= Solution
At leading order in <QED>, the <electron> exchanges one spacelike virtual <photon> with a charged <parton> inside the <proton>.
\Image[/past-exam-of-the-particle-physics-course-of-the-university-of-oxford/2021-dis-photon-exchange.png]
{title=One-photon-exchange <Feynman diagram> for inclusive <electron>-<proton> <deep inelastic scattering>}
The two <Feynman vertices> contribute $e$ and $e e_q$, while the <photon propagator> contributes $1/q^2=-1/Q^2$. Hence the <scattering amplitude> scales as $e^2e_q/Q^2$ and its squared <absolute value> as $e^4e_q^2/Q^4$. Since the <fine-structure constant> is $\alpha=e^2/(4\pi)$, the electromagnetic coupling dependence is $\alpha^2/Q^4$. The numerical $4\pi$ in the stated <differential scattering cross-section> additionally uses the flux, <Lorentz-invariant phase space>, azimuthal integration and the convention defining the <deep-inelastic structure function>; it cannot be deduced from the propagator alone.
For each measured $x,Q^2$ bin form the reduced quantity
$$
\boxed{F_2(x,Q^2)=\frac{xQ^4}{4\pi\alpha^2[1-y+y^2/2]}\frac{d^2\sigma}{dx\,dQ^2}.}
$$
Plot this against $Q^2$ at several fixed $x$ values, normally using a logarithmic $Q^2$ axis. <Bjorken scaling> predicts an approximately horizontal curve at each $x$, or equivalently collapse of different-$Q^2$ data onto one $F_2(x)$ curve. Raw <cross sections> do not collapse because their explicit kinematic factors vary. <QCD> predicts logarithmic <scaling violations>, so exact independence is only the ideal <parton model> limit. The stated extraction also assumes negligible <longitudinal deep-inelastic structure function>, as in the leading massless spin-half <parton> approximation.
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