Reconciling Supersymmetric Grand Unification with ${\alpha }_s(m_Z)\approx 0.11$

Abstract

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

18 pages, LaTex format for text; epsf.sty needed for including 3 Postscript figures in the text. CHANGES: Comments on dark matter and non-minimal supergravity (see end of Sec. 2.3) and several references added; also some minor corrections made.

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