In 1976, S. Weinberg and his student, E. Gildener (GW), proposed
multi-Higgs models of electroweak symmetry breaking which are clas-
sically scale-invariant. If this scale invariance is spontaneously broken,
the Higgs boson is the resulting massless dilaton and, of all the model’s
scalars, its couplings to gauge bosons and fermions are exactly as in
the one-Higgs-doublet Standard Model of Weinberg’s 1967 “Model of
Leptons”. That is, this Higgs boson is aligned. But, since the clas-
sical Higgs potential has an infinitely long flat minimum, there is no
fixed mass scale — i.e., no fixed VEV — at this level and no concrete
meaning to this statement.
This scale invariance is explicitly broken by the renormalization
scale Λ in the one-loop approximation of the Coleman-E. Weinberg
effective potential, the Higgs boson boson gets mass, and its VEV
v is fixed by its relation to Λ. GW assigned its value to be v =
2−1/4G−1/2
F = 246 GeV. Now Higgs alignment means something, but
is it preserved in one-loop order, i.e., is it natural? And what about
higher orders?
In this talk, I will summarize the above in a two-Higgs-doublet
model of the GW mechanism, emphasizing the surprisingly low masses
of the model’s BSM Higgs and the role of the top quark in Higgs
alignment, update the important experimental consequences of this
alignment — stressing the futility of most ATLAS and CMS searches
for BSM Higgses, and preview the extension of these results to two-
loops.
This work was started in 2019 with ́Eric Pilon and extended in 2020
with Estia Eichten. The two-loop extension is done with Eichten.
