Improved spin basis for angular correlation studies in single top quark production at the Fermilab Tevatron

We show in single top quark production that the spin of the top quark is correlated with the direction of the $d$-type quark in the event. For single top-quark production in the $W^{*}$ channel, the $d$-type quark comes dominantly from the antiproton at the Fermilab Tevatron, whereas for the $W$-gluon fusion channel the spectator jet is the $d$-type quark the majority of the time at this machine. Our results are that 98% of the top quarks from the $W^{*}$ process have their spins in the antiproton direction, and 96% of the top quarks in the $W$-gluon fusion process have their spins in the spectator jet direction. We also compare with the more traditional, but less effective, helicity basis. The direction of the top quark spin is reflected in angular correlations in its decay products.