Constraining Supersymmetry

TL;DR

The paper assesses how the MSSM, particularly in the CMSSM framework, stands up to collider, flavor, and cosmological constraints, including the muon $a_μ$ anomaly with the corrected light-by-light sign. It maps the viable regions in parameter space (bulk, coannihilation tails, funnels, focus-point) under bounds from LEP/Tevatron, $b\to sγ$, and relic density $0.1 \le Ω_χ h^2 \le 0.3$, while noting that large sparticle masses remain allowed depending on the region and the $a_μ$ constraint. It introduces a cosmological fine-tuning measure $Δ^Ω$ and contrasts it with electroweak fine-tuning $Δ$, showing these notions may diverge and depend on model choices such as NUHM. Finally, it discusses how upcoming experiments—LHC, high-energy lepton colliders, direct and indirect dark-matter searches, and proton-decay detectors—will comprehensively test the surviving CMSSM parameter space and potentially reveal supersymmetry.

Abstract

We review constraints on the minimal supersymmetric extension of the Standard Model (MSSM) coming from direct searches at accelerators such as LEP, indirect measurements such as b -> s gamma decay and the anomalous magnetic moment of the muon. The recently corrected sign of pole light-by-light scattering contributions to the latter is taken into account. We combine these constraints with those due to the cosmological density of stable supersymmetric relic particles. The possible indications on the supersymmetric mass scale provided by fine-tuning arguments are reviewed critically. We discuss briefly the prospects for future accelerator searches for supersymmetry.

Figures (9)

• Figure 1: Compilations of phenomenological constraints on the CMSSM for (a) $\tan \beta = 10, \mu < 0$, (b) $\tan \beta = 10, \mu > 0$, (c) $\tan \beta = 35, \mu < 0$ and (d) $\tan \beta = 50, \mu > 0$, assuming $A_0 = 0, m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV EFGOSi. The near-vertical lines are the LEP limits $m_{\chi^\pm} = 103.5$ GeV (dashed and black) LEPsusy, shown in (b) only, and $m_h = 114.1$ GeV (dotted and red) LEPHiggs. Also, in the lower left corner of (b), we show the $m_{\tilde{e}} = 99$ GeV contour LEPSUSYWG_0101. In the dark (brick red) shaded regions, the LSP is the charged ${\tilde{\tau}}_1$, so this region is excluded. The light (turquoise) shaded areas are the cosmologically preferred regions with $0.1\leq\Omega_{\chi} h^2\leq 0.3$EFGOSi. The medium (dark green) shaded regions that are most prominent in panels (a) and (c) are excluded by $b \to s \gamma$bsg. The shaded (pink) regions in the upper right regions delineate the $\pm 2 \, \sigma$ ranges of $g_\mu - 2$. For $\mu > 0$, the $\pm 1 \, \sigma$ contours are also shown as solid black lines.
• Figure 2: (a) The large-$m_{1/2}$ 'tail' of the $\chi - {\tilde{\tau}_1}$ coannihilation region for $\tan \beta = 10$, $A = 0$ and $\mu < 0$ourcoann, superimposed on the disallowed dark (brick red) shaded region where $m_{\tilde{\tau}_1} < m_\chi$, and (b) the $\chi - {\tilde{t}_1}$ coannihilation region for $\tan \beta = 10$, $A = 2000$ GeV and $\mu > 0$EOS, exhibiting a large-$m_0$ 'tail'.
• Figure 3: An expanded view of the $m_{1/2} - m_0$ parameter plane showing the focus-point regions focus at large $m_0$ for (a) $tan \beta = 10$, and (b) $\tan \beta = 50$. In the shaded (mauve) region in the upper left corner, there are no solutions with proper electroweak symmetry breaking, so these are excluded in the CMSSM. Note that we have chosen $m_t = 171$ GeV, in which case the focus-point region is at lower $m_0$ than when $m_t = 175$ GeV, as assumed in the other figures. The position of this region is very sensitive to $m_t$. The black contours (both dashed and solid) are as in Fig. \ref{['fig:CMSSM']}, the we do not shade the preferred $g-2$ region.
• Figure 4: Contours of the total sensitivity $\Delta^\Omega$ (\ref{['twelve']}) of the relic density in the $(m_{1/2}, m_0)$ planes for (a) $\tan \beta = 10, \mu > 0, m_t = 175$ GeV, (b) $\tan \beta = 35, \mu < 0, m_t = 175$ GeV, (c) $\tan \beta = 50, \mu > 0, m_t = 175$ GeV, and (d) $\tan \beta = 10, \mu > 0, m_t = 171$ GeV, all for $A_0 = 0$. The light (turquoise) shaded areas are the cosmologically preferred regions with $0.1\leq\Omega_{\chi} h^2\leq 0.3$. In the dark (brick red) shaded regions, the LSP is the charged ${\tilde{\tau}}_1$, so these regions are excluded. In panel (d), the medium shaded (mauve) region is excluded by the electroweak vacuum conditions.
• Figure 5: Contours of the electroweak fine-tuning measure $\Delta$ (\ref{['thirteen']}) in the $(m_{1/2}, m_0)$ planes for (a) $\tan \beta = 10, \mu > 0, m_t = 175$ GeV, (b) $\tan \beta = 35, \mu < 0, m_t = 175$ GeV, (c) $\tan \beta = 50, \mu > 0, m_t = 175$ GeV, and (d) $\tan \beta = 10, \mu > 0, m_t = 171$ GeV, all for $A_0 = 0$. The light (turquoise) shaded areas are the cosmologically preferred regions with $0.1\leq\Omega_{\chi} h^2\leq 0.3$. In the dark (brick red) shaded regions, the LSP is the charged ${\tilde{\tau}}_1$, so this region is excluded. In panel (d), the medium shaded (mauve) region is excluded by the electroweak vacuum conditions.