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

A bstract The discrepancy between the CDF measurement and the Standard Model theoretical prediction 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 pairs at e + e − colliders, and compute the next-to-next-to-leading order mixed QCD-EW corrections to both the integrated cross section and various kinematic distributions. By employing the method of differential equations, we analytically calculate the two-loop master integrals for the mixed QCD-EW virtual corrections to e + e − → W + W − . Utilizing the Magnus transformation, we derive a set of canonical master integrals for each integral family. This canonical basis satisfies a system of differential equations in which the dependence on the dimensional regulator is linearly factorized from the kinematics. We then express all these canonical master integrals as Taylor series in ϵ up to ϵ 4 , with coefficients articulated in terms of Goncharov polylogarithms up to weight four. Upon applying our analytic expressions of these master integrals to the phenomenological analysis of W -pair production, we observe that the $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( αα s ) corrections are significantly impactful in the α (0) scheme, particularly in certain phase-space regions. However, these mixed QCD-EW corrections can be heavily suppressed by adopting the G μ scheme.