The Restoration of Electroweak Symmetry in Single Gauge Boson Production at the LHC

Massive gauge bosons obtain their mass from absorbing a Goldstone boson from the Higgs field. Because they have mass, they have an extra degree of freedom which gives rise to a longitudinal polarization state. The Goldstone Boson Equivalence Theorem predicts that at high energies, the production cross section of a longitudinally polarized massive gauge boson will converge to the production cross section of the Higgs boson. Consequently, longitudinal gauge bosons encode valuable information about the Higgs mechanism. In VBF events, they also provide knowledge of boson-self interactions. This paper studies the energy dependence of VBF events, polarization fraction of the $Z$ boson, and EFT effects to determine if a measurement of a longitudinally polarized $Z$ boson is feasible at the LHC.