The Supersoft and Super-Natural Supersymmetry

The super-natural Supersymmetry (SUSY) provides an elegant solution to the SUSY electroweak fine-tuning (EWFT) problem, and the Supersymmetric Standard Models (SSMs) with Dirac gauginos have the appealing supersoft property that they only cause finite contributions to scalar masses. Because the EWFT issue in this kind of models has not been addressed so far, we analyse it in the minimal $R$-symmetric SSM. Considering gauge mediated SUSY breaking with conformal sequestering, we find that the naive EWFT measure is similar to the other SSMs, except the minor improvements due to supersoft property and extra loop contributions to the Higgs boson mass. We present an effective super-natural SUSY condition: all dimensionful parameters, which give large EWFT measures, are correlated. With such a condition, we show explicitly a precise cancellation between the dominant terms that contribute to the EWFT. The resulting EWFT measure can be of unit order even for supersymmetric particle masses and $\mu$-terms in the TeV range.