Higgsino dark matter in an economical Scherk-Schwarz setup

We consider a minimal natural supersymmetric model based on an extra dimension with supersymmetry breaking provided by the Scherk-Schwarz mechanism. The lightest supersymmetric particle is a neutral, quasi-Dirac Higgsino and, unlike in previous studies, we assume that all Standard Model fields are propagating in the bulk. The resulting setup is minimal, as neither extra matter, effective operators, nor extra $U(1)$ groups are needed in order to be viable. The model has three free parameters which are fixed by the Higgsino mass—set to the range 1.1–1.2 TeV so it can play the role of dark matter, and by the requirements of correct electroweak breaking and the mass of the Higgs. After imposing the previous conditions we find a benchmark scenario that passes all experimental constraints with an allowed range for the supersymmetric parameters. In particular we have found gluinos in the range 2.0–2.1 TeV mass, electroweakinos and sleptons almost degenerate in the range 1.7–1.9 TeV and squarks degenerate in the range 1.9–2.0 TeV. The best discovery prospects are: (i) gluino detection at the high luminosity LHC ($\gtrsim 3{\mathrm{ab}}^{-1}$), and (ii) Higgsino detection at next-generation dark matter direct detection experiments. The model is natural, as the fine-tuning for the fixed values of the parameters is moderate mainly because supersymmetry breaking parameters contribute linearly to the Higgs mass parameter, rather than quadratically as in most models.

Figure 1

Diagrams proportional to $h_t^2$ contributing to ${\mathrm{\Delta }}_t{m}_{\mathcal{H}}^2$. Note that in the loops full towers of bosons, $Q$, $U$, $\widehat{Q}$, $\widehat{U}$, and fermions $q_L$ and $u_R$, are exchanged.

Figure 2

Cyan bands are the electroweak breaking conditions, for $1.1\mathrm{TeV}\le q_H/R\le 1.2\mathrm{TeV}$. The shadowed gray areas are the corresponding (excluded) regions where $m_{{\mathcal{H}}^{\prime }}^2<0$. The red thick solid line is the condition that ${\lambda }^{\mathrm{SM}}=\mathrm{\Delta }\lambda$ at the matching scale ${\mu }_0=q_R/R$.

Figure 3

Diagrams proportional to $h_t^4$ contributing to $\mathrm{\Delta }\lambda$.

Figure 4

Left panel: Contour lines of $\mathrm{\Delta }{\lambda }_{\log }({\mu }_0)$ (blue solid lines) and $\mathrm{\Delta }{\lambda }_{th}({\mu }_0)$ (red dashed lines) in the plane ($q_R$, $q_R/R$) for ${\mu }_0=q_R/R$. Right panel: Contour lines of $\mathrm{\Delta }\lambda ({\mu }_0)$ (red thick solid lines) in the plane ($q_R$, $q_R/R$).