Top quark compositeness: Feasibility and implications

In models of electroweak symmetry breaking in which the standard model fermions get their masses by mixing with composite states, it is natural to expect the top quark to show properties of compositeness. We study the phenomenological viability of having a mostly composite top. The strongest constraints are shown to mainly come from one-loop contributions to the $T$ parameter. Nevertheless, the presence of light custodial partners weakens these bounds, allowing in certain cases for a high degree of top compositeness. We find regions in the parameter space in which the $T$ parameter receives moderate positive contributions, favoring the electroweak fit of this type of model. We also study the implications of having a composite top at the LHC, focusing on the process $pp\to t\overline{t}t\overline{t}(b\overline{b})$ whose cross section is enhanced at high energies.