Does decoherence violate decoupling?

TL;DR

This paper investigates the apparent paradox between decoupling in effective field theories and quantum decoherence, showing that purity depends on the EFT resolution scale and how the environment is traced out, with implications for UV divergences in decoherence.

Contribution

The authors resolve the paradox by demonstrating the dependence of purity on EFT resolution scale and tracing method, providing a practical diagnostic approach.

Findings

Purity of low-energy states depends on the EFT resolution scale.

Decoupling does not necessarily imply absence of decoherence effects.

Implications for ultraviolet divergences in decoherence calculations.

Abstract

Recent calculations in both flat and de Sitter spacetimes have highlighted a tension between the decoupling of high-energy physics from low-energy degrees of freedom and the expectation that quantum systems decohere due to interactions with unknown environments. In effective field theory (EFT), integrating out heavy fields should lead to Hamiltonian time evolution, which preserves the purity of low-energy states. This is consistent with the fact that we never observe isolated quantum states spontaneously decohering in the vacuum due to unknown high-energy physics. However, when a heavy scalar of mass $M$ is traced out, the resulting purity of a light scalar with mass $m$ typically appears to scale as a power of $1/M$ (when $m\ll M$), an effect that cannot be captured by a local effective Hamiltonian. We resolve this apparent paradox by showing that the purity depends on the resolution scale of the EFT and how the environment is traced out. We provide a practical method for diagnosing the purity of low-energy states consistent with EFT expectations, and briefly discuss some of the implications these observations have for how ultraviolet divergences can appear in decoherence calculations.