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

Abstract

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.

Figures (5)

• Figure 1: The KL divergence as a function of $a_1$ and $b_1$. The red dot indicates the position with minimum KL divergence for $^{4}$He, $^{12}$C, $^{56}$Fe and $^{208}$Pb, at the momentum transfer $Q^2 = 10\,{\rm GeV}^2$. The orange and magenta dots mark two representative reference solutions, which will be used for comparisons in Figure \ref{['3xunnormalized']}.
• Figure 2: The obtained structure function $\bar{p}^{A}_{\textrm{poly}}(x)$ with minimum KL divergence (red line), the structure function $p^A(x)$ given by the global fitting of experimental data (black line), and the two reference structure functions $\bar{p}^{A}_{\textrm{ref1}}(x)$ and $\bar{p}^{A}_{\textrm{ref2}}(x)$ (orange and magenta lines).
• Figure 3: The obtained structure function $\bar{p}^{A}_{\textrm{poly}}(x)$ from polynomial form of parameterization (red line), the structure function $\bar{p}^{A}_{\textrm{can}}(x)$ from canonical form of parametrization (blue dashed line), as well as the structure function $p^A(x)$ given by the global fitting of experimental data (black line).
• Figure 4: The obtained gluon nPDFs $\bar{p}^{A}_{g,\textrm{poly}}(x)$ with minimum KL divergence in polynomial parametrization (red line), the $\bar{p}^{A}_{g,\textrm{can}}(x)$ with minimum KL divergence in canonical parametrization (blue dashed line), as well as the gluon nPDFs $p_g^A(x)$ given by the global analysis from EPPS21 (black line).
• Figure 5: The obtained gluon nPDFs $\bar{p}^{A}_{g,\textrm{poly}}(x)$ with minimum KL divergence in polynomial parametrization (red line), the $\bar{p}^{A}_{g,\textrm{can}}(x)$ with minimum KL divergence in canonical parametrization (blue dashed line), as well as the gluon nPDFs $p_g^A(x)$ given by the global analysis from nNNPDF3.0 (black line).