✎ natural_unnatural [Jesse Thaler]

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====== (Un)natural Model Building ======

The principle of naturalness asserts that quantum corrections should be not much larger than semi-classical expectations.  Naturalness is not needed for the theoretical consistency of particle physics, but in the past, apparent breakdowns of naturalness have often been resolved by discovering new natural theories of the universe.  

Today, the most important application of naturalness is to the hypothetical Higgs boson.  In the standard model, the quantum corrections to the mass of the Higgs are 19 orders of magnitude larger than the semi-classical expectation, a problem known as the "hierarchy problem".  This suggests that there should be a natural extension of the standard model in which the quantum corrections are better under control.  Supersymmetry is the most popular natural extension of the standard model, and in supersymmetry, the quantum corrections to the Higgs mass are regulated by additional supersymmetric partner particles.

However, we already know of one example where the principle of naturalness has failed: the so-called cosmological constant.  The cosmological constant characterizes the energy density of the vacuum, and in our universe, the measured value of the cosmological constant is 120 orders of magnitude different from the quantum corrected value.  Moreover, we have no evidence for any new phenomena that could resolve this spectacular failure of naturalness.

Therefore, it is worth exploring the naturalness tension in the Higgs sector, to see how the structure of TeV scale models can change depending on whether the is a natural or unnatural solution to the hierarchy problem. 

===== The Dark Top =====

//Fall 2007 - Spring 2008//

Apart from the Higgs, the two most anticipated particles for discovery at the LHC are a weakly-interacting dark matter candidate (WIMP) and a top partner.  WIMPs are new stable particles that are hypothesized to compose 80 percent of the matter in the universe, and the top partner is a hypothetical particle that controls quantum corrections to the Higgs boson properties.  In most natural models of BSM physics, the WIMP and the top partner are distinct.  With David Poland, we showed how to build a natural model where the WIMP and the top partner could be the //same// particle, a novel possibility with interesting LHC implications.

  * **The Dark Top**.\\ David Poland and Jesse Thaler.\\ [[http://www.arxiv.org/abs/0808.1290|arXiv:0808.1290]].

===== Flavor at the LHC =====

//Spring 2007//

Though the most pressing tensions in the Standard Model revolve around naturalness, there are other tensions that while technically natural are still worthy of study.  One of those tensions is related to "flavor", referring to the six flavors of quarks in Standard Model: down, up, strange, charm, bottom, and top.  Flavor violation occurs when one flavor of quark turns into a different flavor, and the Standard Model predicts a small degree of flavor violation.

To date, experiments have found that the only flavor violation is the minimal flavor violation predicted by the Standard Model.  However, most beyond the Standard Model proposals predict more than just minimal flavor violation.  Given that we have independent motivations for BSM physics, why is it is that minimal flavor violation appears to hold?  It must be that BSM physics respects SM flavor symmetries to a very good approximation.

While the LHC is not the ideal experiment to study flavor-violating effects, we found that certain classes of minimal-flavor-violating BSM theories could be tested at the LHC.  We also identified some novel symmetry patterns that naively appear to violate flavor symmetries, but do indeed predict minimal flavor violation.

  * **Probing Minimal Flavor Violation at the LHC**.\\  Yuval Grossman, Yosef Nir, Jesse Thaler, Tomer Volansky, and Jure Zupan. \\ [[http://link.aps.org/abstract/PRD/v76/e096006|Phys. Rev. D76:096006 (2007)]], [[http://www.arxiv.org/abs/0706.1845|arXiv:0706.1845]].

===== Natural/Unnatural =====

//Fall 2006 - Winter 2007//

In addition to the Higgs boson, another highly anticipated particle is a dark matter candidate.  From observation, we know that 25% of the universe is composed of matter (with the other 75% being the cosmological constant), but the majority of the matter is "dark", meaning it does not interact strongly with photons (or any other standard model particle).  One of the leading candidates for the dark matter is a weakly-interacting massive particle (WIMP), and the WIMP scenario works best if the WIMP has a mass close to the Higgs mass.

Why should the WIMP mass and Higgs mass be similar?  In natural theories, the typical logic goes as follows:  to solve the hierarchy problem in the Higgs sector, we need a bunch of new particles at the TeV scale, and one of those new particles could be a WIMP.  The fact that both the Higgs and the WIMP are both within the LHC reach is a secondary consequence of naturalness.

But in unnatural theories, there is completely different logic possible:  the Higgs and the WIMP could be related by a symmetry, and while it is unnatural for the Higgs mass to be near the TeV scale, if the Higgs happens to be at the TeV scale, then the WIMP will come along for ride.  With this logic, the proximity of the Higgs and the WIMP is a primary consequence of a new symmetry, and has nothing to do with naturalness.

With Aaron Pierce, we constructed an explicit model using this unnatural logic.  Amusingly, one of the secondary consequences of the unnatural model is that it predicts a bunch of extra new particles at TeV scale with spectacular LHC signatures, completing the natural/unnatural logic reversal.

  * **Natural Dark Matter from an Unnatural Higgs Boson and New Colored Particles at the TeV Scale**.\\ Aaron Pierce and Jesse Thaler.  \\ [[http://www.iop.org/EJ/abstract/1029-8479/2007/08/026|JHEP 0708:026 (2007)]], [[http://arxiv.org/abs/hep-ph/0703056|hep-ph/0703056]].

===== Di-Higgs at Dimension Six =====

//Summer 2006//

The Higgs boson is the most anticipated new particle for potential discovery at the LHC.  In the context of the Standard Model, the properties of the Higgs are well-predicted, but the Higgs is very sensitive to additional beyond the Standard Model particles.  In most natural theories, the Higgs properties do not change dramatically, but more exotic scenarios can have large anomalous Higgs interactions.  Assuming the Higgs boson could be discovered through an ordinary single-production channel at the LHC, we studied whether anomalously large Higgs pair-production could be observed.

  * **Disentangling Dimension Six Operators through Di-Higgs Boson Production**.\\ Aaron Pierce, Jesse Thaler, and Lian-Tao Wang. \\ [[http://www.iop.org/EJ/abstract/1029-8479/2007/05/070|JHEP 0705:070 (2007)]], [[http://arxiv.org/abs/hep-ph/0609049|hep-ph/0609049]].

===== Prospects for Mirage Mediation =====

//Spring 2006//

In order for a supersymmetric extension of the standard model to be viable, supersymmetry must be broken.  Moreover, SUSY breaking must be communicated to the standard model in a way that does not introduce large modifications to the known successes of the standard model.  

Mirage mediation is one example of a SUSY breaking communication scheme, and in the literature, there was a proposed limit of mirage mediation that (if it existed) would have minimized the naturalness tension in the Higgs sector.  We showed, however, that this proposed limit was difficult to achieve in practice, and in generic mirage mediation models, there is some residual tension.

  * **Prospects for Mirage Mediation**.\\ Aaron Pierce and Jesse Thaler.\\  [[http://www.iop.org/EJ/abstract/1126-6708/2006/09/017|JHEP 0609:017 (2006)]], [[http://arxiv.org/abs/hep-ph/0604192|hep-ph/0604192]].