Nuclear EMC Effect in a Statistical Model

A simple statistical model in terms of light-front kinematic variables is used to explain the nuclear EMC effect in the range $x \in [0.2,~0.7]$, which was constructed by us previously to calculate the parton distribution functions (PDFs) of the nucleon. Here, we treat the temperature $T$ as a parameter of the atomic number $A$, and get reasonable results in agreement with the experimental data. Our results show that the larger $A$, the lower $T$ thus the bigger volume $V$, and these features are consistent with other models. Moreover, we give the predictions of the quark distribution ratios, \emph{i.e.}, $q^A(x) / q^D(x)$, $\bar{q}^A(x) / \bar{q}^D(x)$, and $s^A(x) / s^D(x)$, and also the gluon ratio $g^A(x) / g^D(x)$ for iron as an example. The predictions are different from those by other models, thus experiments aiming at measuring the parton ratios of antiquarks, strange quarks, and gluons can provide a discrimination of different models.

💡 Research Summary

The paper presents a minimalist statistical description of the nuclear EMC effect, extending a previously developed light‑front parton model of the free nucleon to bound nucleons inside nuclei. In the original model, parton distribution functions (PDFs) are obtained by treating quarks, antiquarks, strange quarks and gluons as a non‑interacting gas in light‑front coordinates, with temperature (T) and chemical potentials as the only thermodynamic parameters. To account for nuclear modifications, the authors introduce a single new hypothesis: the effective temperature of the partonic system depends on the atomic mass number (A). Specifically, larger nuclei are assigned a lower temperature, which, through the ideal‑gas relation, implies a larger effective volume (V). This temperature‑volume correlation is motivated by the physical picture that nucleons in a heavy nucleus experience a more dilute partonic environment, leading to a reduced average kinetic energy per parton.

The authors restrict their analysis to the Bjorken‑(x) region (0.2 \le x \le 0.7), where the classic EMC suppression is most pronounced and where the light‑front statistical approach is expected to be reliable. For each nucleus they determine the temperature (T(A)) by fitting the calculated ratio (F_2^A/F_2^D) to the corresponding experimental data. The resulting temperature decreases by roughly 10–20 MeV when moving from deuterium to iron, while the inferred volume grows by about 5–10 %. These trends are qualitatively consistent with other approaches that invoke mean‑field potentials, nucleon swelling, or short‑range correlations, but they emerge here from a single thermodynamic parameter.

With the temperature fixed for a given (A), the model yields explicit expressions for the nuclear PDFs: \