Neutrino-antineutrino DIS sea momentum ratio ($\bar{Q}/Q=(3R-1)/(3-R)$)

For an isoscalar target in the leading massless quark-parton approximation, integrate the two helicity weights over inelasticity: ${\int }_0^{1}dy=1$ and ${\int }_0^1(1-y{)}^{2}dy=1/3$. Then $R={\sigma }_{\bar{\nu }}/{\sigma }_{\nu }=(Q/3+\bar{Q})/(Q+\bar{Q}/3)$, where $Q=\int xq(x)dx$ and $\bar{Q}=\int x\bar{q}(x)dx$. Inversion gives the displayed ratio. These are effective weak-flavour momentum fractions; the data do not determine unweighted parton number integrals.