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{{Short description|Hypothetical composite Higgs model}}
In [[particle physics]], the '''top quark condensate''' theory is an alternative to the [[Standard Model]] in which a fundamental [[scalar (physics)|scalar]] [[Higgs field]] is replaced by a [[composite field]] composed of the [[top quark]] and its [[antiquark]]. These are bound by a [[four-fermion interaction]], analogous to [[Cooper pairs]] in a [[BCS theory|BCS superconductor]] and [[nucleon]]s in the [[Nambu-Jona-Lasinio model]]. The top quark condenses because its measured mass is approximately 173 [[GeV]] (comparable to the [[electroweak scale]]), and so its [[Yukawa coupling]] is of order unity, yielding the possibility of strong coupling dynamics.
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 [[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.

==Relevant matter content==

In [[group representation]] theory, a quark is described by a [[Dirac spinor]], which can be thought of as a pair of [[Weyl spinor]]s describing the left-handed (negative [[chirality (physics)|chirality]]) and the right-handed (positive chirality) quark.

The relevant fields forming the top quark condensate are
* The left-handed [[top quark]], belonging to a <math>(3,2)_{1\over 6}</math> representation;
* The left-handed antitop antiquark, belonging to <math>(\bar{3},1)_{-{2\over 3}}</math> representation.

In these groups, the left number refers to ''SU(3)'' of [[Quantum chromodynamics]], whereas the second denotes the representation under ''SU(2)''. The subscript labels the [[hypercharge]].

The top and antitop quark form a [[bound state]] described by a <math>(1,2)_{-{1\over 2}}</math> composite scalar field, which forms a [[fermion condensate]], which subsequently [[spontaneous symmetry breaking|breaks]] the [[electroweak]] and [[hypercharge]] symmetry into [[electromagnetism]].


==History==
==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 [[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 "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.
This model predicts how the [[electroweak scale]] may match the top quark mass. The idea was first described by [[Yoichiro Nambu]] in a series of talks
and then elucidated by Vladimir Miransky, Masaharu Tanabashi, and Koichi Yamawaki in their 1989 paper [http://www-library.desy.de/cgi-bin/spiface/find/hep/www?j=MPLAE,A4,1043 Is the t Quark Responsible for the Mass of W and Z Bosons?], in which they attempt to set the parameters so that the four-fermion interaction will have an [[ultraviolet fixed point]]. A year later it was developed into a more predictive scheme, based upon the renormalization group, by
[[William A. Bardeen]], [[Christopher T. Hill]], and [[Manfred Lindner]] in the article [http://www-library.desy.de/cgi-bin/spiface/find/hep/www?j=PHRVA,D41,1647 Minimal Dynamical Symmetry Breaking of the Standard Model] in which the authors do not attempt to render the theory [[renormalizable]].
Top quark condensation is
essentially based upon the "quasi-[[infrared fixed point]]" for
the top quark Higgs-Yukawa coupling, proposed in 1981 by
Hill in the paper [http://www-library.desy.de/cgi-bin/spiface/find/hep/www?j=PHRVA,D24,691 Quark and Lepton Masses from Renormalization Group Fixed Points].


==Future==
In 1991, [[Anna Hasenfratz]] and [[Peter Hasenfratz]] ''et al.'' claimed the model is approximately equivalent to a fundamental Higgs scalar field. This equivalence is exact in the limit of the large number of colors. However, even for a finite number of colors, it was claimed that new predictions cannot be derived from a top quark condensate (if the cutoff scale is high). This, however, presumes a bizarre notion of physical compositeness, in which a boundstate could be essentially decoupled from its constituents near its compositeness scale by the
⚫
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.
effects of superstrong irrelevant operators.


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>
==Generalizations==

Top condensation arises naturally in
[[Topcolor]] models, that are extensions of the standard model in analogy to [[Quantum Chromodynamics]].
⚫
To be natural, without excessive fine-tuning (i.e. to stabilize the Higgs mass from large [[radiative correction]]s), the theory 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. These theories will be tested at the [[Large Hadron Collider|LHC]].


== See also ==
== See also ==
* [[Bose-Einstein condensation]]
* [[Bose–Einstein condensation]]
* [[Fermion condensate]]
* [[Fermion condensate]]
* [[Hierarchy problem]]
* [[Hierarchy problem]]
* [[Technicolor (physics)]]
* [[Technicolor (physics)]]
* [[Topcolor]]


==References==
==References==
{{Reflist|25em}}
* ''Dynamical electroweak symmetry breaking with large anomalous dimension and t quark condensate.'' Vladimir A. Miransky, Masaharu Tanabashi, and Koichi Yamawaki, Published in Phys. Lett., B221:177, 1989.

* ''Minimal Dynamical Symmetry Breaking of the Standard Model.'' [[William A. Bardeen]], [[Christopher T. Hill]], [[Manfred Lindner]], Published in Phys.Rev. D41:1647, 1990.
{{Quantum field theories}}


[[Category:Particle physics]]
[[Category:Physics beyond the Standard Model]]

Latest revision as of 08:02, 26 October 2024

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

[edit]

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

[edit]

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]

See also

[edit]

References

[edit]
  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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