Gluon polarization in $e^+e^-\rightarrow t\bar tG$: polar angle dependence and beam polarization effects

Abstract. We calculate the linear and circular polarization of gluons produced in conjunction with massive quarks in the annihilation process $e^+e^-\rightarrow q \bar q G$. The linear polarization is calculated in the hadron event plane as well as in the gluon-beam plane. Beam polarization and polar orientation effects are included in our discussion. For typical top pair production energies at the Next-Linear-Collider (NLC) the degree of linear polarization in the hadron event plane remains close to its soft gluon value of 100% over most of the energy spectrum of the gluon. The linear polarization in the gluon-beam plane is generally smaller but peaks toward the hard end of the gluon spectrum. The dependence of the linear polarization on beam polarization and on the polar orientation of the gluon is small. The circular polarization is largest for maximal gluon energies and shows a strong dependence on the longitudinal beam polarization. The longitudinal polarization of the beam may therefore be used to tune the circular polarization of the gluon. The massive quark results are compared with the corresponding results for the massless quark case.