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We present a precise analysis of the Higgs mass corrections stemming fromvectorlike top partners in supersymmetric models. We reduce the theoreticaluncertainty compared to previous studies in the following aspects: (i)including the one-loop threshold corrections to SM gauge and Yukawa couplingsdue to the presence of the new states to obtain the $\bar{\text{DR}}$parameters entering all loop calculations, (ii) including the full momentumdependence at one-loop, and (iii) including all two-loop corrections but theones involving $g_1$ and $g_2$. We find that the additional thresholdcorrections are very important and can give the largest effect on the Higgsmass. However, we identify also parameter regions where the new two-loopeffects can be more important than the ones of the MSSM and change the Higgsmass prediction by up to 10 GeV. This is for instance the case in the low$\tan\beta$, small $M_A$ regime. We use these results to calculate theelectroweak fine-tuning of an UV complete variant of this model. For thispurpose, we add a complete $\textbf{10}$ and $\bar{\textbf{10}}$ representationof $SU(5)$ to the MSSM particle content. We embed this model in minimal GaugeMediated Supersymmetry Breaking and calculate the electroweak fine-tuning withrespect to all important parameters. It turns out that the limit on the gluinomass becomes more important for the fine-tuning than the Higgs massmeasurements which is easily to satisfy in this setup.

Precise determination of the Higgs mass in supersymmetric models with vectorlike tops and the impact on naturalness in minimal GMSB