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At energy $E\gg M_X$, the longitudinal polarization behaves as ${ϵ}_L^{\mu }\sim p^{\mu }/M_X$. A Proca theory with arbitrary interactions can therefore produce longitudinal-vector scattering amplitudes growing like powers of $E/M_X$, eventually violating partial-wave unitarity and invalidating perturbation theory.

In a gauge-theory completion, the Higgs mechanism identifies the longitudinal mode with a would-be Goldstone boson. Gauge relations fix the vector, Goldstone, and Higgs couplings. Higgs-exchange diagrams then cancel the leading energy growth of the gauge diagrams, as in longitudinal $W$-boson scattering, leaving amplitudes compatible with perturbative unitarity up to the scale where the full renormalizable theory itself becomes strongly coupled.

The longitudinal polarization of a massive vector behaves as ${ϵ}_L^{\mu }(p)\sim p^{\mu }/m$ at high energy. Generic self-interactions therefore make amplitudes grow as powers of $E/m$, eventually violating partial-wave unitarity and destroying perturbative predictivity. Simply adding a Proca mass also spoils the gauge cancellations that control ultraviolet behavior.

The Standard Model obtains the $W$ and $Z$ masses through the Higgs mechanism inside a renormalizable gauge theory. Goldstone bosons supply the longitudinal polarizations, and relations among gauge and Higgs couplings enforce cancellations of the growing terms. In particular, Higgs exchange cancels the remaining $E^2$ growth in longitudinal vector-boson scattering.