Shifted focus point of the Higgs mass parameter from the minimal mixed mediation of supersymmetry breaking

We employ both the minimal gravity- and the minimal gauge mediations of supersymmetry breaking at the grand unified theory (GUT) scale in a single supergravity framework, assuming the gaugino masses are generated dominantly by the minimal gauge mediation effects. In such a “minimal mixed mediation model,” a “focus point” of the soft Higgs mass parameter, $m_{h_u}^2$ emerges at 3–4 TeV energy scale, which is exactly the stop mass scale needed for explaining the 126 GeV Higgs boson mass without the “$A$-term” at the three-loop level. As a result, $m_{h_u}^2$ can be quite insensitive to various trial stop masses at low energy, reducing the fine-tuning measures to be much smaller than 100 even for a 3–4 TeV low energy stop mass and $-0.5<A_t/m_0\lesssim +0.1$ at the GUT scale. The gluino mass is predicted to be about 1.7 TeV, which could readily be tested at LHC run2.

Figure 1

RG evolutions of $m_{h_u}^2$ with $t$ [$\equiv \log (Q/\mathrm{GeV})]$ for $m_0^2=(7\mathrm{TeV}{)}^2$ [Red], $(4.5\mathrm{TeV}{)}^2$ [Green], and $(2\mathrm{TeV}{)}^2$ [Blue] when $A_t=-0.2m_0$ and $\tan \beta =50$. The tilted solid [dotted] lines correspond to the case of $t_M\approx 37$ (or $Q_M\approx 1.3\times {10}^{16}\mathrm{GeV}$, “Case A”) [$t_M\approx 23$ (or $Q_M=1.0\times {10}^{10}\mathrm{GeV}$, “Case B”)]. The vertical dotted line at $t=t_T\approx 8.2$ ($Q_T=3.5\mathrm{TeV}$) indicates the desired stop decoupling scale. The discontinuities of $m_{h_u}^2(t)$ should appear at the messenger scales.