Direct Bayesian Inference of Helicity Amplitudes from Detector-Level Scattering Data

Abstract

Helicity amplitudes give the most complete description of a variety of scattering reactions used in studies of strong interactions, but they cannot be measured directly: experiments record bilinear combinations of them folded through a detector response, and conventional analyses recover them through multiple stages that introduce discrete ambiguities and require a separate extraction of the absolute cross sections. Here we replace that chain with a single Bayesian inference that determines the experimentally identifiable amplitude parameters directly from detector-level measurements. A score-based diffusion model, trained on a forward simulator, provides the full posterior in each kinematic bin, with the detector response carried by the forward model and positivity of the spin-density matrix guaranteed by the parameterization. The observable amplitude content in electroproduction of final particles grows with polarization of beams and targets, providing additional sensitivity to underlying phases. In simulation, the posterior achieves empirical coverage at or above the nominal level and delivers the angular observables and the separated contributions from longitudinal and transverse photons with their correlations retained. It transfers without retraining to a realistic detector response absent from training and remains reliable in the weakly constrained nucleon-helicity-flip sector, where per-bin likelihood maximization degrades. The result is a general framework for a broad class of inverse problems, phase retrieval, quantum-state tomography, and partial-wave analysis are further instances. Its core requires only a forward simulation of the complete measurement process, instrumental effects are handled within one statistically consistent posterior, applicable across exclusive vector-meson programs at Jefferson Lab, COMPASS, HERMES, and the future Electron-Ion Collider.