  We propose a model-independent and general framework to study the LHC
phenomenology of top partners, i.e. Vector-Like quarks including particles with
different electro-magnetic charge. We consider Vector-Like quarks embedded in
general representations of the weak SU(2)L, coupling to all Standard Model
quarks via Yukawa mixing focusing on the case of a single multiplet. We show
that, with very minimal and quite general assumptions, top partners may be
studied in terms of few parameters in an effective Lagrangian description with
a clear and simple connection with experimental observables. We also
demonstrate that the parametrisation can be applied as well to cases with many
Vector-like multiplets, thus covering most realistic models of New Physics. We
perform a numerical study to understand the conclusions which can be drawn
within such a description and the expected potential for discovery or exclusion
at the LHC. Our main results are a clear connection between branching ratios
and single production channels, and the identification of novel interesting
channels to be studied at the LHC.
