Atoms as electron accelerators for measuring the $e^+e^- \to\,$hadrons cross section

TL;DR

This paper introduces a novel method to measure the hadronic cross section using positron interactions with atomic electrons, offering an alternative to existing techniques for improving the precision of the muon g-2 calculation.

Contribution

The paper proposes a new approach utilizing atomic electron interactions with high-energy positrons to measure hadronic cross sections, bypassing traditional methods like ISR and energy scans.

Findings

Feasible measurement of $\sigma_{ ext{had}}$ from threshold to 1 GeV using positron-atom interactions.

High statistical accuracy achievable with a 12 GeV positron beam at JLab.

Potential to improve the precision of the hadronic vacuum polarization contribution to $(g-2)_$.

Abstract

The hadronic vacuum polarization contribution to $(g-2)_\mu$ can be determined via dispersive methods from $e^+e^-\to\;$hadrons data. We propose a novel approach to measure the hadronic cross section $\sigma_{\mathrm{had}}$ as an alternative to the initial-state radiation and energy scan techniques, which relies on positron annihilation off atomic electrons of a high $Z$ target ($^{238}$U, $Z=92$). We show that by leveraging the relativistic electron velocities of the inner atomic shells, a high-intensity $12\,$GeV positron beam, such as the one foreseen at JLab, can allow to measure $\sigma_{\mathrm{had}}$ with high statistical accuracy from the two-pion threshold up to above $\sqrt{s} \sim 1\,$GeV.