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

TL;DR

The paper quantifies minimum beam-polarization precision requirements for future $e^+e^-$ Higgs factories by deriving a general error-propagation framework $\sigma = \sigma_0\left( A_{0} + A_{-}P_- + A_{+}P_+ + A_{+-}P_-P_+ \right)$ and applying it to Higgsstrahlung, left-right asymmetry at the Z pole, and di-photon–based luminosity measurements. It shows that measurements away from the Z pole typically need beam-polarization precision better than $0.1\%$, while Z-pole $A_e$ measurements demand sub-$2\times 10^{-4}$ precision unless both beams are highly polarized. The work demonstrates that the optimal use of same-sign polarization data fractions can ease or tighten these requirements depending on the observable, and highlights a tension between polarimeter and event-fit methods at high precision. Overall, the results guide collider-design trade-offs among electron/positron polarizations, data-taking strategies, and polarization-measurement capabilities to achieve Higgs-precision goals with polarized $e^+e^-$ colliders.

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 $eeγ$ 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 ($σ_{ZH}$) 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 ($σ_{γγ}$) 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 $0.15\%$.

Figures (6)

• Figure 1: Plot and fit of the single-spin coefficient for the positron beam polarization, $A_+$, as derived in sub-section \ref{['ssec:Gen']}. Values used for computation are taken from a reference on one-loop electroweak and QED corrections to $e^+e^-\!\to\!\gamma\gamma$Bondarenko:2022xmc.
• Figure 2: Plot and fit of the double-spin coefficient for electron and positron beam polarizations, $A_{+-}$, as derived in sub-section \ref{['ssec:Gen']}. Values used for computation are taken from a reference on one-loop electroweak and QED corrections to $e^+e^-\!\to\!\gamma\gamma$Bondarenko:2022xmc.
• Figure 3: Plot of the minimum electron beam polarization precision required for different collider scenarios for reaching an effect on the di-photon cross-section measurement at a precision of $10^{-4}$. For the colliders with no electron beam polarization the precision quoted is an absolute value, not a relative value, to avoid division by zero.
• Figure 4: Plot of the minimum positron beam polarization precision required for different collider scenarios for reaching an effect on the di-photon cross-section measurement at a precision of $10^{-4}$. For the colliders with no positron beam polarization the precision quoted is an absolute value, not a relative value, to avoid division by zero.
• Figure 5: Plot of the minimum electron beam polarization precision required for different amounts of data fractions per polarization sign permutations at the ILC $(P_-,P_+)=(80\%,30\%)$ collider design for reaching an effect on the di-photon cross-section measurement at a precision of $10^{-4}$. For the unpolarized data set, the precision quoted is an absolute value, not a relative value.