Precision studies of quantum electrodynamics at future $e^+e^-$ colliders

TL;DR

This paper analyzes potential deviations from QED in electron-positron to photon-photon collisions at future colliders, providing sensitivity estimates for detecting new physics scales up to 15 TeV.

Contribution

It identifies the dominant observable deviation in the process and estimates the sensitivity of future colliders to new physics scales, including luminosity measurement precision at FCC-ee.

Findings

Deviations are primarily a correction factor in the differential cross section.

Future colliders at 3 TeV can probe new physics scales up to 15 TeV.

Luminosity can be measured with less than 10^{-4} precision at FCC-ee.

Abstract

We classify the possible deviations from the Standard Model in the QED-dominated $\mathrm{e^+e^-}\rightarrow\gamma\gamma$ process under the assumption of a preserved $SU(2)_L \times U(1)_Y$ symmetry. We find that the only deviations really observable in practice correspond to a correction of the differential cross section by a factor $(1 + \frac{c_8~s^2}{8\pi\alpha\Lambda^4}~\sin^2\theta)$, where $\Lambda$ is the scale of new physics, $\theta$ is the polar angle of any of the final state photons and $c_8$ is a constant of order 1. We also provide sensitivity estimates for QED deviations at future $\mathrm{e^+e^-}$ facilities. An $\mathrm{e^+e^-}$ collider operating at $\sqrt{s}=3$ TeV could provide sensitivity to $\Lambda$ scales as large as 15 TeV, provided that acceptances and efficiencies are controlled at the per mille level. Finally, we also discuss the possibility of a measurement of the luminosity at the FCC-ee with $\lesssim 10^{-4}$ precision, using analyses of the $\mathrm{e^+e^-}\rightarrow\gamma\gamma$ process at $\sqrt{s}\approx m_\mathrm{Z}$ energies.