Electroweak naturalness and deflected mirage mediation

We investigate the question of electroweak naturalness within the deflected mirage mediation (DMM) framework for supersymmetry breaking in the minimal supersymmetric standard model. The class of DMM models considered are nine-parameter theories that fall within the general classification of the 19-parameter phenomenological minimal supersymmetric standard model. Our results show that these DMM models have regions of parameter space with very low electroweak fine-tuning, at levels comparable to the phenomenological minimal supersymmetric standard model. These parameter regions should be probed extensively in the current LHC run.

Figure 1

${\mathrm{\Delta }}_{\mathrm{EW}}$ as a function of the LSP mass for the full data set without a cut on the gluino mass and shaded by the gluino mass in TeV.

Figure 2

A plot of ${\mathrm{\Delta }}_{\mathrm{EW}}$ as a function of the LSP mass for points with ${\mathrm{\Delta }}_{\mathrm{EW}}<100$, (left) shaded by the gluino mass in TeV, and (right) shaded by the relic density.

Figure 3

Examples of the Higgs and superpartner spectra for two representative points with small(ish) values of ${\mathrm{\Delta }}_{\mathrm{EW}}$. The left panel is a point with ${\mathrm{\Delta }}_{\mathrm{EW}}<4$ and a low value of the relic density (${\mathrm{\Omega }}_{\chi }{h}^2=2.4\times {10}^{-3}$), for which $M_0=2600\mathrm{GeV}$, ${\alpha }_m=1.21$, $\tan \beta =22$, $(n_M,n_H)=(0.5,0)$, ${\alpha }_g=0.1$, $M_{\text{Mess}}={10}^9\mathrm{GeV}$, and $N=2$. The right panel is a point with ${\mathrm{\Delta }}_{\mathrm{EW}}<120$ and a large value of the relic density (${\mathrm{\Omega }}_{\chi }{h}^2=0.113$), for which $M_0=4800\mathrm{GeV}$, ${\alpha }_m=1.36$, $\tan \beta =38$, $(n_M,n_H)=(1,1)$, ${\alpha }_g=-0.4$, $M_{\text{Mess}}={10}^{14}\mathrm{GeV}$, and $N=1$.

Figure 4

A plot of ${\mathrm{\Delta }}_{\mathrm{EW}}$ as a function of the stop mass (left) and ${\mathrm{\Delta }}_{\mathrm{EW}}$ vs $X_t$ divided by the stop mass (right), with ${\mathrm{\Delta }}_{\mathrm{EW}}<100$ and a 1.3 TeV cut on the gluino mass. The notches in the lower left corners correspond to regions that are excluded by $\mathrm{Br}(b\to s\gamma )$ and $\mathrm{Br}(B_s\to {\mu }^{+}{\mu }^{-})$.

Figure 5

A plot of ${\mathrm{\Delta }}_{\mathrm{EW}}$ vs. the $\mu$ parameter, colored by the gluino mass. The two tails correspond to points in which $m_{H_u}^2$ is positive (top) and negative (bottom) at $M_{\mathrm{SUSY}}$.

Figure 6

${\mathrm{\Delta }}_{\mathrm{EW}}$ vs the stop mass, with the values of the matter modular weight $n_M$ indicated on the left and of the Higgs modular weight $n_H$ on the right, for points with ${\mathrm{\Delta }}_{\mathrm{EW}}<100$.

Figure 7

A comparison of our results with the fine-tuning ranges found in many SUSY models as taken from Refs. [7, 10, 14]. The line for the pMSSM denotes the lower bound determined in Ref. [14]; the arrows denote that the fine-tuning ranges may go below as well as above this line if a more comprehensive scan is performed. The DMM points are further broken down by the modular weights $n_M$ and $n_H$ for the matter and Higgs fields; these points are denoted by $d(n_M,n_H)$. The dashed line represents ${\mathrm{\Delta }}_{\mathrm{EW}}<30$, which is considered not fine-tuned.