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The Gaugino β-Function

We present an elegant exact formula for the gaugino $β$-function in a softly-broken supersymmetric gauge theory, of the form $β_M = {\cal O}(β_g/g)$, where $β_g$ is the gauge $β$ function and ${\cal O}$ is a simple differential operator acting on the gauge coupling $g$ and the Yukawa coupling.