Living Dangerously with Low-Energy Supersymmetry

TL;DR

The paper reframes the SUSY hierarchy problem as a question of electroweak criticality and argues that, in a landscape of many vacua, environmental selection naturally concentrates the soft SUSY-breaking scale $M_S$ near the RG-critical line $Q_c$, producing a little but non-negligible hierarchy between $m_Z$ and $M_S$. It develops statistical and (in some sections) partial dynamical arguments to explain why near-critical spectra are statistically favored, and explores how independent scanning of the $\mu$ parameter modifies predictions for $\mu$, $\tan\beta$, and the Higgs-stop sector. The resulting phenomenology predicts a light Higgs near LEP bounds and stop masses at the TeV scale, with the spectrum and couplings clustered along the critical line, offering testable expectations for the LHC. However, the conclusions depend on the assumed priors and landscape structure, highlighting a probabilistic, rather than deterministic, path to low-energy SUSY.

Abstract

We stress that the lack of direct evidence for supersymmetry forces the soft mass parameters to lie very close to the critical line separating the broken and unbroken phases of the electroweak gauge symmetry. We argue that the level of criticality, or fine-tuning, that is needed to escape the present collider bounds can be quantitatively accounted for by assuming that the overall scale of the soft terms is an environmental quantity. Under fairly general assumptions, vacuum-selection considerations force a little hierarchy in the ratio between m_Z^2 and the supersymmetric particle square masses, with a most probable value equal to a one-loop factor.

Figures (5)

• Figure 1: The running of the Higgs mass parameter $m_2^2$ as a function of the RG scale $Q$. The top frame shows the case of a generic supersymmetric setup, leading to $|m_2^2(M_S)|=O(M_S^2)$ and $M_S\ll Q_c\ll M_P$. The bottom frame corresponds to a fine-tuned choice of soft terms, such that $|m_2^2(M_S)|\ll M_S^2$ and $M_S \simeq Q_c$.
• Figure 2: The phase diagram of the minimal supersymmetric SM, assuming a universal scalar mass $m^2$, a gaugino unified mass $M$, a Higgsino mass $\mu$, and trilinear term $A=0$, with all parameters defined at the GUT scale. The top Yukawa coupling is fixed such that $m_t=172.7$ GeV and $\tan\beta =10$ in the usual phase with electroweak breaking. Some contours are shown for masses of the lightest stop ($M_{{\tilde{t}}_1}$), the gluino ($M_{\tilde{g}}$), and the lightest chargino ($M_{\chi^+}$). The green (gray) area shows the region of parameters allowed after LEP Higgs searches.
• Figure 3: Same as fig. \ref{['fig1']}, zooming in the allowed region where the Higgs pseudoscalar mass is close to $m_Z$.
• Figure 4: The critical line separating the broken and unbroken phases. Here $\mu$ is defined at the scale $M_S$ and we have fixed the top Yukawa coupling corresponding to $m_t=172.7$ GeV for large $\tan\beta$. Scalar universality and gaugino unification is assumed with boundary conditions at the GUT scale $m^2=M^2=M_S^2$, $A=0$ and $B=0$ (solid line), $B=\sqrt{2}M_S$ (dashed line).
• Figure 5: The solid lines are the boundaries of the regions of Higgs mass ($m_h$) and lightest stop mass ($M_{{\tilde{t}}_1}$) obtained by requiring $\ln Q_c/M_S=1/6$ and by scanning the ratios of soft parameters in the range $1/2<m^2_{\tilde{U}}/m^2_{\tilde{Q}}<2$, $0.8<A_t/m_{\tilde{Q}}<1$, $1/2<M_3^2/m^2_{\tilde{Q}}<2$, $1/10<M_{1,2}^2/m_{\tilde{Q}}^2<1$, under the constraint $M_3>200$ GeV, $M_2>100$ GeV, $M_1> 50$ GeV, for the three values of $m_t$ indicated in the figure. The purple dot-dashed line is the boundary of the analogous region obtained for $1<A_t/m_{\tilde{Q}}<3$ and $m_t=172.7$ GeV. The dashed line is the present lower bound on a SM Higgs-boson mass $m_h>114.4$ GeV.