  We have measured the angular distribution of recoiling daughter nuclei
emitted from the Gamow-Teller $\beta$ decay of spin-polarized $^{80}$Rb. The
asymmetry of this distribution vanishes to lowest order in the Standard Model
(SM) in pure Gamow-Teller decays, producing an observable very sensitive to new
interactions. We measure the non-SM contribution to the asymmetry to be
$A_{T}$= 0.015 $\pm$ 0.029 (stat) $\pm$ 0.019 (syst), consistent with the SM
prediction. We constrain higher-order SM corrections using the measured
momentum dependence of the asymmetry, and their remaining uncertainty dominates
the systematic error. Future progress in determining the weak magnetism term
theoretically or experimentally would reduce the final errors. We describe the
resulting constraints on fundamental 4-Fermi tensor interactions.
