# Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO

## TL;DR

This paper shows that the classical double copy method, used to relate dilaton-gravity to Yang-Mills theory for two massive particles, breaks down at higher orders in perturbative expansions.

## Contribution

It identifies the failure of the classical double copy procedure at NNLO in the effective action for dilaton-gravity.

## Key findings

- Double copy fails at NNLO in post-Minkowskian expansion
- Breakdown occurs at 3PM or 2PN orders
- Challenges the universality of the classical double copy approach

## Abstract

We demonstrate that a recently proposed classical double copy procedure to construct the effective action of two massive particles in dilaton-gravity from the analogous problem of two color charged particles in Yang-Mills gauge theory fails at next-to-next-to-leading orders in the post-Minkowskian (3PM) or post-Newtonian (2PN) expansions.