✎ lhc_inverse [Jesse Thaler]

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====== The LHC Inverse Problem ======

We eagerly await data from the Large Hadron Collider (LHC) and we anticipate that LHC data will provide hints for what physics lies beyond the Standard Model (BSM).  In studies that explore how accurately the LHC can determine the parameters of a specific BSM scenario, it is found that the LHC can often achieve a remarkable level of precision.  

However, this seems to contradict the well-known fact that there are only a limited number of observables that the LHC can measure.  In particular, if a BSM scenario predicts the production of dark matter candidates at the LHC, then these dark matter particles pass invisibly through the detector, resulting in a fundamental loss of information.

How it is then that we can measure the parameters of a given theory very accurately even though there are relatively few measurements we can make?  The answer seems to be that the loss of information at the LHC results in //discrete// ambiguities in mapping LHC data back to theoretical models.  That is, even if one model fits the data very well with small error bars, there will be a (possibly large) number of other models that also fit the data equally well.  Moreover, precisely because the error bars are small, these other "degenerate" models are hard to find through brute force scanning.

The presence of discrete ambiguities in interpreting LHC data is known as the LHC Inverse Problem.  It is an "inverse problem" because it is well-known how to solve the forward problem of determining the potential LHC signatures for a particular model, while in real life were are trying to invert this process and determine the underlying model from a set of measured LHC signatures.  Because these ambiguities are discrete, it seems likely that simple observables might be able to resolve at least some of these degeneracies.  This inspires us to search for new methods to analyze LHC data.

===== MARMOSET =====

//Fall 2006 - Spring 2007//

  * **MARMOSET: The Path from LHC Data to the New Standard Model via On-Shell Effective Theories**.\\  Nima Arkani-Hamed, Bruce Knuteson, Stephen Mrenna, Philip Schuster, Jesse Thaler, Natalia Toro, and Lian-Tao Wang. \\ [[http://www.arxiv.org/abs/hep-ph/0703088|hep-ph/0703088]]

===== SUSY and the LHC Inverse Problem  =====

//Summer/Fall 2005//

The Minimal Supersymmetric Standard Model (MSSM) is one of the leading candidates for a theory beyond the standard model.  The MSSM predicts a new supersymmetric partner particle for every standard model particle, effectively doubling the known number of fundamental states.  

In principle, the spectrum of these partner states can yield information about the ultraviolet structure of the standard model.  However, we found that given a generic strategy for analyzing LHC data, there are often discrete ambiguities in trying to determine the pattern of supersymmetric states.  Moreover, these ambiguities are difficult to identify, because they correspond to drastically rearranging the MSSM spectrum.

This study offered an explicit confirmation of the LHC Inverse Problem.  

  * **Supersymmetry and the LHC Inverse Problem**.\\ Nima Arkani-Hamed, Gordon L. Kane, Jesse Thaler, and Lian-Tao Wang.\\  [[http://www.iop.org/EJ/abstract/1126-6708/2006/08/070|JHEP 0608:070 (2006)]] [[http://www.arXiv.org/abs/hep-ph/0512190|hep-ph/0512190]].

===== LHC Olympics =====

//Summer 2005 - Summer 2007//

The LHC Olympics were a series of four workshops where theorists attempted to determine the underlying theoretical structure from pseudo-LHC "blackbox" data.  Using crude but semi-realistic data analysis methods, we learned firsthand the challenges of interpreting ambiguous data, and developed an intuition for the LHC Inverse Problem.