Abstract
If the top quark is a composite state made out of some constituents, then 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 $t\overline{t}$ 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.
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