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

Abstract: In this work, we present an attempt 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. The obtained results are consistent with the latest global fits of experimental data. Moreover, we have extended this methodology to the determination of the gluon nPDFs, achieving results that exhibit remarkable consistency with global QCD fits. These results indicate that KL divergence may offer us a new window and perspective on the structure and nature of nucleons -- particularly in cases where limited experimental and theoretical QCD constraints are available.