Focus point supersymmetry redux

Recent results from Higgs boson and supersymmetry searches at the Large Hadron Collider provide strong new motivations for supersymmetric theories with heavy superpartners. We reconsider focus point supersymmetry (FP SUSY), in which all squarks and sleptons may have multi-TeV masses without introducing fine-tuning in the weak scale with respect to variations in the fundamental SUSY-breaking parameters. We examine both FP SUSY and its familiar special case, the FP region of minimal supergravity, also known as the constrained minimal supersymmetric standard model (mSUGRA/CMSSM), and show that they are beautifully consistent with all particle, astroparticle, and cosmological data, including Higgs boson mass limits, null results from SUSY searches, electric dipole moments, $b\to s\gamma$, $B_s\to {\mu }^{+}{\mu }^{-}$, the thermal relic density of neutralinos, and dark matter searches. The observed deviation of the muon’s anomalous magnetic moment from its standard model value may also be explained in FP SUSY, although not in the FP region of mSUGRA/CMSSM. In light of recent data, we advocate refined searches for FP SUSY and related scenarios with heavy squarks and sleptons, and we present a simplified parameter space within mSUGRA/CMSSM to aid such analyses.

Figure 1

Contours of the light Higgs boson mass $m_h$ in black (dotted) and lightest neutralino mass $m_{\chi }$ in red (dashed) in the $(m_0,M_{1/2})$ plane for $\tan \beta =10$ (a) and 50 (b), $A_0=0$, and $\mu >0$. On the blue (solid) lines, the neutralino relic density is ${\Omega }_{\chi }\simeq 0.23$.

Figure 2

Upper limits on $\sin {\varphi }_{CP}$ from neutron EDM constraints in black (dotted) and electron EDM constraints in green (dashed) for $\tan \beta =10$ (a) and 50 (b), $A=0$, and $\mu >0$. On the blue (solid) line, the neutralino relic density is ${\Omega }_{\chi }\simeq 0.23$.

Figure 3

Contours of (a) $m_0$ (in TeV) and (b) $\mu$ (in GeV) in the $(\tan \beta ,M_{1/2})$ plane. Every point in the parameter space is in the FP region and satisfies ${\Omega }_{\chi }\simeq 0.23$, $A_0=0$, and $\mu >0$.

Figure 4

Contours of $m_h$ (a) and $m_{\chi }$ (b) in the $(\tan \beta ,M_{1/2})$ plane. Every point in the parameter space is in the FP region and satisfies ${\Omega }_{\chi }\simeq 0.23$, $A_0=0$, and $\mu >0$.

Figure 5

Contours of $\Delta B(b\to s\gamma$) in units of ${10}^{-4}$ (a) and $\Delta B(B_s\to {\mu }^{+}{\mu }^{-})$ in units of ${10}^{-8}$ (b) due to SUSY in the $(\tan \beta ,M_{1/2})$ plane. Every point in the parameter space is in the FP region and satisfies ${\Omega }_{\chi }\simeq 0.23$, $A_0=0$, and $\mu >0$.

Figure 6

(a) Higgsino-ness $a_{\tilde{H}}$ for neutralinos in the FP region consistent with various relic densities. The right-most point on each curve corresponds to $M_{1/2}=1\mathrm{TeV}$. (b) The spin-independent $\chi$-nucleon cross section ${\sigma }^p$ as a function of $f_s$ for a model in the FP region with $(m_0,M_{1/2})=(3\mathrm{TeV},550\mathrm{GeV})$. The shaded regions indicate the $1\sigma$ uncertainties on the various $f_s$ determinations. In both plots, $\tan \beta =10$, $A_0=0$, and $\mu >0$.

Figure 7

Contours of ${\sigma }^p$ in zeptobarns for $\mu >0$ (top panels) and for $\mu <0$ (bottom panels), with $f_s=0.05$ (left panels) and $f_s=0.36$ (right panels). In each panel, the shaded region is excluded by XENON100 [52].

Figure 8

Contours of the supersymmetric contribution to $(g-2{)}_{\mu }$ in units of ${10}^{-9}$. Every point in the parameter space is in the FP region and satisfies ${\Omega }_{\chi }\simeq 0.23$, $A_0=0$, and $\mu >0$.

Figure 9

Contours of $M_{\tilde{\mu }}$ required to eliminate the discrepancy between the theoretical and experimental values for $(g-2{)}_{\mu }$ (a) and to reduce the discrepancy to $2\sigma$ (b). This model framework is a slight modification of mSUGRA/CMSSM in which all scalars have GUT-scale mass $m_0$, except for the smuons and muon sneutrino, which have physical mass $M_{\tilde{\mu }}$. In the shaded regions, the $\tilde{\mu }$ becomes the LSP. To specify all parameters aside from the smuon and muon sneutrino masses, every point in the parameter space is in the FP region and satisfies ${\Omega }_{\chi }\simeq 0.23$, $A_0=0$, and $\mu >0$.

Figure 10

A slice through the mSUGRA parameter space from Fig. 2a for a fixed $M_{1/2}=850\mathrm{GeV}$, showing results for the chargino mass $M_{{\tilde{\chi }}_1^{+}}$ from SOFTSUSY (blue dots) and for ${\Omega }_{\chi }{h}^2$ from MicrOMEGAs (red crosses). The cyan shaded region is excluded by chargino searches at LEP, and the horizontal dotted lines mark the $3\sigma$ preferred region for ${\Omega }_{\chi }{h}^2$.