For massive Proca fields with quartic self-interaction, the massless limit is not smooth: classical hyperbolicity loss persists at arbitrarily small mass, and the Vainshtein mechanism does not restore unitarity at scales comparable to the mass.
Hell, The massless limit of massive gauge theories , Ph.D
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Massless limit of massive self-interacting vector fields
For massive Proca fields with quartic self-interaction, the massless limit is not smooth: classical hyperbolicity loss persists at arbitrarily small mass, and the Vainshtein mechanism does not restore unitarity at scales comparable to the mass.