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In particle physics, the top quark condensate theory (or top condensation) is an alternative to the Standard Model fundamental Higgs field, where the Higgs boson is a composite field, composed of the top quark and its antiquark. The top quark-antiquark pairs are bound together by a new force called topcolor, analogous to the binding of Cooper pairs in a BCS superconductor, or mesons in the strong interactions. The top quark is very heavy, with a measured mass of approximately 174 GeV (comparable to the electroweak scale), and so its Yukawa coupling is of order unity, suggesting the possibility of strong coupling dynamics at high energy scales. This model attempts to explain how the electroweak scale may match the top quark mass.

History

The idea was described by Yoichiro Nambu^{[citation needed]} and subsequently developed by Miransky, Tanabashi, and Yamawaki (1989)^[1]^[2] and William A. Bardeen, Christopher T. Hill, and Manfred Lindner (1990),^[3] who connected the theory to the renormalization group, and improved its predictions.

The renormalization group reveals that top quark condensation is fundamentally based upon the infrared fixed point for the top quark Higgs-Yukawa coupling, proposed by Pendleton and Ross (1981)^[4] and Hill.^[5] The "infrared" fixed point originally predicted that the top quark would be heavy, contrary to the prevailing view of the early 1980s. Indeed, the top quark was discovered in 1995 at the large mass of 174 GeV. The infrared-fixed point implies that it is strongly coupled to the Higgs boson at very high energies, corresponding to the Landau pole of the Higgs-Yukawa coupling. At this high scale a bound-state Higgs forms, and in the "infrared", the coupling relaxes to its measured value of order unity by the renormalization group. The Standard Model renormalization group fixed point prediction is about 220 GeV, and the observed top mass is roughly 20% lower than this prediction. The simplest top condensation models are now ruled out by the LHC discovery of the Higgs boson at a mass scale of 125 GeV. However, extended versions of the theory, introducing more particles, can be consistent with the observed top quark and Higgs boson masses.

Future

The composite Higgs boson arises "naturally" in Topcolor models, that are extensions of the standard model using a hypothetical force analogous to quantum chromodynamics. To be "natural", that is, without excessive fine-tuning (i.e. to stabilize the Higgs mass from large radiative corrections), the hypothesis requires new physics at a relatively low energy scale. Placing new physics at 10 TeV, for instance, the model predicts the top quark to be significantly heavier than observed (at about 600 GeV vs. 171 GeV). Top Seesaw models, also based upon Topcolor, circumvent this difficulty.

The predicted top quark mass would come into improved agreement with the fixed point if there are many additional Higgs scalars beyond the standard model. This may be indicating a rich spectroscopy of new composite Higgs fields at energy scales that can be probed with the LHC and its upgrades.^[6]^[7]

References

^ Miransky, V.A.; Tanabashi, Masaharu; Yamawaki, Koichi (1989). "Dynamical electroweak symmetry breaking with large anomalous dimension and t quark condensate". Physics Letters B. 221 (2). Elsevier BV: 177–183. Bibcode:1989PhLB..221..177M. doi:10.1016/0370-2693(89)91494-9. ISSN 0370-2693.
^ Miransky, V.A.; Tanabashi, Masaharu; Yamawaki, Koichi (10 June 1989). "Is the t Quark Responsible for the Mass of W and Z Bosons?". Modern Physics Letters A. 04 (11). World Scientific: 1043–1053. Bibcode:1989MPLA....4.1043M. doi:10.1142/s0217732389001210. ISSN 0217-7323.
^ Bardeen, William A.; Hill, Christopher T. & Lindner, Manfred (1990). "Minimal dynamical symmetry breaking of the standard model". Physical Review D. 41 (5): 1647–1660. Bibcode:1990PhRvD..41.1647B. doi:10.1103/PhysRevD.41.1647. PMID 10012522.
^ Pendleton, B.; Ross, G.G. (1981). "Mass and mixing angle predictions from infra-red fixed points". Physics Letters B. 98 (4). Elsevier BV: 291–294. Bibcode:1981PhLB...98..291P. doi:10.1016/0370-2693(81)90017-4. ISSN 0370-2693.
^ Hill, C.T. (1981). "Quark and Lepton masses from Renormalization group fixed points". Physical Review D. 24 (3): 691. Bibcode:1981PhRvD..24..691H. doi:10.1103/PhysRevD.24.691.
^ Hill, Christopher T.; Machado, Pedro; Thomsen, Anders; Turner, Jessica (2019). "Where are the next Higgs bosons?". Physical Review. D100 (1): 015051. arXiv:1904.04257. Bibcode:2019PhRvD.100a5051H. doi:10.1103/PhysRevD.100.015051. S2CID 104291827.
^ Hill, Christopher T.; Machado, Pedro; Thomsen, Anders; Turner, Jessica (2019). "Scalar Democracy". Physical Review D. 100 (1): 015015. arXiv:1902.07214. Bibcode:2019PhRvD.100a5015H. doi:10.1103/PhysRevD.100.015015. S2CID 119193325.

