Compute complete three-loop electroweak corrections for Z-resonance pseudo‑observables

Develop and provide the complete three‑loop electroweak corrections required to compute Z‑resonance pseudo‑observables with the precision demanded by future e+e− colliders, enabling predictions for cross sections and asymmetries that match the targeted O(10^−4) experimental accuracy.

Background

At the Z pole, future e+e− colliders aim to measure two-fermion observables with relative uncertainties at or below 10^−4. The established pseudo‑observable framework parameterizes the Z resonance and requires high-order electroweak corrections to match experimental precision.

The authors explicitly note that three‑loop electroweak corrections needed for this level of precision are not yet fully available, identifying a concrete theoretical gap whose resolution is essential for interpreting high‑precision data and for robust global fits.