An analysis of nuclear parton distribution function based on Kullback-Leibler divergence

In this work, we propose a method to quantify the difference between nuclear parton distribution functions (nPDFs) in different nuclei and parton distribution functions (PDFs) in free nucleons using the Kullback-Leibler (KL) divergence, a measure widely employed in quantum information theory. By introducing certain constraints and the "minimum relative entropy" hypothesis, we can determine the shape of the structure function in the intermediate-$x$ region, which is intimately connected with the renowned EMC effect. For quark nPDFs, our results align with the latest global fits to experimental data. This agreement suggests that the KL divergence-based methodology may provide novel insight into the structure of nucleons, particularly in cases where experimental data and theoretical QCD constraints are limited, such as those pertinent to gluon nPDFs. Therefore, we applied this methodology to gluon nPDFs, analyzing the results from two commonly used global fitting groups, EPPS21 and nNNPDF3.0. Our analysis reveals that the EPPS21 results align more closely with the "minimum relative entropy" hypothesis. This finding underscores the utility of the proposed method and provides a valuable reference for future global fitting of nPDFs.