Towards a Fully Automated Differential $\text{NNLO}_\text{EW}$ Generator for Lepton Colliders

TL;DR

This work introduces a fully automated YFS-based framework for matching $NLO_{EW}$ and $NNLO_{EW}$ corrections in lepton colliders, implemented in SHERPA, to achieve precision on par with future experiments. The approach uses local infrared subtraction from the Yennie-Frautschi-Suura theorem to order-by-order subtract IR divergences while resumming soft photon logs to all orders, enabling a process-independent treatment of higher-order electroweak corrections. The authors explicitly define IR-finite residuals for $NLO_{EW}$ and $NNLO_{EW}$ corrections, implement real-virtual, double-real, and partial double-virtual subtractions, and validate pole cancellations and numerical stability across multiple processes, including $oldsymbol{ m uar{ u}}$ production near the $Z$-pole and $oldsymbol{ m bc+bc}$ production with BESIII data. Their results show a substantial reduction in theoretical uncertainties at $NNLO_{EW}$ and demonstrate the method's applicability to a wide range of lepton-collider observables, with GRIFFIN interfacing to supply two-loop EW information. The work paves the way for robust, high-precision simulations at future lepton colliders and outlines the remaining steps to achieve complete automation as two-loop amplitude tools mature.

Abstract

Future proposed lepton collider experiments will reach unprecedented levels of accuracy. To ensure the success of these experiments, and to fully exploit their wealth of data, the precision of theory calculations must reach comparable or even better levels. One bottleneck in achieving this precision target lies in the systematic, process-independent inclusion of higher-order corrections at Next-to-Next-to-Leading Order in the electroweak coupling $\text{NNLO}_\text{EW}$ while ensuring the correct matching with modern all-orders resummation techniques. Here, we present a solution to this problem, based on the Yennie-Frautschi-Suura theorem, which employs a local infrared (IR) subtraction to remove divergences and its matching to an all-order resummation of the soft and soft-collinear logarithms.

Figures (9)

• Figure 1: Explicit cancellation of infrared (IR) divergences, as described in \ref{['EQ:OneLoopIR']}, using massive regularisation. The plot includes the finite sum (green), as well as the individual contributions from the virtual term (blue) and the subtraction term (red). The y-axes have been rescaled to improve readability.
• Figure 2: Cancellation of the IR poles according to \ref{['EQ:OneLoopIR']} using dimensional regularization. The bins correspond to the number of decimal places at which the cancellation was achieved, typically at the level of machine (double floating point) precision. Note that for processes which contain, e.g., 4 charged fermions in the final state in addition to the two incoming charged leptons, we are left with a total of 15 unique dipoles entering the subtraction.
• Figure 3: Magnitude of the subtracted real correction, normalized to the Born-level baseline, in the IR limit of vanishing photon momentum.
• Figure 4: Cancellation of the IR poles according to \ref{['EQ:RealLoopIR']} using dimensional regularization. The bins correspond to the number of decimal places at which the cancellation was achieved.
• Figure 5: The scaling behaviour for our double real correction, \ref{['eq:RealRealSub']}, normalized to the Born contribution, for the various processes. In the case where both photons become soft, we plot the results against the energy of the hardest photon on the x-axis.