Neutron structure function via a maximum entropy analysis

We employ the maximum entropy method to extract the valence quark distributions of the neutron at a low scale, $Q_0^2$. At this initial scale, the neutron is defined to contain only three valence quarks, with no contributions from sea quarks or gluons. The distributions of these initial valence quarks are constrained by principles from quark models, quark-hadron duality, and quark confinement. Employing the DGLAP equations supplemented by parton-parton recombination corrections, we derive the neutron structure function $F_2^{\rm n}$ at higher scales $Q^2$. The resulting ratio of the neutron to proton structure functions, $F_2^{\rm n}$/$F_{2}^{\rm p}$, aligns well with the world deep inelastic scattering data at Bjoken variable $x<0.7$, particularly when accounting for uncertainties from model-dependent corrections. Notably, this ratio is in agreement with the JLab MARATHON data after considering the quark-hadron duality assumption, especially in the region of $x \gtrsim 0.7$. Additionally, our findings for $F_2^{\rm n}$/$F_{2}^{\rm p}$ correspond well with the JLab BONuS experimental results after considering the impact of nucleon resonance contamination in the region $x \gtrsim 0.4, 0.5, 0.6$. We further compare our predictions for $F_2^{\rm n}$/$F_{2}^{\rm p}$ and the $u/d$ ratios in the limit as $x \rightarrow 1$ with existing theoretical calculations. Finally, we observe a minor violation of isospin symmetry between the proton and neutron, evidenced by the differences in valence quark distributions and the first-order moments of these distributions.