If the top quark is a composite state made out of some constituents, its
interaction with the gluon will be modified. We introduce the leading effective
operators that contribute to the radius and anomalous magnetic moment of the
top quark and study their effect on the cross section for top anti-top
production at the Tevatron and the LHC. Current measurements of the cross
sections set a stringent limit on the scale of compositeness. This limit is
comparable to similar limits obtained for light quarks and those from
electroweak precision measurements. It can be used to constrain the parameter
space of some composite Higgs models.Comment: 18 pages, 9 figures, 1 table. Analysis extended to quadratic
contributions of the effective couplings. Study of top spin polarizations
added. New confidence intervals obtained. Figures of the bounds replaced.
Bounds on C2 result weaker. Version accepted for publication in PR