Physical Implications of the Extrapolation and Statistical Bootstrap of the Nucleon Structure Function Ratio $\frac{F_2^n}{F_2^p}$ for Mirror Nuclei $^3$He and $^3$H

Abstract

A nuclear physics example of statistical bootstrap is used on the MARATHON data nucleon structure function ratio, $\frac{F_2^n}{F_2^p}$, in the quark momentum fraction $x_B\rightarrow0$ and $x_B\rightarrow1$ regions. The extrapolated $F_2$ ratio value as quark momentum fraction $x_B\rightarrow 1$ approaches 0.4 and this value is compared to theoretical predictions. The extrapolated ratio when $x_B\rightarrow 0$ favors the simple model of isospin symmetry with the complete dominance of seaquarks at low momentum fraction. At high-$x_B$, the proton quark distribution function ratio $d/u$ is derived from the $x\rightarrow 1$ ratio $\frac{F_2^n}{F_2^p}\rightarrow 0.4$ and found to be $d/u \rightarrow 1/6$. Our extrapolated values for both the $\frac{F_2^n}{F_2^p}$ ratio and the $d/u$ parton distribution function ratio most closely match perturbative QCD values from quark counting and helicity conservation arguments but still differ by roughly $7\%$. The mismatch to theoretical predictions may be ameliorated if two compatible models act simultaneously in the nucleon wavefunction. One such example is nucleon wavefunctions composed of a linear combination of a quark-diquark state and a 3-valence quark correlated state with coefficients that combine to give the extrapolated $F_2$ ratio of $0.4$.