Probing the vacuum as a chiral medium

TL;DR

This paper investigates how a vacuum with definite chirality affects circular birefringence of photons, introducing derivative corrections to the Heisenberg-Euler approach, and explores experimental regimes where these effects can be observed.

Contribution

It extends the Heisenberg-Euler framework by incorporating derivative corrections and demonstrates their equivalence through multiple theoretical approaches, also analyzing experimental detectability.

Findings

Derivative corrections are essential for chiral vacuum birefringence.

Equivalence established between three theoretical approaches.

Potential experimental regimes to observe these effects.

Abstract

We study the circular birefringence experienced by linearly polarised photons colliding with a circularly polarised background creating a vacuum of definite chirality (handedness). For this scenario the standard Heisenberg-Euler approach fails and must be supplemented by derivative corrections which we match to known Hilbert series. Choosing a plane wave background, we find equivalence between three approaches: (i) adding derivative corrections to the Heisenberg-Euler Lagrangian; (ii) improving the locally constant field approximation to the one-loop polarisation tensor; (iii) performing a low-energy expansion of the direct $2\to 2$ QED photon-photon scattering amplitude. Going beyond plane-wave backgrounds, we analyse an example of a circularly polarised standing wave sensitive to derivative corrections. We find a parameter regime where these corrections could be probed in experiments.