The Gaugino $β$-Function

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