  We discuss hard rescattering effects that can be measured using CP-even,
T$_{\rm N}$-odd triple-product observables in polarized $Z$ decays to three
jets. We show that the standard model contributions, from both QCD and
electroweak rescattering, are very small. Thus these measurements are
potentially sensitive to physics beyond the standard model. We investigate one
such contribution which involves a new gauge boson coupling to baryon number.
