Unified Maximally Natural Supersymmetry

Maximally Natural Supersymmetry, an unusual weak-scale supersymmetric extension of the Standard Model based upon the inherently higher-dimensional mechanism of Scherk-Schwarz supersymmetry breaking (SSSB), possesses remarkably good fine tuning given present LHC limits. Here we construct a version with precision $SU(2{)}_{\mathrm{L}}\times U(1{)}_{\mathrm{Y}}$ unification: $\sin^2 \theta_W(M_Z) \simeq 0.231$ispredictedto$\pm 2%$byunifying$SU(2){\rm L} \times U(1){\rm Y} $intoa5D$SU(3)_{\rm EW}$ theory at a Kaluza-Klein scale of $1\mathrm{/}{R}_5\sim 4.4\mathrm{T}\mathrm{e}\mathrm{V}$, where SSSB is simultaneously realised. Full unification with $SU(3{)}_{\mathrm{C}}$ is accommodated by extending the 5D theory to a $N=4$ supersymmetric $SU(6)$ gauge theory on a 6D rectangular orbifold at $1\mathrm{/}{R}_6\sim 40\mathrm{T}\mathrm{e}\mathrm{V}$. TeV-scale states beyond the SM include exotic charged fermions implied by $SU(3{)}_{\mathrm{E}\mathrm{W}}$ with masses lighter than $\sim 1.2\mathrm{T}\mathrm{e}\mathrm{V}$, and squarks in the mass range $1.4,{\rm TeV} - 2.3,{\rm TeV}$, providing distinct signatures and discovery opportunities for LHC run II.