Testing the minimal direct gauge mediation at the LHC

We reexamine the models with gauge mediation in view of the minimality and the Higgs boson mass. As a result, we arrive at a very simple model of direct gauge mediation which does not suffer from the flavor problems nor the $CP$ problems. The minimal supersymmetric Standard Model spectrum is determined by only three parameters, the size of the effective supersymmetry breaking, the messenger scale, and the messenger number. Surprisingly, such a very simple model is not only consistent with all the current constraints but also is testable at the upgraded LHC experiments. In particular, we show that the parameter space which is consistent with the Higgs boson mass at around 126 GeV can be tested through the stable stau searches at the 14 TeV run of the LHC. The gravitino is a viable candidate for a dark matter. We also give a short discussion on a possible connection of our model to the recently discovered x-ray line signal at 3.5 keV in the X-ray Multi-Mirror Mission Newton x-ray observatory data.

Figure 1

The lightest Higgs boson mass (red solid line), stop mass ($m_{\tilde{t}}\equiv \sqrt{m_{{\tilde{Q}}_3}{m}_{{\tilde{U}}_3^c}}$) (black solid line), and predicted $\tan \beta$ (black dashed line). Here $m_t=173.3\mathrm{GeV}$ and ${\alpha }_S(m_Z)=0.1184$.

Figure 2

The stau mass as a function of $\tan \beta$. Here, we take $\tan \beta$ to be an input parameter, and the Higgs $B$ parameter is determined by Eq. (13).

Figure 3

Contours of the NLSP mass and Higgs boson mass for the different messenger numbers. The Higgs $B$-term is taken as $\mathrm{B}(\text{Mess})=0$. In the left (right) region of the blue line, the stau (neutralino) is the NLSP.

Figure 4

Contours of the gravitino mass decided by $k$.

Figure 5

The decay length of the NLSP [$c{\tau }_{\text{NLSP}}(0.1/k{)}^2$] in the unit of meter.

Figure 6

Upper bound for the messenger scale from the electron EDM ($|d_e|<8.7\times 10^{-29}e\mathrm{cm}$). Here, we assume that the relevant phase arises from the Higgs $B$-term as $B=B_{\text{GMSB}}+i|m_{3/2}|$.