Upper bound on the mass scale of superpartners in minimal N=2 supersymmetry

If N=2 supersymmetry breaks to N=1 supersymmetry at an intermediate scale $m_2$ and then, later on, N=1 supersymmetry breaks and produces standard model at a scale $m_{susy}$ such that $m_2 > m_{susy}$, renormalization group evolution of three gauge couplings are altered above the scale $m_2$, changing the unification scale and the unified coupling. We show that when we enforce this general condition $m_2 > m_{susy}$ on the solutions of the renormalization group equations, the condition is translated into an upper bound on the scale $m_{susy}$. Using presently favored values of $\alpha_1(m_z),\alpha_2(m_z),\alpha_3(m_z)$, we get $m_{susy} < 4.5 \times 10^9$ GeVs for the central value of $\alpha_3(m_Z)$. When low energy threshold effect is present, this bound gets smeared yet remains generally stable in the $10^9-10^{10}$ GeV range. We also show that if we demand string unification instead of having an unified gauge theory, this constraint can be changed by exotic hypercharge normalizations.