Scaling properties of nuclear parton distributions in short-range-correlation motivated two-component parametrization

We provide some critical remarks on the recently proposed two-component parametrization of nuclear parton distribution functions, which was motivated by the apparent correlation between the nuclear modifications of structure functions and nucleon-nucleon short-range correlation phenomena. This parametrization, we show, is invariant under a rescaling transformation of the involved abundance coefficients, which means that the global normalization of these coefficients cannot be meaningfully determined in a fit, and only their ratios should be studied for finding evidence of short-range-correlation type behavior at parton level. As we show, however, the current constraints for the nuclear-mass dependence of these coefficients allow also for interpretations different from short-range correlations. Nevertheless, this two-component parametrization exhibits a similar scaling relation for DIS structure functions as demonstrated in earlier works, and, as we demonstrate, yields testable predictions for structure-function and hard-process cross-section ratios. We also note on the non-trivial isospin dependence of the short-range-correlation motivated parametrization, which under proton-neutron pair dominance assumption can lead to charge-symmetry-violation resembling terms.

💡 Research Summary

This paper presents a critical analysis of a recently proposed two-component parametrization for nuclear parton distribution functions (nPDFs), which is motivated by the observed correlation between nuclear modifications in deep-inelastic scattering and nucleon-nucleon short-range correlation (SRC) phenomena. The author provides both an appraisal of the model’s strengths and a detailed critique of its fundamental limitations.

The core of the model lies in decomposing the PDF of a bound nucleon into a linear combination of two components: the PDF of a free (or quasi-free) nucleon and the PDF of a nucleon within a universal SRC pair. The relative weight of these components is governed by nucleus-dependent abundance coefficients, C_A^p and C_A^n. The paper first formalizes this approach, showing how it leads to specific, testable predictions for nuclear modification factors.

The most significant criticism raised is the demonstration of a “rescaling invariance.” The author proves mathematically that a simultaneous transformation—scaling all abundance coefficients by an arbitrary factor X and inversely adjusting the SRC PDFs—leaves the total nuclear PDF completely unchanged. This implies that the absolute normalization of the extracted C_A coefficients is arbitrary and parametrization-dependent; it cannot be meaningfully determined from a global fit to data. The only physically meaningful quantities are the ratios of these coefficients between different nuclei (e.g., C_A1 / C_A2), which are invariant under this transformation. This insight aligns with findings in nuclear structure theory, where absolute pair counts can be scheme-dependent, but their ratios are robust.

Despite this limitation, the model yields powerful and testable consequences. It enforces a specific scaling relation: for any parton flavor, momentum fraction x, and energy scale Q, the ratio of nuclear modification factors for two different nuclei must be a constant, equal to the ratio of their abundance coefficients. This is a strong prediction that can be tested not only with structure function data but also with cross-section ratios for hard processes like jet production in proton-nucleus collisions.

The paper also delves into the non-trivial implications for isospin symmetry. Assuming isospin symmetry holds for the SRC PDFs themselves and imposing proton-neutron pair dominance leads to effective charge-symmetry-violation (CSV)-like terms in the average bound-nucleon PDFs for non-isoscalar nuclei. The author clarifies that these are nuclear environment effects and not fundamental CSV from the electroweak sector, but they are a notable feature of the model that requires careful consideration in data analysis.

Finally, the SRC-motivated parametrization is compared to traditional nPDF global fits like EPPS21. The SRC model allows for a more flexible mass dependence (independent coefficients per nucleus) but is more restrictive in forcing a universal scaling across all parton flavors and x-values via a single coefficient ratio. In contrast, parametrizations like EPPS21 allow for flavor- and x-dependent scaling exponents but assume a simpler power-law mass dependence. The SRC coefficients are argued to have a clearer physical interpretation (abundance), whereas the reference nucleus in fits like EPPS21 is an arbitrary choice.

In conclusion, the paper argues that while the SRC-motivated two-component model offers an appealing physical picture and generates falsifiable predictions for future experiments at the EIC and LHC, its current formulation has inherent ambiguities due to rescaling invariance. The absolute values of the SRC abundances are not uniquely determinable, and current data do not exclusively favor an SRC interpretation. Nevertheless, the model provides a valuable framework for exploring scaling relations in nuclear partonic structure and will be subject to stringent tests with upcoming high-precision data.