✎ little_higgs [Jesse Thaler]

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====== Little Higgs Models ======

//Summer 2004 - Spring 2006//

The hypothetical Higgs boson is responsible for generating masses for almost all of the fundamental Standard Model particles. For theoretical consistency, the Higgs boson must be lighter than 1 TeV, but a naïve quantum calculation suggests that the natural mass of the Higgs boson should be closer  to 10<sup>16</sup> TeV than 1 TeV, a discrepancy known as the "hierarchy problem." By far the most popular mechanism for explaining the lightness of the Higgs boson is supersymmetry (SUSY), which is based on a  new fundamental symmetry that effectively doubles the size of the Standard Model. Little Higgs theories address the hierarchy problem in a different way, postulating that the Higgs boson is not a fundamental particle but a composite particle. 

===== The Bestest Little Higgs =====

  * **The Bestest Little Higgs**.\\ Martin Schmaltz, Daniel Stolarski, Jesse Thaler. \\ [[http://www.arxiv.org/abs/1006.1356|arXiv:1006.1356]].

===== Collective Quartics and Dangerous Singlets in Little Higgs =====

  * **Collective Quartics and Dangerous Singlets in Little Higgs.**\\ Martin Schmaltz and Jesse Thaler.\\ [[http://www.iop.org/EJ/abstract/1126-6708/2009/03/137|JHEP 0903:137 (2009)]], [[http://www.arxiv.org/abs/0812.2477|arXiv:0812.2477]].

===== Little M-theory  =====

{{ research:littletech.gif|A Moose Model of the Universe}}

//Fall 2005 - Spring 2006//

In string theory, "M-theory" refers to a mother/master/membrane/matrix theory that interpolates between the Type 1 string, Type 2A string, Type 2B string, heterotic //SO(32)// string, heterotic //E8×E8// string, and 11-dimensional supergravity.  M-theory reveals that string theory has a much richer structure than any one stringy limit.

In little Higgs model building, there were many seemingly different models for a composite Higgs, such as the simple group little higgs, the minimal moose little higgs, the holographic higgs, and little technicolor.  We showed that in analogy with "M-theory", there was a "little m-theory" whose limits reproduced all known little Higgs models but which has a richer particle structure than any individual little Higgs models.  

In our context, "m" also stood for "moose", an antlered-looking diagram that encodes information about particle theories in a compact and intuitive way.

  * **Little M-theory**.\\ Hsin-Chia Cheng, Jesse Thaler, and Lian-Tao Wang.\\  [[http://www.iop.org/EJ/abstract/1126-6708/2006/09/003|JHEP 0609:003 (2006)]], [[http://arxiv.org/abs/hep-ph/0607205|hep-ph/0607205]].

===== (Reverse) Engineering Vacuum Alignment =====

//Spring 2006//

The vacuum refers to the lowest attainable energy configuration of a system.  An important fact about the vacuum is that it need not have the same degree of symmetry as the laws of physics that govern the system, a possibility referred to as spontaneous symmetry breaking.

When a system has multiple different symmetries active at the same time, spontaneous symmetry breaking can lead to the question of vacuum alignment.  That is, at the classical level there can be many different stable alignments between the different symmetry patterns, but quantum effects usually choose a preferred direction in symmetry breaking space.

With Clifford Cheung, we found a class of theories for which one could choose different vacuum alignments at will by making different assumptions about the ultraviolet physics.  This allowed us to consider naively unstable low energy vacuum structures which are nevertheless stable because of novel ultraviolet physics.

  * **(Reverse) Engineering Vacuum Alignment**.\\ Clifford Cheung and Jesse Thaler.\\  [[http://www.iop.org/EJ/abstract/1126-6708/2006/08/016|JHEP 0608:016 (2006)]], [[http://arxiv.org/abs/hep-ph/0604259|hep-ph/0604259]].

