 Solution

ID: past-exam-of-the-particle-physics-course-of-the-university-of-oxford/2018/2/c/solution

The leading subprocess is

u \overset{ˉ}{d} \to W^{+}

. There are two beam assignments, and charge conjugation relates antiproton PDFs to proton PDFs. Therefore

\frac{d σ}{d y} \propto u_{p} (x_{+}) \overset{ˉ}{d}_{\overset{p}{ˉ}} (x_{-}) + \overset{ˉ}{d}_{p} (x_{+}) u_{\overset{p}{ˉ}} (x_{-}) = u (x_{+}) d (x_{-}) + \overset{ˉ}{d} (x_{+}) \overset{u}{ˉ} (x_{-}) .

In a narrow-width leading-order normalization the prefactor is

π g^{2} / (12 s)

when

∣ V_{u d} ∣ = 1

; only the PDF dependence is needed for the fractions below.

Write the common sea PDF as

S = \overset{u}{ˉ} = \overset{ˉ}{d} = \overset{s}{ˉ} = \overset{c}{ˉ} = Σ/8

L_{VV} = u_{v} (x_{+}) d_{v} (x_{-}), L_{V S} = u_{v} (x_{+}) S (x_{-}) + S (x_{+}) d_{v} (x_{-}), L_{SS} = 2 S (x_{+}) S (x_{-}) .

The factor two in the sea-sea term includes both beam assignments. The antiproton's valence antiquarks make valence-valence Annihilation possible.

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