Researchers have proposed a new mathematical formulation to infer the proton's parton distribution functions (PDFs) from deep inelastic scattering (DIS) data. This problem, traditionally addressed by fitting model parameters to global experimental data, is now reformulated as a linear tensor reconstruction inverse problem. The novelty lies in the ability to solve a system of coupled linear functional integral equations, which promises a less biased extraction of PDFs from model parameterizations.

The approach leverages the mathematical structures inherent in the integral equations defined by perturbative quantum chromodynamics (pQCD) and global analysis. By treating global analysis as a coupled system of linear integral equations, a proof-of-concept methodology for its solution has been developed. To concretize this approach, the study reviews all next-to-leading order (NLO) accuracy results for inclusive virtual photon, neutral current, charged current, heavy flavor production, and neutrino deep-inelastic lepton-proton scattering.

This mathematical inference methodology paves the way for a model-bias-free extraction of proton PDFs from world DIS data. It aligns with the spirit of indirect measurements used in mathematical inverse problems, allowing for robust uncertainty estimation with reduced bias from model parametrization. All of this is achieved while closely adhering to the established paradigm of pQCD and global analysis, suggesting a significant advance in the precision and reliability of determining the proton's internal structure.