Physical implications of the extrapolation and statistical bootstrap of nucleon structure function ratios F2nF2p for mirror nuclei He3 and H3

Abstract

A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio data in the quark momentum fraction regions ${x}_{B}\ensuremath{\rightarrow}0$ and ${x}_{B}\ensuremath{\rightarrow}1$. The extrapolated ${F}_{2}$ ratio as quark momentum fraction ${x}_{B}\ensuremath{\rightarrow}1$ is $\frac{{F}_{2}^{n}}{{F}_{2}^{p}}\ensuremath{\rightarrow}0.4\ifmmode\pm\else\textpm\fi{}0.05$ and this value is compared to theoretical predictions. The extrapolated ratio when ${x}_{B}\ensuremath{\rightarrow}0$ favors the simple model of isospin symmetry with the complete dominance of sea quarks at low momentum fraction. At high-${x}_{B}$, the proton quark distribution function ratio $d/u$ is derived from the ${F}_{2}$ ratio and found to be $d/u\ensuremath{\rightarrow}1/6$. Our extrapolated values for both the $\frac{{F}_{2}^{n}}{{F}_{2}^{p}}$ ratio and the $d/u$ parton distribution function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation arguments, and a Dyson-Schwinger equation with a contact interaction model. In addition, it is possible to match the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously in the nucleon wave function. One such example is nucleon wave functions composed of a linear combination of a quark-diquark state and a three-valence quark correlated state with coefficients that combine to give the extrapolated ${F}_{2}$ ratio at ${x}_{B}=1$.