Supersymmetry and the LHC Inverse Problem

TL;DR

This work tackles the inverse problem of deducing underlying theory from LHC signatures in the MSSM framework. By simulating a large MSSM parameter space and mapping to 1808 signatures, the authors show the inverse map comprises a finite set of disconnected islands (degeneracies) due to discrete electroweak-ino ambiguities, with an effective signature-space dimensionality around 5–6. They classify degeneracies into Flippers, Sliders, and Squeezers, and demonstrate that including sleptons in cascade decays substantially reduces degeneracies, highlighting the need for additional, orthogonal observables. The study provides a practical methodology for quantifying degeneracies, discusses limitations and future directions, and argues for applying the inverse-map framework to other beyond-Standard-Model theories to interpret early LHC data and guide post-discovery analyses.

Abstract

Given experimental evidence at the LHC for physics beyond the standard model, how can we determine the nature of the underlying theory? We initiate an approach to studying the "inverse map" from the space of LHC signatures to the parameter space of theoretical models within the context of low-energy supersymmetry, using 1808 LHC observables including essentially all those suggested in the literature and a 15 dimensional parametrization of the supersymmetric standard model. We show that the inverse map of a point in signature space consists of a number of isolated islands in parameter space, indicating the existence of "degeneracies"--qualitatively different models with the same LHC signatures. The degeneracies have simple physical characterizations, largely reflecting discrete ambiguities in electroweak-ino spectrum, accompanied by small adjustments for the remaining soft parameters. The number of degeneracies falls in the range 1<d<100, depending on whether or not sleptons are copiously produced in cascade decays. This number is large enough to represent a clear challenge but small enough to encourage looking for new observables that can further break the degeneracies and determine at the LHC most of the SUSY physics we care about. Degeneracies occur because signatures are not independent, and our approach allows testing of any new signature for its independence. Our methods can also be applied to any other theory of physics beyond the standard model, allowing one to study how model footprints differ in signature space and to test ways of distinguishing qualitatively different possibilities for new physics at the LHC.

Figures (30)

• Figure 1: The Inverse Map from LHC Observables to Theoretical Models. Given observed signals for physics beyond the standard model, how can we determine the underlying theoretical model?
• Figure 2: The Inverse Map in the Best and Worst of All Possible Worlds. Ideally, the image of LHC data onto parameter space would specify an unique underlying model. In the most pessimistic scenario, LHC data would suggest the physics beyond the standard model without giving us any clues as which model describes the new physics.
• Figure 3: Our Picture of the Inverse Map. In the context of low-energy supersymmetry, we find that the inverse map of LHC data consists of a number of disconnected and widely separated regions in parameter space. This indicates the presence of degeneracies---different underlying models that share the same LHC signatures.
• Figure 4: The Birthday Problem for the MSSM. We simulate $m$ models and associate each model with a bin in signature space. For $m \ll N$ it is unlikely for any given pair of models to share the same LHC signatures, but there is a statistical expectation value $N_2 \sim m^2/(2N)$ for the total number of pairs that end up in the same bin.
• Figure 5: The $(\Delta S^2, \Delta P^2)$ plot in the best of all possible worlds. The expected confidence range on model parameters is defined by the maximum value of $\Delta P^2$ at the $\Delta S^2$ corresponding to statistical fluctuations.