===== Little Technicolor =====

//Spring 2005//

One of the remarkable facts about physics is that different models of the ultraviolet can yield the same infrared phenomena. This fact explains why we don't say that Newtonian gravity is wrong just because we know about Einstein's general relativity, or why we still teach Maxwell's electrodynamics even though electromagnetism is replaced by the electroweak interactions at high energies. Newton's and Maxwell's idea are still relevant for low energy physics, and we shouldn't be surprised that at sufficiently high energies or sufficiently short distances, their theories are superseded by more complete descriptions. 

This ultraviolet/infrared separation is the reason we need to build ever more powerful particle accelerators to probe the high energy frontier. We cannot figure out the details of high energy physics simply by doing really accurate experiments at low energies; there will remain a fundamental ambiguity unless we actually probe high energies directly. Indeed, the Large Hadron Collider (LHC) being built at CERN in Geneva is trying to figure out what theory replaces the Standard Model of particle physics. Of course, nothing we will learn at the LHC will invalidate the successes of the Standard Model; like Newton's and Maxwell's theories, the Standard Model will still be a very accurate description of physics at sub-LHC energies.

Another aspect of ultraviolet/infrared separation is that if a theoretical model has desirable infrared properties but questionable ultraviolet properties, then there is very likely a different ultraviolet model with the same infrared physics. I studied this possibility in the context of Little Higgs (LH) theories. By deconstructing the AdS/CFT dual of a certain LH theory, I not only reproduced the known formalisms of CCWZ and HLS, but I also found that the model could actually arise from a scaled-up version of QCD (the theory that describes how quarks form protons and neutrons).

The original title of this work was a bizarre acronym soup: A(QCd)S/(CCWZ)FT HLS/LH. Scaled-up QCD is also generically referred to as technicolor (the "C" in QCD stands for "chromo", i.e. color), hence the final title "Little Technicolor".

  * **Little Technicolor**.\\  Jesse Thaler.\\ [[http://www.iop.org/EJ/abstract/1126-6708/2005/07/024|JHEP 0507:024 (2005)]], [[http://www.arXiv.org/abs/hep-ph/0502175|hep-ph/0502175]].

===== A Little Higgs in AdS Space =====

//Summer/Fall 2004//

In the theoretical high energy physics community, there are two main avenues of contemporary research. The first is loosely called String Theory, where theorists explore the properties of UV complete theories (i.e. theories that make sense up to arbitrarily large energies). The second is usually referred to as Phenomenology, where theorists construct models that may only be valid up to a finite energy but which have the power to predict what we will see at the next generation of particle accelerators.

One of the most interesting ideas coming out of String Theory is the so-called AdS/CFT correspondence, which is a proposed duality between a non-gravitational theory in four dimensions (CFT) and a gravitational theory in five dimensions (AdS). At first, it might seem like such a duality would have no phenomenological implications, because our universe appears to be a gravitational theory in four dimensions. In turns out, however, that by introducing "branes" into the AdS picture, the dual theory is an approximate CFT with gravity, something that has the potential to model our universe.

More interestingly, with a bit of ingenuity the brane-AdS theory can be modified to model the Higgs mechanism, the central feature of the Standard Model of particle physics. Because the Standard Model is a phenomenological model, it is not UV complete, but via the AdS/CFT correspondence, we see hints that the Standard Model might be embedded in an interesting UV complete framework.

With fellow grad student Itay Yavin, we apply the AdS/CFT correspondence to the "Littlest Higgs", one of many models of the Higgs mechanism. The Littlest Higgs has the advantage of being an economical extension of Standard Model (unlike the Supersymmetric Standard Model which introduces many more particle types) and of being a beautiful example of the Higgs boson arising from (and later triggering) spontaneous symmetry breaking. In other word, we have constructed a UV complete extension of the Standard Model which draws on some of the most fascinating ideas from both String Theory and Phenomenology.

  * **The Littlest Higgs in Anti-de Sitter Space**.\\ Jesse Thaler and Itay Yavin.\\  [[http://www.iop.org/EJ/abstract/1126-6708/2005/08/022/|JHEP 0508:022 (2005)]], [[http://www.arXiv.org/abs/hep-ph/0501036|hep-ph/0501036]].