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Extensions of the Standard Model that include vector-like quarks commonlyalso include additional particles that may mediate new production or decaymodes. Using as example the minimal linear $\sigma$ model, that reduces to theminimal $SO(5)/SO(4)$ composite Higgs model in a specific limit, we considerthe phenomenology of vector-like quarks when a scalar singlet $\sigma$ ispresent. This new particle may be produced in the decays $T \to t \sigma$, $B\to b \sigma$, where $T$ and $B$ are vector-like quarks of charges $2/3$ and$-1/3$, respectively, with subsequent decay $\sigma \to W^+ W^-, ZZ, hh$. Byscanning over the allowed parameter space we find that these decays may bedominant. In addition, we find that the presence of several new particlesallows for single $T$ production cross sections larger than those expected inminimal models. We discuss the observability of these new signatures inexisting searches.

Exotic Vector-Like Quark Phenomenology in the Minimal Linear $\sigma$ Model