Proton Structure from Neural Simulation-Based Inference at the LHC

Abstract: The precise determination of the parton distribution functions (PDFs) of the proton is an essential ingredient for LHC analyses, including for those at the upcoming High-Luminosity LHC. So far, PDFs are determined from global fits to binned low-dimensional data obtained from unfolded hard-scattering cross section measurements. In this work we demonstrate for the first time the feasibility of neural simulation-based inference (NSBI) for constraining the proton PDFs using a high-dimensional unbinned data set. Exploiting the full statistical power of unbinned data removes the loss of information inherited by the binning procedure. As a proof-of-concept, we determine the gluon PDF from simulated data of top quark pair production at the LHC with $\sqrt{s}=13$ TeV. Taking into account both experimental and theoretical systematic uncertainties in the detector-level features, we demonstrate how the NSBI pipeline achieves significant improvements in precision compared to existing low-dimensional binned analyses. Our results illustrate the potential of unbinned inference to reduce the reliance on coarse approximations of uncertainties and their correlations entering PDF determinations, hence contributing to a new paradigm of unbinned detector-level ML-assisted measurements at the LHC.