  In 2013 the Nobel Prize in Physics was awarded to Francois Englert and Peter
Higgs for their work in 1964 along with the late Robert Brout on the mass
generation mechanism (the Higgs mechanism) in local gauge theories. This
mechanism requires the existence of a massive scalar particle, the Higgs boson,
and in 2012 the Higgs boson was finally discovered at the Large Hadron Collider
after being sought for almost half a century. In this article we review the
work that led to the discovery of the Higgs boson and discuss its implications.
We approach the topic from the perspective of a dynamically generated Higgs
boson that is a fermion-antifermion bound state rather than an elementary field
that appears in an input Lagrangian. In particular, we emphasize the connection
with the Barden-Cooper-Schrieffer theory of superconductivity. We identify the
double-well Higgs potential not as a fundamental potential but as a mean-field
effective Lagrangian with a dynamical Higgs boson being generated through a
residual interaction that accompanies the mean-field Lagrangian. We discuss
what we believe to be the key challenge raised by the discovery of the Higgs
boson, namely determining whether it is elementary or composite, and through
study of a conformal invariant field theory model as realized with critical
scaling and anomalous dimensions, suggest that the width of the Higgs boson
might serve as a suitable diagnostic for discriminating between an elementary
Higgs boson and a composite one. We show that the contribution to the
cosmological constant due to a composite Higgs boson is more tractable and
under control than the contribution due to an elementary Higgs boson, and is
potentially completely under control if there is an underlying conformal
symmetry not just in a critical scaling matter sector, but equally in the
gravity sector to which the matter sector couples.
