Study of Constrained Minimal Supersymmetry

TL;DR

This study tests the viability of a Constrained Minimal Supersymmetric Standard Model (CMSSM) by enforcing gauge-coupling unification, radiative electroweak symmetry breaking, and a suite of experimental and cosmological constraints. By solving the full two-loop RGEs with accurate threshold handling and minimizing the 1-loop Higgs potential, the authors derive a self-consistent, relatively predictive parameter region (COMPASS) where sparticle spectra typically lie below ~1 TeV and the lightest neutralino is the LSP. They show that neutralino dark matter, together with relic-density and age constraints, strongly shapes the allowed spectrum and DM scenarios (CDM/MDM), while BR($b\to s\gamma$) and precision measurements like αs(mZ) provide further discriminants. The work demonstrates that most CMSSM predictions are testable at LEP II, FNAL, and future colliders, and highlights a pathway from experimental data to the underlying high-scale Lagrangian, with notable implications for Higgs physics and SUSY phenomenology.

Abstract

Taking seriously phenomenological indications for supersymmetry, we have made a detailed study of unified minimal SUSY, including effects at the few percent level in a consistent fashion. We report here a general analysis without choosing a particular unification gauge group. We find that the encouraging SUSY unification results of recent years do survive the challenge of a more complete and accurate analysis. Taking into account effects at the 5-10% level leads to several improvements of previous results, and allows us to sharpen our predictions for SUSY in the light of unification. We perform a thorough study of the parameter space. The results form a well-defined basis for comparing the physics potential of different facilities. Very little of the acceptable parameter space has been excluded by LEP or FNAL so far, but a significant fraction can be covered when these accelerators are upgraded. A number of initial applications to the understanding of the SUSY spectrum, detectability of SUSY at LEP II or FNAL, BR($b\to sγ$), Width($Z\to b\bar b$), dark matter, etc, are included in a separate section. We formulate an approach to extracting SUSY parameters from data when superpartners are detected. For small tan(beta) or large $m_top$ both $M_half$ and $M_0$ are entirely bounded from above at O(1 tev) without having to use a fine-tuning constraint.

Figures (35)

• Figure 1: Regions in the $m_t-\tan\beta$ plane consistent with bottom-tau Yukawa unification. The region bounded by the solid lines represents the region of parameter space consistent with $m_b/m_\tau=1$ at $M_X$ for $4.7\leq m_b^{\rm pole}\leq 5.1{\rm\,GeV}$. The region between the dashed lines is consistent with $m_b/m_\tau=0.9$ at $M_X$. Here we have taken the effective scale of SUSY to be $90{\rm\,GeV}$ and $\alpha_s(m_Z)=0.120$.
• Figure 2: Same as Fig. \ref{['mbone:fig']} but now with $\alpha_s(m_Z)=0.112$. Notice that the available parameter space has increased markedly.
• Figure 3: The running of the sparticle masses from the GUT scale to the electroweak scale, for a sample set of input parameters (see "Solution 3" in Table \ref{['apps:tab2']} later in this paper). The bold lines are the three soft gaugino masses, $m_{\widetilde{g}}$, $M_2$ (labelled $\widetilde{W}$) and $M_1$ (labelled $\widetilde{B}$). The light solid lines are the squark (${\tilde{q}}_L$, ${\tilde{q}}_R$, $\widetilde{t}_L$, $\widetilde{t}_R$) and slepton (${\tilde{l}}_L$, ${\tilde{l}}_R$) soft masses, where we ignore $D$-term contributions and the mixing of the stops for this figure. Finally, the dashed lines represent the soft Higgs masses, $m_1$ and $m_2$ (see Eq. \ref{['vtree:eq']}), labelled by $H_d$ and $H_u$. The onset of EWSB is signalled by $m_2^2$ going negative, which is shown on the plot as $m_2$ going negative for convenience.
• Figure 4: Plots of the ($m_{1/2},m_0$) plane showing regions excluded by lack of EWSB (labeled E), neutralino not being the LSP (L), the age of the Universe less than 10 billion years (A), $m_{\chi_1^\pm}<47{\rm\,GeV}$ (C), BR$(b\to s\gamma)>5.4\times10^{-4}$ (B), and SM-like lightest Higgs mass $m_h<60{\rm\,GeV}$ (H). We take $m_t=145{\rm\,GeV}$, ${\rm sgn}\,\mu_0=-1$, and several representative choices of $\tan\beta$ and $A_0$. In window (a) $\tan\beta=1.5$, $A_0/m_0=0$, in (b) $\tan\beta=5$, $A_0/m_0=0$, in (c) $\tan\beta=5$, $A_0/m_0=-2$, and in (d) $\tan\beta=20$, $A_0/m_0=3$. In window (a), the regions excluded by each criterion are identified separately, while for windows (b)--(d) only the total envelope is shown. For each case, the limit imposed by our fine-tuning constraint $f\leq50$ is shown as a dotted line, disfavoring regions above and to the right of the line. Notice the importance of combining several different criteria in constraining the parameter space. (Only the most limiting constraints are marked.) Note that in window (a) the ($m_{1/2},m_0$) allowed region is bounded entirely by the physics constraints, without a fine-tuning constraint, though $m_{1/2}$ extends to larger values than allowed by this constraint (see also Fig. \ref{['caseone:fig']}).
• Figure 5: Same as in Fig. \ref{['envsone:fig']} but for $m_t=145{\rm\,GeV}$, ${\rm sgn}\,\mu_0=+1$, and in (a) $\tan\beta=5$, $A_0/m_0=0$, in (b) $\tan\beta=5$, $A_0/m_0=-2$, in (c) $\tan\beta=5$, $A_0/m_0=2$, and in (d) $\tan\beta=10$, $A_0/m_0=-2$.