Diagnosing degenerate Higgs bosons at 125 GeV.

We develop diagnostic tools that would provide incontrovertible evidence for the presence of more than one Higgs boson near 125 GeV in the LHC data.

Accurate mass determinations in decay chains with missing energy.

Many beyond the standard model theories include a stable dark matter candidate that yields missing or invisible energy in collider detectors. If observed at the CERN Large Hadron Collider, we must determine if its mass and other properties (and those of its partners) predict the correct dark matter relic density. We give a new procedure for determining its mass with small error.

Escaping the large fine-tuning and little hierarchy problems in the next to minimal supersymmetric model and h --> aa decays.

We demonstrate that the next to minimal supersymmetric model can have small fine-tuning and modest top-squark mass while still evading all experimental constraints. For small tan(beta (large tan(beta), the relevant scenarios are such that there is always (often) a standard-model-like Higgs boson that decays to two lighter--possibly much lighter--Higgs pseudoscalars.