Pole restructuring from multiplicative disorder

Determine whether replacing the additive random source with a random mass or other multiplicative disorder displaces, broadens, or otherwise restructures the heavy-field poles of the disorder-averaged retarded propagator and spectral function, potentially modifying the effective principal-series parameter μ and the cosmological-collider exponents 3/2 ± iμ.

Background

The paper analyzes an additive, spatially quenched random source that enters linearly in the massive spectator equation. Because this source contributes only a deterministic retarded response for each realization, disorder averaging modifies the statistical propagator while leaving the retarded propagator, spectral function, and heavy-field poles unchanged.

The conclusion identifies random mass or more general multiplicative disorder as a qualitatively different extension. Such disorder would enter the quadratic propagation operator itself rather than merely adding a source, so it could alter the averaged propagation spectrum and thereby change the cosmological-collider clock frequency. The unresolved issue is whether the resulting pole modification would specifically appear as displacement, broadening, or another form of spectral restructuring.