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

Abstract

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 $α_1(m_z),α_2(m_z),α_3(m_z)$, we get $m_{susy} < 4.5 \times 10^9$ GeVs for the central value of $α_3(m_Z)$. 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.

Substantially enlarged version. Accepted in Mod. Phys. Lett A