Neutrino neutral-to-charged current ratio ($R_{\nu }={\sigma }_{\mathrm{NC}}^{\nu N}/{\sigma }_{\mathrm{CC}}^{\nu N}$)

For an isoscalar valence target and massless leading-order scattering, $R_{\nu }=G_L^2+G_R^2/3$, where $G_{L/R}^2=(g_{L/R}^u{)}^2+(g_{L/R}^d{)}^2$. The factor $1/3$ is ${\int }_0^1(1-y{)}^{2}dy$. With Standard Model quark couplings and $w={\sin }^2{\theta }_W$, this becomes $1/2-w+20w^2/27$. Sea quarks and threshold, nuclear and QCD corrections matter beyond this limit.