W-pair production at future lepton colliders

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Future e+e- colliders, such as the ILC or FCC-ee, offer fantastic possibilities for high-precision measurements to challenge the Standard Model. For instance, from a scan of the total WW production cross section over its energy threshold, the W-boson mass could be determined with a precision of 3MeV (ILC) and even 0.5-1MeV (FCC-ee), respectively.This research project aims at providing the needed highly precise predictions for the cross section of the process e+e- -> WW -> 4fermions (ee4f) to account for the great expected experimental accuracy, in particular in the WW threshold region where sub-permille precision of the total cross section is required.For WW analyses at LEP2, a precision of ~2% at threshold and of ~0.5% above was sufficient, so that radiative corrections of next-to-leading order (NLO) were needed only in the W resonance regions, leading to the concept of the "double-pole approximation". Some years after LEP2, the state-of-the-art predictions were improved in two ways: Firstly, the NLO corrections for the ee4f process were calculated, after solving problems with the gauge-invariant treatment of the W resonances and in the evaluation of multi-leg one-loopamplitudes. Secondly, the complete NLO corrections and some leading higher-order terms were calculated within an Effective Field Theory (EFT) designed to describe the WW threshold region.To reach the ultimately required precision in the WW threshold region, the ee4f and EFT predictions have to be merged and extended. The ee4f calculation provides the necessary precision in the off-shell tails of the cross section, while the EFT offers the possibility to go beyond NLO in the W resonance regions. Significant improvements are needed in either direction. In the ee4f branch all four-fermion final states have to be treated in full NLO precision, including all process-specific interferences, and effects from initial-state radiation have to be included beyond NLO. The recent progress in automated NLO calculations is vital to achieve this. The EFT calculation has to be extended to the complete next-to-next-to-leading order (NNLO) level, posing conceptual and technical challenges. The conceptual progress in the EFT at NNLO will provide several spin-off results that are useful in similar calculations, e.g. for heavy-quark pair production. The technical challenges in the hard two-loop corrections can only be mastered owing to the dramatic progress in multi-loop calculations of recent years. The final outcome of the planned project will be a Monte Carlo program merging the refinedNLO ee4f and NNLO EFT parts in the WW threshold region with a smooth transition to NLO ee4f predictions at intermediate and high energies.