Summary of Aspen discussions on perturbative uncertainties beyond 7-point variations

This writeup elaborates on constructive discussions which took place at the Aspen Center for Physics, Aug - Sep 2024, during the program “Tightening the gap between scattering amplitudes and events at the LHC at higher orders”. Building on already existing theoretical understanding from the study of scattering amplitudes and resummations at higher orders, we suggest to complement standard 7-point renormalisation- and factorisation-scale variations by additional estimates of missing higher-order terms which are known to be present in the perturbative series. We also summarise a recent proposal for at least one way that non-Gaussian theory uncertainties might be treated within a frequentist framework. This may help to provide more robust and comprehensive uncertainty estimates for experimental and phenomenological applications of perturbative calculations.