Five-loop QCD corrections to the rho parameter

Compute the five-loop QCD corrections to the electroweak rho parameter, particularly the top-quark-induced contributions relevant to the predicted W-boson mass and FCC-ee precision measurements.

Background

The paper calculates four-loop QCD corrections involving top quarks to the electroweak parameters Δrˉ\Delta\bar r and Δκ\Delta\kappa, using a large-top-mass expansion. The resulting corrections produce W-boson mass shifts that are already comparable to or larger than the projected FCC-ee uncertainties.

The authors observe that the apparent perturbative convergence suggests that five-loop effects may also be experimentally relevant, especially in the on-shell mass scheme. They therefore identify the computation of the presently unknown five-loop QCD corrections to the rho parameter as a concrete higher-order calculation needed to complete the precision prediction.

References

We estimate that at least in the on-shell scheme this will also hold true for the so far unknown five-loop corrections, which makes their computation highly desirable.

— Relations between electroweak parameters to order $α_s^3$  (2610.08282 - Maier et al., 6 Oct 2026) in Section Conclusions