Maximally Natural Supersymmetry

We consider 4D weak scale theories arising from 5D supersymmetric (SUSY) theories with maximal Scherk-Schwarz breaking at a Kaluza-Klein scale of several TeV. Many of the problems of conventional SUSY are avoided. Apart from 3rd family sfermions the SUSY spectrum is heavy, with only $\sim 50\%$ tuning at a gluino mass of $\sim 2\mathrm{TeV}$ and a stop mass of $\sim 650\mathrm{GeV}$. A single Higgs doublet acquires a vacuum expectation value, so the physical Higgs boson is automatically standard-model-like. A new $U(1{)}^{\prime }$ interaction raises $m_h$ to 126 GeV. For minimal tuning the associated $Z^{\prime }$, as well as the 3rd family sfermions, must be accessible to LHC13. A gravitational wave signal consistent with hints from BICEP2 is possible if inflation occurs when the extra dimensions are small.

Figure 1

(a) Schematic of the minimal model. In five dimensions are the SM gauge fields, the first two families $F_{1,2}$, Higgs doublets $H_{u,d}$, and superpartners implied by 5D SUSY. The 3rd generation chiral multiplets are brane localized. SUSY is broken nonlocally by BCs. (b) Full model including embedding in yet higher-dimensional bulk. The 5D $U(1{)}^{\prime }$ is broken via $y$-dependent VEVs (driven by the brane-localized superpotential $\mathrm{\Delta }W$) of bulk fields, ${\mathrm{\Phi }}_{1,2}$, of charges $\pm 1$. After SSSB, $F_X\sim 1/R^2$ is induced for $X$, a brane-localized singlet field.

Figure 2

Contributions to the Higgs soft mass $m_{H_u}^2$ in units of $1/R^2$. The positive 1-loop electroweak contribution (blue) and the negative 2-$\text{loop}+\text{leading}$ log top-stop sector contribution (red) combine to give a positive mass squared (black). Contributions from higher-dimension operators of Eq. (4) can lead to successful EWSB, indicated by the dotted black curve. The dashed bands show the uncertainty for $\overline{\mathrm{MS}}$ top mass $m_t(M_t)=160_{-4}^{+5}\mathrm{GeV}$.

Figure 3

Schematic spectrum of new states of primary experimental interest.

Figure 4

Fine-tuning ${\mathrm{\Delta }}^{-1}$ (solid lines) as function of $1/R$ and the $Z^{\prime }$ mass, Eq. (8). Iso-contours of stop mass are dashed. Limits from LHC8 searches for $\tilde{t}\to t+\mathrm{MET}$ [84, 85] (red) and $Z^{\prime }$ resonance searches [88, 89] (green) are shaded. Subdominant limits $m_{\tilde{g}}\approx 1/(2R)\gtrsim 1.3\mathrm{TeV}$ from $\tilde{g}\to t\overline{t}/b\overline{b}+\mathrm{MET}$ searches (blue) are also shaded [91, 92].