Improving parton shower predictions via precision moments of energy flow polynomials

Abstract

We study conceptual and practical aspects of using maximum-entropy reweighting to upgrade parton-shower event samples with higher-accuracy theoretical constraints. Our approach produces strictly positive per-event weights that improve parton-shower predictions while preserving full event-level exclusivity, allowing any observable to be computed without rebinning or regeneration. On the conceptual side, we explain how theoretical principles can help determine which constraints to use and which kinds of priors lead to efficient reweighting. On the practical side, we perform a proof-of-concept study with hemisphere observables in $e^+e^- \to$ hadrons, and show that even when the parton-shower prior is degraded by removing the non-singular parts of the QCD splitting functions, a small set of precision calculations can restore the correct behavior. We use energy flow polynomials (EFPs) as a systematic basis for infrared- and collinear-safe constraints, and study how information transfers from constrained to unconstrained observables. We find rapid information saturation, where a compact set of EFP moments achieves broad improvements across observable space, including for standard hemisphere observables never used in training. By construction, the imposed moments of the posterior are formally as accurate as the precision inputs, while the improvement of any other observable is an empirical statement about information transfer that we quantify numerically. Physics-motivated basis reductions from collinear power counting achieve comparable performance to complete bases, and mixed moments combining polynomial and logarithmic terms outperform pure alternatives. These results suggest a systematic approach to improving parton-shower event generators, where theoretical constraints of the highest accuracy translate into full phase-space predictions of experimental relevance.