Irreducible Bhabha background in the detection of muonium-antimuonium conversion

TL;DR

This paper analyzes the irreducible Bhabha scattering background in muonium-antimuonium conversion experiments, quantifying its impact and proposing helicity measurement as a mitigation strategy.

Contribution

It provides a detailed calculation of the Bhabha background rate and assesses its significance for current and future experiments, highlighting the importance of helicity measurements.

Findings

Background is negligible for MACE but significant for lower conversion probabilities.

Helicity measurement can reduce background to below 10^{-22}.

Bhabha scattering can mimic muonium-antimuonium conversion signals at very low probabilities.

Abstract

Experiments such as MACS and the proposed MACE study muonium-antimuonium conversion by the energies of the final-state $e^\pm$. The $e^+$ and $e^-$ from an antimuonium decay tend to be non-relativistic and relativistic, respectively, and vice versa for muonium. However, these $e^\pm$ can exchange their energies by hard Bhabha scattering, causing muonium to fake an antimuonium decay signal. We compute the rate for this background and find that, while negligible for MACE, it will become larger than the signal for conversion probabilities less than $10^{-18}$. Measuring the helicity of the $e^-$ will reduce this to $10^{-22}$.