Automation of amplitude-level QED resummation with ACRAIC

Precision electroweak predictions for future $e^{+}{e}^{-}$ colliders will require levels of precision unmatched in collider physics and the modelling of multiple-photon emissions, and the exponentiation of the associated logarithms needs to be carefully considered. The Yennie-Frautschi-Suura theorem subtracts the infrared singularities to all orders and exponentiates them, leaving infrared-finite remainders which can be calculated order-by-order. Coherent exponentiation performs this subtraction at the amplitude level, preserving the interference between emissions, but has so far been available only for fermion-pair production, with hand-coded amplitudes. We present ACRAIC, an automated, amplitude-level realization of this subtraction for general scattering processes in Sherpa. This method allows us to construct an $\mathcal{O}(\alpha )$ and $\mathcal{O}({\alpha }^2)$ amplitude level subtraction scheme, in which the infrared-finite remainders are tree-level helicity amplitudes with partition-dependent propagator shifts, computed by the Berends–Giele recursion, and the one-loop electroweak virtual enters through a per-helicity factor from the loop provider. At $\mathcal{O}({\alpha }^2)$ two independent matchings agree on the size of the missing higher orders to $\sim {10}^{-3}$, and the estimated perturbative uncertainty shrinks by about an order of magnitude relative to $\mathcal{O}(\alpha )$.