Natural Scherk-Schwarz Theories of the Weak Scale

Natural supersymmetric theories of the weak scale are under growing pressure given present LHC constraints, raising the question of whether untuned supersymmetric (SUSY) solutions to the hierarchy problem are possible. In this paper, we explore a class of 5-dimensional natural SUSY theories in which SUSY is broken by the Scherk-Schwarz mechanism. We pedagogically explain how Scherk-Schwarz elegantly solves the traditional problems of 4-dimensional SUSY theories (based on the MSSM and its many variants) that usually result in an unsettling level of fine-tuning. The minimal Scherk-Schwarz set up possesses novel phenomenology, which we briefly outline. We show that achieving the observed physical Higgs mass motivates extra structure that does not significantly affect the level of tuning (always better than $\sim 10\%$) and we explore three qualitatively different extensions: the addition of extra matter that couples to the Higgs, an extra $U(1)^\prime$ gauge group under which the Higgs is charged and an NMSSM-like solution to the Higgs mass problem.