# Massive vector bosons: is the geometrical interpretation as a spontaneously broken gauge theory possible at all scales?

January 12, 2015

The usual derivation of the Lagrangian of a
model for massive vector bosons, by spontaneous
symmetry breaking of a gauge theory, implies that the prefactors
of the various interaction terms are uniquely determined functions of the coupling
constant(s) and the masses. Since, under the renormalization group (RG) flow,
different interaction terms get different
loop-corrections, it is uncertain, whether these functions remain fixed under
this flow. We investigate this question for the $U(1)$-Higgs-model to 1-loop order
in the framework of Epstein-Glaser renormalization. Our main result reads: choosing the
renormalization mass scale(s) in a way corresponding
to the minimal subtraction scheme, the geometrical interpretation as a spontaneously
broken gauge theory gets lost under the RG-flow. This holds also for the
clearly stronger property of BRST-invariance of the Lagrangian. On the other
hand we prove that physical consistency, which is a weak form of BRST-invariance
of the time-ordered products, is maintained under the RG-flow.

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