[1] Miransky, V.A.; Tanabashi, Masaharu; Yamawaki, Koichi (1989). "Dynamical electroweak symmetry breaking with large anomalous dimension and t quark condensate". Physics Letters B. 221 (2). Elsevier BV: 177–183. Bibcode:1989PhLB..221..177M. doi:10.1016/0370-2693(89)91494-9. ISSN 0370-2693.

[2] Miransky, V.A.; Tanabashi, Masaharu; Yamawaki, Koichi (10 June 1989). "Is the t Quark Responsible for the Mass of W and Z Bosons?". Modern Physics Letters A. 04 (11). World Scientific: 1043–1053. Bibcode:1989MPLA....4.1043M. doi:10.1142/s0217732389001210. ISSN 0217-7323.

[3] Bardeen, William A.; Hill, Christopher T. & Lindner, Manfred (1990). "Minimal dynamical symmetry breaking of the standard model". Physical Review D. 41 (5): 1647–1660. Bibcode:1990PhRvD..41.1647B. doi:10.1103/PhysRevD.41.1647. PMID 10012522.

[4] Pendleton, B.; Ross, G.G. (1981). "Mass and mixing angle predictions from infra-red fixed points". Physics Letters B. 98 (4). Elsevier BV: 291–294. Bibcode:1981PhLB...98..291P. doi:10.1016/0370-2693(81)90017-4. ISSN 0370-2693.

[5] Hill, C.T. (1981). "Quark and Lepton masses from Renormalization group fixed points". Physical Review D. 24 (3): 691. Bibcode:1981PhRvD..24..691H. doi:10.1103/PhysRevD.24.691.

[6] Hill, Christopher T.; Machado, Pedro; Thomsen, Anders; Turner, Jessica (2019). "Where are the next Higgs bosons?". Physical Review. D100 (1): 015051. arXiv:1904.04257. Bibcode:2019PhRvD.100a5051H. doi:10.1103/PhysRevD.100.015051. S2CID 104291827.

[7] Hill, Christopher T.; Machado, Pedro; Thomsen, Anders; Turner, Jessica (2019). "Scalar Democracy". Physical Review D. 100 (1): 015015. arXiv:1902.07214. Bibcode:2019PhRvD.100a5015H. doi:10.1103/PhysRevD.100.015015. S2CID 119193325.

