373:
369:
357:
338:
327:
324:
303:
299:
272:
265:
259:
254:
250:
246:
243:
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206:
194:
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177:
173:
167:
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158:
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133:
123:
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119:
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109:
105:
101:
97:
89:
87:
85:
81:
77:
73:
69:
61:
59:
57:
53:
48:
46:
42:
37:
33:
19:
1590:
1586:
1580:
1537:
1531:
1525:
1482:
1476:
1467:
1434:
1430:
1424:
1399:
1393:
1384:
1359:
1355:
1349:
1322:
1318:
1308:
1281:
1275:
1262:
1249:
1211:
1198:
1187:
1109:
1098:
940:
761:
730:
476:
287:
111:
93:
65:
56:universality
49:
35:
29:
104:Higgs boson
1621:Categories
1547:1902.07214
1492:1904.04257
1402:(3): 691.
1390:Hill, C.T.
1362:(4): 291.
1356:Phys. Lett
1241:References
1572:119193325
1517:104291827
1230:Top quark
1203:Footnotes
1124:≈
1062:≈
904:≈
901:μ
780:≈
777:μ
672:−
636:−
615:−
563:π
532:≈
511:μ
508:∂
503:∂
491:μ
457:μ
405:∈
339:μ
244:−
191:π
168:≈
149:μ
146:∂
142:∂
134:μ
108:top quark
102:" to the
90:Top Quark
1459:10012522
1224:See also
1595:Bibcode
1552:Bibcode
1497:Bibcode
1439:Bibcode
1404:Bibcode
1364:Bibcode
1327:Bibcode
1286:Bibcode
1173:
1161:
358:) and
321:is the
113:running
94:In the
66:In the
32:physics
1570:
1515:
1457:
1144:
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