Reconciling Supersymmetric Grand Unification with $α_s(m_Z)\approx 0.11$

Abstract

We argue that supersymmetric grand unification of gauge couplings is not incompatible with small $α_s$, even without large GUT-scale corrections, if one relaxes a usual universal gaugino mass assumption. A commonly assumed relation $M_2\simeq m_{\rm gluino}/3$ is in gross contradiction with $α_s\approx 0.11$. Instead, small $α_s$ favors $M_2\gg m_{\rm gluino}$. If this is indeed the case our observation casts doubt on another commonly used relation $M_1\simeq 0.5 M_2$ which originates from the same constraint of a common gaugino mass at the GUT scale. One firm prediction emerging within the small $α_s$ scenario with the unconstrained gaugino masses is the existence of a relatively light gluino below $\sim$ 200\gev.