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.

References

To match the experimental precision, these have to be computed including three-loop electroweak corrections, which are not fully available today.

— Focus topics for the ECFA study on Higgs / Top / EW factories  (2401.07564 - Blas et al., 2024) in Section TwoF — Theoretical and phenomenological aspects

These amplitudes are almost always calculated at a fixed order in some perturbative expansion, and pushing known amplitudes to ever higher orders is an important open question in particle physics.

— A High- and Variable-Dimensional Measurement of the $Z$+jets Differential Cross Section with the ATLAS Experiment and Artificial Intelligence  (2608.28449 - Greif, 28 Aug 2026) in Chapter 1, Section 1, subsection on open problems related to calculating within the Standard Model