Naturalness, Supersymmetry and Implications for LHC and Dark Matter

TL;DR

This paper explores the structure of the Hyperbolic Branch in radiative electroweak symmetry breaking, identifying focal regions that impact LHC searches and dark matter constraints, with implications for supersymmetric models.

Contribution

It classifies the focal regions within the Hyperbolic Branch and analyzes their phenomenological implications for LHC and dark matter constraints.

Findings

Focal Point lies on the boundary of a Focal Curve.

LHC-7 constraints deplete the Focal Point region.

Focal Curves and Surfaces remain largely unaffected by current LHC constraints.

Abstract

It is shown that the Hyperbolic Branch of the radiative electroweak symmetry breaking contains in it three regions: the Focal Point, Focal Curves, and Focal Surfaces. Further, the Focal Point is shown to lie on the boundary of a Focal Curve. These focal regions allow for a small $\mu$ while scalar masses can become large and may lie in the several TeV region. It is shown that for the mSUGRA model the current LHC-7 constraint depletes the Focal Point region while regions on Focal Curves and Focal Surfaces remain largely intact. The LHC implications for models which lie on Focal Curves are briefly discussed as well as the implications of dark matter constraints for the Focal Point, Focal Curves and Focal Surfaces are discussed.