Mixed QCD-EW corrections to W-pair production at electron-positron colliders

The discrepancy between the CDF measurement and the Standard Model theoretical predictions for the W-boson mass underscores the importance of conducting high-precision studies on the W boson, which is one of the predominant objectives of proposed future e^+e^- colliders. We investigate in detail the production of W-boson pair at e^+e^- colliders and calculate the mixed QCD-EW corrections at the next-to-next-to-leading order. By employing the method of differential equations, we analytically compute the two-loop master integrals for the mixed QCD-EW corrections to e^+e^- → W^+W^-. By utilizing the Magnus transformation, we derive a canonical set of master integrals for each integral family. This canonical basis fulfills a system of differential equations where the dependence on the dimensional regulator, ϵ, is linearly factorized from the kinematics. Finally, these canonical master integrals are given as Taylor series in ϵ up to ϵ^4, with coefficients written as combinations of Goncharov polylogarithms up to weight four. Upon applying our analytic expressions of these master integrals to the phenomenological analysis on W-pair production, we find that the 𝒪(αα_s) corrections hold substantial significance in the α(0) scheme, especially in the vicinity of the top-pair resonance (√(s) = 2 m_t) induced by top-loop integrals. However, these corrections can be heavily suppressed by adopting the G_μ scheme.