Application of the constituent quark exchange model to the parton distributions and the EMC ratios of $^{12}C$ and $^{14}N$ nuclei

TL;DR

This paper reformulates the quark exchange model for $^{12}C$ and $^{14}N$ nuclei to derive their parton distributions and EMC ratios, showing that leading-order calculations suffice for accurate results across various experimental data.

Contribution

It introduces a combined constituent quark exchange model to accurately predict EMC ratios of light nuclei, demonstrating the adequacy of LO calculations at relevant scales.

Findings

EMC ratios are largely independent of the hard scale $Q^2$.

LO and NLO EMC ratios are nearly identical at fixed $Q^2$.

Results align well with experimental data from multiple collaborations.

Abstract

The quark exchange model (QEM) is reformulated for the $A=12$ and $14$ systems to obtain the constituent quark distributions of $^{12}C$ and $^{14}N$ nuclei, respectively. Afterwards, the different types of the point-like parton distribution functions (PDFs), i.e., the valence quarks, the sea quarks and the gluons, are extracted from the constituent quark model (CQM), at the hadronic scale $Q_0^2=0.34$ $GeV^2$ to generate the constituent quark exchange model (CQEM = QEM $\oplus$ CQM) PDFs. From the resulted PDFs, the structure functions and the European Muon Collaboration (EMC) ratios of the above-mentioned nuclei at the appropriate hadronic scale are calculated. To make our results more comparable with the available experimental data, we evolve the PDFs, by using the standard DGALP evolution equations, to the higher hard scales. Subsequently, the EMC ratios of $^{12}C$ and $^{14}N$ nuclei at the some higher energy scales, corresponding to the scales of available data, are calculated, at the leading (LO) and the next-to-leading (NLO) orders of pQCD. By doing so, it is observed that the EMC ratios do not significantly depend on the hard scale $Q^2$, and the outcomes are consistent with the various experimental data such as HERMES, BCDMS, JLab, SLAC, NMC, and EMC. Especially, in the mid-range of Bjorken $x$ values, the results are so desirable. Like our previous works for the $^4He$ and $^6Li$ nuclei, we again observe that at a fixed scale $Q^2$, the LO and the NLO EMC ratios with high precision are approximately the same. Therefore, one can conclude that at a given hard scale, the LO approximation is good enough for calculating the EMC ratios of light nuclei.