Unstable Particles near Threshold

We explore physics of unstable particles when mother particle mass is around the sum of its daughter particle masses. In this case, the conventional wave function renormalization factor is ill-defined. We propose a simple resolution of the threshold singularity problem which still allows the use of narrow width approximation by defining branching ratio in terms of spectral density. The resonance peak and shape is different for different decay channels and no single decay width can be assigned to the unstable particles. Non-exponential decay happens in all time scales.