Is Natural SUSY Natural?

We study the fine tuning associated to a `Natural Supersymmetry' spectrum with stops, after RG running, significantly lighter than the first two generation sfermions and the gluino. In particular, we emphasise that this tuning should be measured with respect to the parameters taken to be independent at the assumed UV boundary of the renormalisation group flow, and improve the accuracy of previous approximate expressions. It is found that, if running begins at $10^{16}~\rm{GeV}$ $\left(10^5~\rm{GeV}\right)$, decreasing the UV stop mass below $0.75$ $\left(0.4\right)$ of the weak scale Majorana gluino mass does not improve the overall fine tuning of the theory. In contrast, it is possible to raise the first two generation sfermion masses out of LHC reach without introducing additional tuning. After running, regions of parameter space favoured by naturalness and consistent with LHC bounds typically have IR stop masses of order 1.5 TeV (0.75 TeV), and fine tuning of at least 400 (50) for high (low) scale mediation. We also study the fine tuning of theories with Dirac gluinos. These allow for substantial separation of the gluino and sfermion masses and, regardless of the scale of mediation, lead to relatively low fine tuning of order 50. Hence viable models can still favour light stops, but this requires extra structure beyond the MSSM field content.

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