The Decay Amplifier

When dark matter particles annihilate near a kinematic threshold, they produce slow-moving unstable particles. These slow particles spend more time under the influence of long-range forces, which distorts their wavefunctions — the Sommerfeld enhancement.

The standard calculation treats the product particles as stable. This paper includes their decay width in the Schrödinger equation and finds that the decay process itself becomes part of the enhancement mechanism.

Narrow-width particles create resonant bound states that amplify the annihilation rate at specific energies. Wider decay widths demand treatment of off-shell final states — particles that don’t quite have the right mass to exist as real particles but contribute to the process anyway.

The instability of the product isn’t a correction to the calculation. It’s a qualitatively new contribution. The rate at which the product falls apart changes how efficiently it was created.

This feeds back into predictions for dark matter abundance: the relic density calculation — how much dark matter should exist today given the early universe’s conditions — changes substantially when you account for the products’ mortality.

The general principle: when a process creates something unstable, the instability is not a post-process effect. It’s part of the process itself. The system doesn’t first create and then destroy — the destruction shapes the creation from the start.