= Solution
Treat a <nucleon> as incoherent collinear spin-half <quarks> and <antiquarks> carrying fractions $x$ of its <momentum>. Neglect their <masses> and transverse motion, use a <Charged current>[charged-current] four-fermion interaction, and take $Q^2\ll m_W^2$. The subprocess <energy> is $\hat s\simeq xs$. <Antineutrino> scattering on a <quark> has the same selected-current <helicity> factor $(1-y)^2$ as in part a; crossing to an <antiquark> changes the allowed <spin> pairing and gives a flat distribution. Multiplying the elementary strength by the respective <Parton distribution functions>[parton densities] gives
$$
\boxed{\frac{d^2\sigma(\bar\nu N)}{dx\,dy}=\frac{G_F^2sx}{\pi}\left[(1-y)^2q(x)+\bar q(x)\right].}
$$
Here $q,\bar q$ are the effective <Parton distribution function>[weak flavour combinations] with the <Isoscalar target>[isoscalar] proton-neutron average and <CKM matrix>[CKM weights] absorbed into their definitions. With only light <Flavor eigenstates>[flavours] and <Charge symmetry of nucleon parton distributions>[charge symmetry], the relevant up and down combinations coincide on an <Isoscalar target>[isoscalar target]. Rescaling those density definitions requires rescaling the prefactor consistently.
The equation is a leading-order scaling result: it neglects logarithmic <QCD> evolution, heavy-quark thresholds, <Higher twist>[higher-twist] and <Deep inelastic scattering>[target-mass] corrections, <Nuclear parton distribution function>[nuclear modifications], and <W boson propagator>[weak-propagator] suppression. The current produces $\mu^+$ for an incident <muon> <antineutrino>. At higher <momentum> transfer the weak propagator supplies a factor approximately $[m_W^2/(m_W^2+Q^2)]^2$, and at low <energy> <resonance> and quasielastic scattering invalidate a pure <Deep inelastic scattering>[DIS] description.
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