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 {{Short description|Hypothetical composite Higgs model}}
-In [[particle physics]], the '''top quark condensate''' theory (or '''top condensation''') is an alternative to the [[Standard Model]] fundamental [[Higgs field]], where the Higgs boson is a [[composite field]], composed of the [[top quark]] and its [[antiquark]].
+In [[particle physics]], the '''top quark condensate''' theory (or '''top condensation''') is an alternative to the [[Standard Model]] fundamental [[Higgs field]], where the Higgs boson is a [[composite field]], composed of the [[top quark]] and its [[antiquark]]. The [[top quark]]-[[antiquark]] pairs are bound together by a new force called [[topcolor]], analogous to the binding of [[Cooper pairs]] in a [[BCS theory|BCS superconductor]], or mesons in the strong interactions. The top quark is very heavy, with a measured mass of approximately 174&nbsp;[[GeV]] (comparable to the [[electroweak scale]]), and so its [[Yukawa coupling]] is of order unity, suggesting the possibility of strong coupling dynamics at high energy scales. This model attempts to explain how the [[electroweak scale]] may match the top quark mass.
-The [[top quark]]-[[antiquark]] pairs are bound together by a new force called [[topcolor]], analogous to the binding of [[Cooper pairs]] in a [[BCS theory|BCS superconductor]], or mesons in the strong interactions. The top quark is very heavy, with a measured mass of approximately 174&nbsp;[[GeV]] (comparable to the [[electroweak scale]]), and so its [[Yukawa coupling]] is of order unity, suggesting the possibility of strong coupling dynamics at high energy scales. This model attempts to explain how the [[electroweak scale]] may match the top quark mass.
 ==History==
-The idea was described by [[Yoichiro Nambu]]{{citation needed|date=May 2020}} and subsequently developed by Miransky, Tanabashi, and Yamawaki (1989)<ref>{{cite journal |last1=Miransky |first1=V.A. |last2=Tanabashi |first2=Masaharu |last3=Yamawaki |first3=Koichi |title=Dynamical electroweak symmetry breaking with large anomalous dimension and t quark condensate |journal=Physics Letters B |publisher=Elsevier BV |volume=221 |issue=2 |year=1989 |issn=0370-2693 |doi=10.1016/0370-2693(89)91494-9 |pages=177–183 |bibcode=1989PhLB..221..177M}}</ref><ref>{{cite journal |last1=Miransky |first1=V.A. |last2=Tanabashi |first2=Masaharu |last3=Yamawaki |first3=Koichi |title=Is the t Quark Responsible for the Mass of W and Z Bosons? |journal=Modern Physics Letters A |publisher=World Scientific |volume=04 |issue=11 |pages=1043–1053 |date=1989-06-10 |df=dmy-all |issn=0217-7323 |doi=10.1142/s0217732389001210 |bibcode=1989MPLA....4.1043M}}</ref> and Bardeen, Hill, and Lindner (1990),<ref>{{cite journal |author1=Bardeen, William A. |author2=Hill, Christopher T. |author3=Lindner, Manfred |name-list-style=amp |year=1990 |title=Minimal dynamical symmetry breaking of the standard model |journal=Physical Review D |volume=41 |issue=5 |pages=1647–1660 |doi=10.1103/PhysRevD.41.1647 |bibcode=1990PhRvD..41.1647B |pmid=10012522}}</ref> who connected the theory to the [[renormalization group]], and improved its predictions.
+The idea was described by [[Yoichiro Nambu]]{{citation needed|date=May 2020}} and subsequently developed by Miransky, Tanabashi, and Yamawaki (1989)<ref>{{cite journal |last1=Miransky |first1=V.A. |last2=Tanabashi |first2=Masaharu |last3=Yamawaki |first3=Koichi |title=Dynamical electroweak symmetry breaking with large anomalous dimension and t quark condensate |journal=Physics Letters B |publisher=Elsevier BV |volume=221 |issue=2 |year=1989 |issn=0370-2693 |doi=10.1016/0370-2693(89)91494-9 |pages=177–183 |bibcode=1989PhLB..221..177M}}</ref><ref>{{cite journal |last1=Miransky |first1=V.A. |last2=Tanabashi |first2=Masaharu |last3=Yamawaki |first3=Koichi |title=Is the t Quark