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 SU(2) × SU(2). Each SU(2) factor may be visualised as the SU(2) group living at a particular point along an additional dimension of space. Consequently, many virtues[which?] of extra-dimensional[disambiguation needed] 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 SU(2) 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.
- Steven Weinberg, "Approximate Symmetries and Pseudo-Goldstone Bosons", Physical Review Letters 29:1698 (1972).
- Howard Georgi and A. Pais, "Calculability and naturalness in gauge theories", Physical Review D10:539 (1974).
- Howard Georgi and A. Pais, "Vacuum symmetry and the pseudo-Goldstone phenomenon", Physical Review D12:508 (1975).
- Nima Arkani-Hamed, Andrew G. Cohen, Howard Georgi, "Electroweak symmetry breaking from dimensional deconstruction", Physics Letters B513:232 (2001).
- Nima Arkani-Hamed, Andrew G. Cohen, Thomas Gregoire, Jay G. Wacker, "Phenomenology of electroweak symmetry breaking from theory space", JHEP 0208:020 (2002).
- N. Arkani-Hamed, A. G. Cohen, E. Katz, A. E. Nelson, "The Littlest Higgs", JHEP 0207:034 (2002).
- Martin Schmaltz and David Tucker-Smith, "Little Higgs Review", Ann.Rev.Nucl.Part.Sci.55:229-270,2005.