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.
Higgs, Broken Symmetries and the Masses of Gauge Bosons , Phys
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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.