Train-Resolved Statistical Recovery of Weak SAXS Signals in Liquids at the European XFEL

Abstract

We present a train-resolved SAXS methodology for recovering weak scattering signals from high-repetition-rate XFEL datasets and apply it to aqueous L-cysteine solutions measured at the European XFEL. Independent scale-plus-offset fitting was performed for matched cysteine and water train pairs, followed by subtraction of transmission-matched water--water controls. The 0.5 M dataset reveals a reproducible sign-changing residual SAXS signal that increases with incident XFEL transmission and remains after removal of detector-wide scaling, additive offsets, and matched water--water control residuals. Convergence and block-averaging analyses show that the residual emerges progressively as independent train pairs are accumulated and exhibits uncertainty scaling close to the expected inverse square-root dependence on N. These results establish a statistically robust transmission-dependent residual SAXS contribution whose microscopic origin remains unresolved, while demonstrating that train-resolved observables combined with matched controls can substantially improve sensitivity to weak scattering signals in high-repetition-rate XFEL experiments.