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.