= Parton convolution normalization for a hadronic tensor
{title2=$W^{\mu\nu}=\sum_f\int_0^1\frac{d\xi}{\xi}[f_f(\xi)+\bar f_f(\xi)]w_f^{\mu\nu}(\xi P,q)$}
In the incoherent <massless collinear parton approximation>, $f_f(\xi)d\xi$ is the number of quarks in a momentum-fraction interval, not a covariantly normalized external state weight. A single-particle response divided by its external-state normalization is proportional to $w/(2k^0)$; the hadron normalization is $2P^0$. Thus converting a number-weighted parton sum to the target tensor contributes $P^0/k^0=1/\xi$. This gives the displayed convolution, including antiquarks. The <spin-averaged electromagnetic parton tensor> and $\delta(2\xi P\cdot q-Q^2)=\delta(\xi-x)/(2P\cdot q)$ then give $F_1=\tfrac12\sum_fQ_f^2(f_f+\bar f_f)$ and $F_2=x\sum_fQ_f^2(f_f+\bar f_f)$, proving the <Callan-Gross relation> at this order. Target masses, transverse momentum and radiative effects are beyond this leading approximation.
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