Valence-only proton and neutron structure-function moments (source code)

= Valence-only proton and neutron structure-function moments
{title2=$\int_0^1F_2^p(x)\,dx/x=1,\quad\int_0^1F_2^n(x)\,dx/x=2/3$}

With only up/down valence quarks and no antiquarks, the <quark number sum rule> and leading <parton model> expression give the charge-squared number moment $\int F_2(x)dx/x=\sum_fQ_f^2N_f$. The squared charges are $4/9$ for up and $1/9$ for down, so the <proton> has $8/9+1/9=1$ and the <neutron> has $4/9+2/9=2/3$. Restricting the flavour list to up/down does not itself remove antiquarks; the no-sea assumption is essential for these individual moments.