= Ultraviolet and unitary-gauge limits of the Proca propagator
{title2=$D_\xi=-i[P_T/(k^2+M^2)+\xi P_L/(k^2+\xi M^2)]$}
In mostly-plus signature, the <unitary gauge> limit $\xi\to\infty$ leaves the longitudinal <Proca propagator> term $-iP_L/M^2$. Its ultraviolet scaling is constant in the <momentum> magnitude, whereas finite $\xi$ gives $1/k^2$ scaling. Thus taking the gauge-parameter limit before the ultraviolet limit obscures ordinary power-counting <renormalizability>. A conserved external current annihilates the longitudinal term, so the exchange between two such currents still falls as $1/k^2$. The issue does not make a free massive-vector <Gaussian integral> inconsistent.
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