Prospects for higher-order corrections to W-pair production near threshold in the EFT approach

The precise measurement of the mass of the W-boson plays an essential role for precision tests of the Standard Model (SM) and indirect searches for new physics through global fits to electroweak observables. Cross-section measurements near the W-pair production threshold at a possible future e −e + collider promise to reduce the experimental uncertainty to the level of 3 MeV at an International Linear Collider (ILC) [1, 2], while a high-luminosity circular collider offers a potential improvement to 0.5 MeV in case of the FCC-ee [3, 4] or 1 MeV at the CEPC [5]. At the point of highest sensitivity, an uncertainty of the cross-section measurement of 0.1% translates to an uncertainty of ∼ 1.5 MeV on MW [3]. Therefore a theoretical prediction for the cross section with an accuracy of ∆σ ∼ 0.01% at threshold is required to fully exploit the potential of a future circular e −e + collider. Theory predictions using the double-pole approximation (DPA) [6] at next-to-leading order (NLO) [7–11] successfully described LEP2 results with an accuracy of better than 1% above threshold. An extension of the DPA to NNLO appears to be appropriate for a future e −e + collider operating above the W-pair threshold, e.g. for the interpretation of anomalous triple-gauge-coupling measurements at √ s = 240 GeV. However, the accuracy of the DPA at NLO degrades to 2-3% near threshold. In this region the combination of a full NLO calculation of four-fermion production [12, 13] with leading NNLO effects obtained using effective-field-theory (EFT) methods [14, 15] reduces the theory uncertainty of the total cross section below 0.3%; sufficient for the ILC target uncertainty but far above that of FCC-ee. This raises the question of the methods required to reach a theory accuracy ∼ 0.01%. In this contribution, this issue is addressed from the EFT point of view. The discussion is limited to the total cross section, where the EFT approach is best developed so far, although cuts on the W decay products can also be incorporated [15]. To reach the target accuracy, it will also be essential to have theoretical control of effects beyond the pure electroweak effects considered here. In particular it is assumed that next-to-leading logarithmic corrections (α/π) 2 ln(m2 e /s) from collinear initial-state photon radiation (ISR), which have been estimated to be . 0.1% [12], will be resummed to all orders. QCD effects, which are important in particular for the fully hadronic decay modes, are only briefly considered. In Section 7.1 aspects of the EFT approach are reviewed from an updated perspective using insight into the factorization of soft, hard, and Coulomb corrections [16]. The NLO and leading NNLO results are summarized and compared to the NLOee4f calculation [12]. In Section 7.2 the structure of the EFT expansion and calculations of subsets of corrections are used to estimate the magnitude of the NNLO and leading N3LO corrections and to assess if such calculations are sufficient to meet the FCC-ee target accuracy.