Multi-TeV Scalars are Natural in Minimal Supergravity

TL;DR

For a top quark mass fixed to its measured value, there are natural regions of minimal supergravity parameter space where all squarks, sleptons, and heavy Higgs scalars have masses far above 1 TeV and are possibly beyond the reach of the Large Hadron Collider at CERN.

Abstract

For a top quark mass fixed to its measured value, we find natural regions of minimal supergravity parameter space where all squarks, sleptons, and heavy Higgs scalars have masses far above 1 TeV and are possibly beyond the reach of the Large Hadron Collider at CERN. This result is simply understood in terms of ``focus point'' renormalization group behavior and holds in any supergravity theory with a universal scalar mass that is large relative to other supersymmetry breaking parameters. We highlight the importance of the choice of fundamental parameters for this conclusion and for naturalness discussions in general.

Figures (3)

• Figure 1: Contours of constant fine-tuning $c$ (solid) and $m_{\tilde{u}_L}$ in GeV (dotted) in the $(m_0, M_{1/2})$ plane for $\tan\beta = 10$, $A_0=0$, and $\mu>0$. The shaded regions are excluded by the requirement that the lightest supersymmetric particle be neutral (top left) and by the chargino mass limit of 90 GeV (bottom and right).
• Figure 2: The RG evolution of $m_{H_u}^2$ for fixed $M_{1/2} = 200$ GeV, $A_0=0$, $\tan\beta=10$, $\mu>0$, $m_t = 175$ GeV, and several values of $m_0$ (shown, in GeV). The RG behavior of $m_{H_u}^2$ exhibits a focus point near the weak scale, where $m_{H_u}^2$ takes its weak scale value $\sim -(300\ \rm{ GeV})^2$, irrespective of $m_0$.
• Figure 3: Contours of $\mu$ (solid) and $m_h$ (dotted) in GeV for input parameters as in Fig. \ref{['fig:finetune']}.