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Colloquium on the Higgs Boson

In 2013 the Nobel Prize in Physics was awarded to Francois Englert and Peter Higgs for their development in 1964 of 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 observed at the Large Hadron Collider after being sought for almost half a century. In this pedagogical article we review the work of these Nobel recipients 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 BCS 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 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.