Model-independent framework for searches of top partners

38 pages, 1 figure, 20 tablesInternational audienceWe 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. 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 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