We show how to observe sizable angular correlations between the decay products of the top quark and those of the anti-top quark in top quark pair production and decay at hadron colliders. These correlations result from the large asymmetry in the rate for producing like-spin versus unlike-spin top quark pairs provided the appropriate spin axes are used. The effects of new physics at production or decay on these correlations are briefly discussed.

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 production in the W * channel, the d-type quark comes dominantly from the antiproton at the 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.

We apply the solution to the recursion relation for the double-off-shell quark current to the problem of computing one loop amplitudes with an arbitrary number of gluons. We are able to compute amplitudes for photon-gluon scattering, electron-positron annihilation to gluons, and gluon-gluon scattering via a quark loop in the case of like-helicity gluons. In addition, we present the result for the one-loop gluon-gluon scattering amplitude when one of the gluons has opposite helicity from the others.12.38. Bx, 11.80.Cr

We use the solutions to the recursion relations for double-off-shell fermion currents to compute helicity amplitudes for n-photon scattering and electronpositron annihilation to photons in the massless limit of QED. The form of these solutions is simple enough to allow all of the integrations to be performed explicitly. For n-photon scattering, we find that unless n = 4, the amplitudes for the helicity configurations (+++ · · · +) and (−++ · · · +) vanish to oneloop order.11.80.Cr, 12.20.Ds Typeset using REVT E X 1

A comparison is made between the off-diagonal and helicity spin bases for top quark pair production at the FNAL Tevatron. In the off-diagonal basis, 92% of the top quark pairs are in the spin configuration up-down plus downup, whereas in the helicity basis only 70% are left-right plus right-left. The off-diagonal basis maximizes the spin asymmetry and hence the measured angular correlations between the decay products, which are more than twice as big in this basis as compared to the helicity basis. In addition, for the process qq → tt, we give a very simple analytic expression for the matrix element squared which includes all spin correlations between the production and subsequent decay of the top quarks.