Effective theory approach to unstable particle production

Using the hierarchy of scales between the mass, $M$, and the width, $\Gamma$, of a heavy, unstable particle we construct an effective theory that allows calculations for resonant processes to be systematically expanded in powers of the coupling $\alpha$ and $\Gamma/M$. We illustrate the method by computing the next-to-leading order line shape of a scalar resonance in an abelian gauge-Yukawa model.