= Hadronic photon spectral density
{title2=$\rho_h(s)$}
Define the inclusive photon-field tensor for hadronic final states by $W_A^{\mu\nu}=2\pi\rho_h(s)(-g^{\mu\nu}+q^\mu q^\nu/s)$ for timelike $q$ with $s=q^2$ and $q^0>0$. Here each final state has relativistic normalization and the sum includes the four-momentum delta function. This <hadronic photon spectral density> has mass dimension $-2$. At leading electromagnetic order, $\rho_h=e^2\rho_J/s$, with $\rho_J$ the dimensionless <hadronic electromagnetic-current spectral density>. Stating the tensor convention prevents mismatched powers of $s$ or $e$ in an inclusive cross-section.
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