Massive-vector spin average ($\overline{|\mathcal{M}{|}^2}=\frac{1}{3}{\sum }_{\mathrm{spins}}|\mathcal{M}{|}^2$)

An unpolarized decay of a massive spin-one particle averages the squared amplitude over three parent spin states. Its polarization sum is $-{\eta }_{\mu \nu }+p_{\mu }{p}_{\nu }/m^2$. For a conserved external current the longitudinal $p_{\mu }{p}_{\nu }$ term drops out, but this does not replace the spin average by $1/2$: the physical massive parent still has three states.