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.
Quantum Stability of Generalized Proca Theories
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We establish radiative stability of generalized Proca effective field theories. While standard powercounting arguments would conclude otherwise, we find non-trivial cancellations of leading order corrections by explicit computation of divergent one-loop diagrams up to four-point. These results are crosschecked against an effective action based generalized Schwinger-DeWitt method. Further, the cancellations are understood as coming from the specific structure of the theory through a decoupling limit analysis which at the same time allows for an extension of the results to higher orders.
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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.