Top quark condensate
Encyclopedia
In particle physics
, the top quark condensate theory is an alternative to the Standard Model
in which a fundamental 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 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.
theory, a quark is described by a Dirac spinor, which can be thought of as a pair of Weyl spinors describing the left-handed (negative chirality
) and the right-handed (positive chirality) quark.
The relevant fields forming the top quark condensate are
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
composite scalar field, which forms a fermion condensate, which subsequently breaks
the electroweak and hypercharge
symmetry into electromagnetism
.
in a series of talks
and then elucidated by Vladimir Miransky, Masaharu Tanabashi, and Koichi Yamawaki in their 1989 paper 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 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 Quark and Lepton Masses from Renormalization Group Fixed Points.
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
effects of superstrong irrelevant operators.
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 corrections), 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 LHC
.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, the top quark condensate theory is an alternative to the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
in which a fundamental scalar
Scalar (physics)
In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...
Higgs field is replaced by a composite field
Composite field
In quantum field theory, a composite field is a field defined in terms of other more "elementary" fields. It might describe a composite particle or it might not. It might be local, or it might be nonlocal...
composed of the top quark
Top quark
The top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin-, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
and its antiquark. These are bound by a four-fermion interaction, analogous to Cooper pairs in a BCS superconductor
BCS theory
BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
and nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
s in the Nambu-Jona-Lasinio model
Nambu-Jona-Lasinio model
In quantum field theory, the Nambu–Jona-Lasinio model is a theory of nucleons and mesons constructed from interacting Dirac fermions with chiral symmetry which parallels the construction of Cooper pairs from electrons in the BCS theory of superconductivity...
. The top quark condenses because its measured mass is approximately 173 GeV
GEV
GEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...
(comparable to the electroweak scale), and so its Yukawa coupling is of order unity, yielding the possibility of strong coupling dynamics.
Relevant matter content
In group representationGroup representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication...
theory, a quark is described by a Dirac spinor, which can be thought of as a pair of Weyl spinors describing the left-handed (negative chirality
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
) and the right-handed (positive chirality) quark.
The relevant fields forming the top quark condensate are
- The left-handed top quarkTop quarkThe top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin-, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
, belonging to a
representation; - The left-handed antitop antiquark, belonging to
representation.
In these groups, the left number refers to SU(3) of Quantum chromodynamics
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
, whereas the second denotes the representation under SU(2). The subscript labels the hypercharge
Hypercharge
In particle physics, the hypercharge Y of a particle is related to the strong interaction, and is distinct from the similarly named weak hypercharge, which has an analogous role in the electroweak interaction...
.
The top and antitop quark form a bound state
Bound state
In physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space...
described by a
composite scalar field, which forms a fermion condensate, which subsequently breaksSpontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
the electroweak and hypercharge
Hypercharge
In particle physics, the hypercharge Y of a particle is related to the strong interaction, and is distinct from the similarly named weak hypercharge, which has an analogous role in the electroweak interaction...
symmetry into electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
.
History
This model predicts how the electroweak scale may match the top quark mass. The idea was first described by Yoichiro NambuYoichiro Nambu
is a Japanese-born American physicist, currently a professor at the University of Chicago. Known for his contributions to the field of theoretical physics, he was awarded a one-half share of the Nobel Prize in Physics in 2008 for the discovery of the mechanism of spontaneous broken symmetry in...
in a series of talks
and then elucidated by Vladimir Miransky, Masaharu Tanabashi, and Koichi Yamawaki in their 1989 paper 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
William A. Bardeen
William Allen Bardeen is an American theoretical physicist at the Fermi National Accelerator Laboratory. He is the son of John Bardeen and Jane Maxwell Bardeen....
, Christopher T. Hill
Christopher T. Hill
Christopher T. Hill is a theoretical physicist at the Fermi National Accelerator Laboratory. He did undergraduate work in physics at M.I.T. , and graduate work at Caltech...
, and Manfred Lindner
Manfred Lindner
Manfred Lindner is a German physicist and director at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany.-Life and Scientific Work:...
in the article 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
Infrared fixed point
In physics, an infrared fixed point is a set of coupling constants, or other parameters that evolve from initial values at very high energies , to fixed stable values, usually predictable, at low energies...
" for
the top quark Higgs-Yukawa coupling, proposed in 1981 by
Hill in the paper Quark and Lepton Masses from Renormalization Group Fixed Points.
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
effects of superstrong irrelevant operators.
Generalizations
Top condensation arises naturally inTopcolor
Topcolor
In theoretical physics, Topcolor is a model of dynamical electroweak symmetry breaking in which the top quark and anti-top quark form a top quark condensate and act effectively like the Higgs boson. This is analogous to the phenomenon of superconductivity....
models, that are extensions of the standard model in analogy to Quantum Chromodynamics
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
.
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 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
Topcolor
In theoretical physics, Topcolor is a model of dynamical electroweak symmetry breaking in which the top quark and anti-top quark form a top quark condensate and act effectively like the Higgs boson. This is analogous to the phenomenon of superconductivity....
,
circumvent this difficulty. These theories will be tested at the LHC
Large Hadron Collider
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
.
See also
- Bose-Einstein condensation
- Fermion condensate
- Hierarchy problemHierarchy problemIn theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...
- Technicolor (physics)Technicolor (physics)Technicolor theories are models of physics beyond the standard model that address electroweak symmetry breaking, the mechanism through which elementary particles acquire masses...
- TopcolorTopcolorIn theoretical physics, Topcolor is a model of dynamical electroweak symmetry breaking in which the top quark and anti-top quark form a top quark condensate and act effectively like the Higgs boson. This is analogous to the phenomenon of superconductivity....