Extraction of Drell–Yan Angular Coefficients Using Neural Ratio Estimation in $pp$ Collisions at 120 GeV Beam Energy

Bayesian inference offers a principled and robust framework for parameter estimation and uncertainty quantification across a wide range of scientific applications. However, conventional approaches require explicit likelihood functions, which are often analytically intractable in realistic experimental conditions. To address this, we employ ``simulation-based inference" (SBI), a ``likelihood-free" approach that leverages simulations to estimate posterior distributions. Specifically, we use neural classifiers to approximate the likelihood-to-evidence ratio, enabling efficient posterior sampling. We apply this methodology to extract dimuon decay angular distribution coefficients in the Drell–Yan process using LH$_{2}$​ target data from the E906/SeaQuest experiment. The results demonstrate that SBI can provide robust and scalable inference for complex particle physics observables.