= Transverse decomposition of an unpolarized hadronic tensor
{title2=$W^{\mu\nu}=-T^{\mu\nu}F_1+\widetilde P^\mu\widetilde P^\nu F_2/(P\cdot q)$}
For electromagnetic <deep inelastic scattering> with an unpolarized target, <Lorentz invariance>, parity and <current conservation> leave two independent <deep-inelastic structure functions>. With $T^{\mu\nu}=g^{\mu\nu}-q^\mu q^\nu/q^2$ and $\widetilde P=P-(P\cdot q/q^2)q$, both tensor structures are transverse to $q$. Terms with a free $q$ index disappear on contraction with a conserved <leptonic tensor>, although such terms can still be necessary to make the full <hadronic tensor> transverse.
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