Beam polarization precision requirements for future $e^+e^-$ Higgs factories

TL;DR

This paper analyzes the minimum beam polarization precision needed at future $e^+e^-$ Higgs factories, highlighting how positron polarization impacts measurement accuracy and proposing precision targets for various observables.

Contribution

It quantifies polarization precision requirements for future Higgs factories, revealing how positron polarization influences measurement sensitivities and constraints.

Findings

Improved positron polarization relaxes precision requirements for some measurements.

Measurements involving $P_ ext{eff}$ are less sensitive to polarization precision.

High-precision polarization control (better than 0.1%) is necessary for certain Higgs and electroweak measurements.

Abstract

We present work on quantifying the minimum requirements for beam polarization precision at future $e^+e^-$ Higgs factories. We find that, under the assumption of a high electron beam polarization ($P_-$) that the positron polarization ($P_+$) is of key importance but for reasons both known and newly discovered. We have discovered that improved positron polarization leads to a less strict requirement on the beam polarization precision for measurements that scale only with the effective polarization, $P_\mathrm{eff}$. Conversely, measurements that scale with the product of beam polarizations, $P_-P_+$, such as those that contain the $eeZ$ or $ee\gamma$ vertex, have their polarization precision demands get more strict as positron polarization increases. We check the polarization precision demands for $10^{-3}$ on the Higgsstrahlung cross-section ($\sigma_{ZH}$) at 250~GeV, $10^{-4}$ on the electron left-right asymmetry ($A_{\rm e}$) at the Z pole, and $10^{-4}$ on the di-photon cross-section ($\sigma_{\gamma \gamma}$) from the Z pole to 3~TeV. We find that, for measurements away from the Z pole, the goals can plausibly be attained if one can achieve precision on beam polarization better than $0.1\%$. For measurements of $A_{\rm e}$ at $10^{-4}$, colliders must do better than $0.02\%$ on beam polarization precision, or determine ways to upgrade their beam polarization values towards unity, where the requirements decrease to better than $0.15\%$.