Higgs mass and vacuum stability with high-scale supersymmetry

In the high-scale (split) MSSM, the measured Higgs mass sets an upper bound on the supersymmetric scalar mass scale MSUSY around $10^{11}$ ($10^{8}$) GeV, for $\tan\beta$ in the standard range and the central value of the top quark mass $m_t$. This article discusses how maximal MSUSY is affected by negative threshold corrections to the quartic Higgs coupling arising from the sbottom and stop trilinear couplings. In the high-scale MSSM with very high $\tan\beta$, the electroweak vacuum decay due to the large bottom Yukawa coupling rules out the possibility of raising MSUSY beyond the above limit. In cases with large $A_b$ or $A_t$, MSUSY as a common mass of the extra fermions and scalars can be as high as $10^{17}$ GeV remaining consistent with $m_h$ and the vacuum longevity if $m_t$ is smaller than the central value by $2\sigma$. For the central value of $m_t$, the upper limit on MSUSY does not change very much owing to the metastability, which is the case also in the split MSSM even with $\pm 2\sigma$ variations in $m_t$.