= Spin-averaged electromagnetic parton tensor
{title2=$S^{\mu\nu}=Q^2T^{\mu\nu}+4\widetilde k^\mu\widetilde k^\nu$}
For an on-shell massless <quark> with incoming momentum $k$ and outgoing momentum $k+q$, average the initial spin and sum the final spin. The <gamma matrix trace identities> give $S^{\mu\nu}=\tfrac12\operatorname{Tr}[\not k\gamma^\mu(\not k+\not q)\gamma^\nu]=2[k^\mu(k+q)^\nu+k^\nu(k+q)^\mu-g^{\mu\nu}k\cdot q]$. On shell $2k\cdot q=Q^2=-q^2$, and defining $T^{\mu\nu}=-g^{\mu\nu}+q^\mu q^\nu/q^2$ and $\widetilde k=k-(k\cdot q/q^2)q$ yields the displayed transverse decomposition. With the hadronic-tensor prefactor $1/(4\pi)$, one-particle <Lorentz-invariant phase space> gives $w_f^{\mu\nu}=(Q_f^2/2)\delta_+((k+q)^2)S^{\mu\nu}$. The antiquark has the same unpolarized tensor and squared electric charge.
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