Responsible for the Mass of W and Z Bosons? |journal=Modern Physics Letters A |publisher=World Scientific |volume=04 |issue=11 |pages=1043–1053 |date=1989-06-10 |df=dmy-all |issn=0217-7323 |doi=10.1142/s0217732389001210 |bibcode=1989MPLA....4.1043M}}</ref> and [[William A. Bardeen]], [[Christopher T. Hill]], and [[Manfred Lindner]] (1990),<ref>{{cite journal |author1=Bardeen, William A. |author2=Hill, Christopher T. |author3=Lindner, Manfred |name-list-style=amp |year=1990 |title=Minimal dynamical symmetry breaking of the standard model |journal=Physical Review D |volume=41 |issue=5 |pages=1647–1660 |doi=10.1103/PhysRevD.41.1647 |bibcode=1990PhRvD..41.1647B |pmid=10012522}}</ref> who connected the theory to the [[renormalization group]], and improved its predictions.
-The renormalization group reveals that top quark condensation is fundamentally based upon the ‘''[[infrared fixed point]]''’ for the top quark Higgs-Yukawa coupling, proposed by Pendleton and Ross (1981).<ref>{{cite journal |last1=Pendleton |first1=B. |last2=Ross |first2=G.G. |title=Mass and mixing angle predictions from infra-red fixed points |journal=Physics Letters B |publisher=Elsevier BV |volume=98 |issue=4 |pages=291–294 |year=1981 |issn=0370-2693 |doi=10.1016/0370-2693(81)90017-4|bibcode=1981PhLB...98..291P }}</ref> and Hill,<ref>{{cite journal |last1=Hill |first1=C.T. |title=Quark and Lepton masses from Renormalization group fixed points |journal=Physical Review D |year=1981 |volume=24 |issue=3 |page=691 |doi=10.1103/PhysRevD.24.691 |bibcode=1981PhRvD..24..691H}}</ref>
+The renormalization group reveals that top quark condensation is fundamentally based upon the ''[[infrared fixed point]]'' for the top quark Higgs-Yukawa coupling, proposed by Pendleton and Ross (1981)<ref>{{cite journal |last1=Pendleton |first1=B. |last2=Ross |first2=G.G. |title=Mass and mixing angle predictions from infra-red fixed points |journal=Physics Letters B |publisher=Elsevier BV |volume=98 |issue=4 |pages=291–294 |year=1981 |issn=0370-2693 |doi=10.1016/0370-2693(81)90017-4|bibcode=1981PhLB...98..291P }}</ref> and Hill.<ref>{{cite journal |last1=Hill |first1=C.T. |title=Quark and Lepton masses from Renormalization group fixed points |journal=Physical Review D |year=1981 |volume=24 |issue=3 |page=691 |doi=10.1103/PhysRevD.24.691 |bibcode=1981PhRvD..24..691H}}</ref> The "infrared" fixed point originally predicted that the top quark would be heavy, contrary to the prevailing view of the early 1980s. Indeed, the [[top quark]] was discovered in 1995 at the large mass of 174&nbsp;GeV. The infrared-fixed point implies that it is strongly coupled to the Higgs boson at very high energies, corresponding to the [[Landau pole]] of the Higgs-Yukawa coupling. At this high scale a bound-state Higgs forms, and in the "infrared", the coupling relaxes to its measured value of order unity by the [[renormalization group]]. The Standard Model [[renormalization group]] fixed point prediction is about 220&nbsp;GeV, and  the observed top mass is roughly 20% lower than this prediction. The simplest top condensation models are now ruled out by the [[Large Hadron Collider|LHC]] discovery of the Higgs boson at a mass scale of 125&nbsp;GeV. However, extended versions of the theory, introducing more particles, can be consistent with the observed top quark and Higgs boson masses.
-The ‘infrared’ fixed point originally predicted that the top quark would be heavy, contrary to the prevailing view of the early 1980s. Indeed, the [[top quark]] was discovered in 1995 at the large mass of 174&nbsp;GeV. The infrared-fixed point implies that it is strongly coupled to the Higgs boson at very high energies, corresponding to the [[Landau pole]] of the Higgs-Yukawa coupling. At this high scale a bound-state Higgs forms, and in the ‘infrared’, the coupling relaxes to its measured value of order unity by the [[renormalization group]]. The Standard Model [[renormalization group]] fixed point prediction
