= Solution
The leading subprocess is $u\bar d\to W^+$. There are two beam assignments, and <charge conjugation> relates <antiproton> <Parton distribution functions>[PDFs] to <proton> <Parton distribution functions>[PDFs]. Therefore
$$
\frac{d\sigma}{dy}\propto u_p(x_+)\bar d_{\bar p}(x_-)+\bar d_p(x_+)u_{\bar p}(x_-)
=u(x_+)d(x_-)+\bar d(x_+)\bar u(x_-).
$$
In a narrow-width leading-order <normalization> the prefactor is $\pi g^2/(12s)$ when $|V_{ud}|=1$; only the <Parton distribution function>[PDF] dependence is needed for the fractions below.
Write the common sea <Parton distribution function>[PDF] as $S=\bar u=\bar d=\bar s=\bar c=\Sigma/8$. The <Valence and sea decomposition of proton-antiproton W production> gives the three <parton> luminosities
$$
\boxed{\mathcal L_{VV}=u_v(x_+)d_v(x_-),\quad
\mathcal L_{VS}=u_v(x_+)S(x_-)+S(x_+)d_v(x_-),\quad
\mathcal L_{SS}=2S(x_+)S(x_-).}
$$
The factor two in the sea-sea term includes both beam assignments. The <antiproton>'s <Valence quark>[valence antiquarks] make valence-valence <Annihilation> possible.
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