Ultraviolet and unitary-gauge limits of the Proca propagator ($D_{\xi }=-i[P_T/(k^2+M^2)+\xi P_L/(k^2+\xi M^2)]$)

In mostly-plus signature, the unitary gauge limit $\xi \to \infty$ leaves the longitudinal Proca propagator term $-i{P}_L/M^2$. 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.