  The forward-backward asymmetry in top pair production at the Tevatron has
long been in tension with the Standard Model prediction. One of the only viable
new physics scenarios capable of explaining this anomaly is an s-channel
axigluon-like resonance, with the quantum numbers of the gluon but with
significant axial couplings to quarks. While such a resonance can lead to a
clear bump or excess in the ttbar or dijet mass spectra, it may also simply be
too broad to cleanly observe. Here, we point out that broad ttbar resonances
generally lead to net top and antitop polarizations transverse to the
production plane. This polarization is consistent with all discrete spacetime
symmetries, and, analogous to the forward-backward asymmetry itself, is absent
in QCD at leading order. Within the parameter space consistent with the
asymmetry measurements, the induced polarization can be sizable, and might be
observable at the Tevatron or the LHC.
