Little Higgs
Encyclopedia
In particle physics
, little Higgs models are based on the idea that the Higgs boson
is a pseudo-Goldstone boson
arising from some global symmetry
breaking at a TeV energy scale. The main goal of little Higgs models is to use the spontaneous breaking of such approximate global symmetries to stabilize the mass of the Higgs boson(s) responsible for electroweak symmetry breaking.
Although the idea was first suggested in the 1970s, a viable model was only constructed by Nima Arkani-Hamed
, Andy Cohen, and Howard Georgi
in the spring of 2001. The idea was explored further by Nima Arkani-Hamed, Andy Cohen, Thomas Gregoire, and Jay Wacker in the spring of 2002. Also in 2002, several other papers appeared that refined the ideas of little Higgs theories, notably the Littlest Higgs by Nima Arkani-Hamed, Andy Cohen, Emmanuel Katz, and Ann Nelson
.
Little Higgs theories were an outgrowth of dimensional deconstruction
. In these theories, the gauge group has the form of a direct product
of several copies of the same factor, for example
. Each 
factor may be visualised as the 
group living at a particular point along an additional dimension
of space. Consequently, many virtues of extra-dimensional
theories may be reproduced even though the little Higgs theory is 3+1-dimensional. The little Higgs models are able to predict a naturally-light Higgs particle.
The main idea behind the little Higgs models is that the one-loop contribution to the tachyonic Higgs boson mass coming from the top quark cancels (the other one-loop contributions are small enough that they don't really matter; the top Yukawa coupling is huge (because related to its mass) and all the other Yukawa couplings and gauge couplings are small). The reason is that, simplifying, a loop is proportional to the coupling constant (following the example above) of one of the
groups. Because of the symmetries of the theory the contributions cancel until you have a two-loop contribution involving both groups. This protects the Higgs boson mass for about one order of magnitude, which is good enough to evade many of the precision electroweak constraints.
In 2005 Martin Schmaltz and David Tucker-Smith posted on arXiv.org a pedagogical review on Little Higgs models.
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...
, little Higgs models are based on the idea that the Higgs boson
Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
is a pseudo-Goldstone boson
Pseudo-Goldstone boson
Pseudo-Goldstone bosons arise in a quantum field theory with both spontaneous and explicit symmetry breaking. The controlling approximate symmetries, if they were exact, would be spontaneously broken , and would thus engender massless Goldstone bosons. The additional explicit symmetry breaking...
arising from some global symmetry
Global symmetry
A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.-See also:...
breaking at a TeV energy scale. The main goal of little Higgs models is to use the spontaneous breaking of such approximate global symmetries to stabilize the mass of the Higgs boson(s) responsible for electroweak symmetry breaking.
Although the idea was first suggested in the 1970s, a viable model was only constructed by Nima Arkani-Hamed
Nima Arkani-Hamed
Nima Arkani-Hamed is a leading Canadian American theoretical physicist with interests in high-energy physics, string theory and cosmology....
, Andy Cohen, and Howard Georgi
Howard Georgi
Howard Mason Georgi III, born January 6, 1947 in San Bernardino, California, is Harvard College Professor and Mallinckrodt Professor of Physics at Harvard University...
in the spring of 2001. The idea was explored further by Nima Arkani-Hamed, Andy Cohen, Thomas Gregoire, and Jay Wacker in the spring of 2002. Also in 2002, several other papers appeared that refined the ideas of little Higgs theories, notably the Littlest Higgs by Nima Arkani-Hamed, Andy Cohen, Emmanuel Katz, and Ann Nelson
Ann Nelson
This article is for Ann Elizabeth Nelson the physicist, not actress Ann Nelson who played Mrs. Berg on Fame . Ann Elizabeth Nelson is a particle physicist at the University of Washington. She was a student of Howard Georgi and has been a member of the university's Particle Theory Group since 1994...
.
Little Higgs theories were an outgrowth of dimensional deconstruction
Dimensional deconstruction
In theoretical physics, dimensional deconstruction is a method to construct d-dimensional theories that behave as higher-dimensional theories in a certain range of energies...
. In these theories, the gauge group has the form of a direct product
Direct product of groups
In the mathematical field of group theory, the direct product is an operation that takes two groups and and constructs a new group, usually denoted...
of several copies of the same factor, for example
. Each factor may be visualised as the group living at a particular point along an additional dimensionDimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
of space. Consequently, many virtues of extra-dimensional
Extra dimensions
Several speculative physical theories have introduced extra dimensions of space for various reasons:*Kaluza-Klein theory introduces extra dimensions to explain the fundamental forces other than gravity ....
theories may be reproduced even though the little Higgs theory is 3+1-dimensional. The little Higgs models are able to predict a naturally-light Higgs particle.
The main idea behind the little Higgs models is that the one-loop contribution to the tachyonic Higgs boson mass coming from the top quark cancels (the other one-loop contributions are small enough that they don't really matter; the top Yukawa coupling is huge (because related to its mass) and all the other Yukawa couplings and gauge couplings are small). The reason is that, simplifying, a loop is proportional to the coupling constant (following the example above) of one of the
groups. Because of the symmetries of the theory the contributions cancel until you have a two-loop contribution involving both groups. This protects the Higgs boson mass for about one order of magnitude, which is good enough to evade many of the precision electroweak constraints.In 2005 Martin Schmaltz and David Tucker-Smith posted on arXiv.org a pedagogical review on Little Higgs models.