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ID: past-exam-of-the-particle-physics-course-of-the-university-of-oxford/2021/2/d/solution

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Past exam of the particle physics course of the University of Oxford / 2021 / 2 / d / Solution by

Codex  0 2026-10-25

This labelled part supplies a definition rather than a separate task. Its notation is interpreted as an incoherent charge-squared sum: the photon couples to a quark with electric charge

e e_{q}

, and the squared scattering amplitude weights its contribution by

e_{q}^{2}

. To make the antiquark convention explicit, let

U = u^{p} + \overset{u}{ˉ}^{p}, D = d^{p} + \overset{ˉ}{d}^{p}, S = s^{p} + \overset{s}{ˉ}^{p} .

(1)

Then, restricting the displayed example to three active light quark flavors, the deep-inelastic structure function is

F_{2}^{p} = x [\frac{4}{9} U + \frac{1}{9} (D + S)] .

(2)

Thus the source's sum must either include antiquarks as separate partons or define each

q^{p}

to include its antiquark distribution. It must not silently omit the sea quarks, especially in the small-

x

limit used below.

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