Probing "Continuous Spin" QED with Rare Atomic Transitions

TL;DR

This paper explores the theoretical implications of continuous spin particles (CSP) in QED, demonstrating how a non-zero CSP parameter could alter atomic transition rates and open new decay channels, with potential experimental consequences.

Contribution

It develops a formalism for bound state atomic transitions in scalar QED with non-zero CSP parameter using path integral methods, revealing new decay channels and modified transition rates.

Findings

Non-zero CSP parameter introduces new atomic decay channels.

Transition rates can be significantly affected for certain CSP values.

Potential for laboratory tests of CSP effects in atomic systems.

Abstract

An intriguing and elementary possibility is that familiar massless particles like the photon could be "continuous spin" particles (CSP) with a small but non-zero spin Casimir $\rho$. In this case, the familiar two polarization states of the photon are accompanied by an infinite tower of integer spaced helicity modes, with couplings dictated entirely by Lorentz symmetry and the parameter $\rho$. We present a formalism for computing bound state atomic transitions for scalar QED when $\rho \neq 0$, employing path integral methods not often used for bound state computations, but that readily generalize to the CSP case. We compute several illustrative amplitudes and show that $\rho\neq 0$ opens new decay channels for atomic transitions with rates controlled by $\rho\alpha/\omega$ for transition frequency $\omega$. These new channels can appreciably modify the rates of "forbidden" transitions. For example, the lifetime of the hydrogen $2s$ state would be affected at $O(1)$ for $\rho\sim 0.1$ eV, suggesting new directions for fundamental tests of QED in laboratory experiments.