Single top quark production at the LHC: Understanding spin

We show that the single top quarks produced in the Wg-fusion channel at a proton-proton collider at a center-of-mass energy s=14 TeV posses a high degree of polarization in terms of a spin basis which decomposes the top quark spin in its rest frame along the direction of the spectator jet. A second useful spin basis is the η-beamline basis, which decomposes the top quark spin along one of the two beam directions, depending on which hemisphere contains the spectator jet. We elucidate the interplay between the two- and three-body final states contributing to this production cross section in the context of determining the spin decomposition of the top quarks, and argue that the zero momentum frame helicity is undefined. We show that the usefulness of the spectator and η-beamline spin bases is not adversely affected by the cuts required to separate the Wg-fusion signal from the background.