-is about 220&nbsp;GeV, and  the observed top mass is roughly 20% lower than this prediction.
-The simplest top condensation models are now ruled out by the [[Large Hadron Collider|LHC]] discovery of the Higgs boson at a mass scale of 125&nbsp;GeV. However, extended versions of the theory, introducing more particles, can be consistent with the observed top quark and Higgs boson masses.
 ==Future==
-The composite Higgs boson arises naturally in [[Topcolor]] models, that are extensions of the standard model using a new force analogous to [[quantum chromodynamics]]. To be natural, without excessive fine-tuning (i.e. to stabilize the Higgs mass from large radiative corrections), the theory requires new physics at a relatively low energy scale. Placing new physics at 10&nbsp;TeV, for instance, the model predicts the top quark to be significantly heavier than observed (at about 600&nbsp;GeV vs. 171&nbsp;GeV). ''Top Seesaw'' models, also based upon [[Topcolor]], circumvent this difficulty.
+The composite Higgs boson arises "naturally" in [[Topcolor]] models, that are extensions of the standard model using a hypothetical force analogous to [[quantum chromodynamics]]. To be "natural", that is, without excessive fine-tuning (i.e. to stabilize the Higgs mass from large radiative corrections), the hypothesis requires new physics at a relatively low energy scale. Placing new physics at 10&nbsp;TeV, for instance, the model predicts the top quark to be significantly heavier than observed (at about 600&nbsp;GeV vs. 171&nbsp;GeV). ''Top Seesaw'' models, also based upon [[Topcolor]], circumvent this difficulty.
-The predicted top quark mass comes into improved agreement with the fixed point if there are many additional Higgs scalars beyond the standard model. This may be indicating a rich spectroscopy of new composite Higgs fields at energy scales that can be probed with the LHC and its upgrades.<ref>{{cite journal |title=Where are the next Higgs bosons? |journal=Physical Review |year=2019 |volume=D100 |issue=1 |pages=015051 |doi=10.1103/PhysRevD.100.015051 |arxiv=1904.04257 |last1=Hill |first1=Christopher T. |last2=Machado |first2=Pedro |last3=Thomsen |first3=Anders |first4=Jessica |last4=Turner |bibcode=2019PhRvD.100a5051H|s2cid=104291827 }}</ref><ref>{{cite journal |title=Scalar Democracy|journal=Physical Review D |year=2019 |volume=100 |issue=1 |pages=015015 |doi=10.1103/PhysRevD.100.015015 |arxiv=1902.07214 |last1=Hill |first1=Christopher T. |last2=Machado |first2=Pedro |last3=Thomsen |first3=Anders |first4=Jessica |last4=Turner |bibcode=2019PhRvD.100a5015H|s2cid=119193325 }}</ref>
+The predicted top quark mass would come into improved agreement with the fixed point if there are many additional Higgs scalars beyond the standard model. This may be indicating a rich spectroscopy of new composite Higgs fields at energy scales that can be probed with the LHC and its upgrades.<ref>{{cite journal |title=Where are the next Higgs bosons? |journal=Physical Review |year=2019 |volume=D100 |issue=1 |pages=015051 |doi=10.1103/PhysRevD.100.015051 |arxiv=1904.04257 |last1=Hill |first1=Christopher T. |last2=Machado |first2=Pedro |last3=Thomsen |first3=Anders |first4=Jessica |last4=Turner |bibcode=2019PhRvD.100a5051H|s2cid=104291827 }}</ref><ref>{{cite journal |title=Scalar Democracy|journal=Physical Review D |year=2019 |volume=100 |issue=1 |pages=015015 |doi=10.1103/PhysRevD.100.015015 |arxiv=1902.07214 |last1=Hill |first1=Christopher T. |last2=Machado |first2=Pedro |last3=Thomsen |first3=Anders |first4=Jessica |last4=Turner |bibcode=2019PhRvD.100a5015H|s2cid=119193325 }}</ref>
-The general idea of a composite Higgs boson, connected in a fundamental way to the top quark, remains compelling, though the full details may not yet be understood.
 == See also ==