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The present talk is based on the assumption that New Bound States (NBSs) oftop-anti-top quarks (named T-balls) exist in the Standard Model (SM): a) thereexists the scalar 1S - bound state of 6t+6\bar t - the bound state of 6top-quarks with their 6 anti-top-quarks; b) the forces which bind thesetop-quarks are very strong and almost completely compensate the mass of the 12top-anti-top-quarks forming this bound state; c) such strong forces areproduced by the interactions of top-quarks via the virtual exchange of thescalar Higgs bosons having the large value of the top-quark Yukawa couplingconstant g_t\simeq 1. Theory also predicts the existence of the NBS 6t + 5\bart, which is a color triplet and a fermion similar to the t'-quark of the fourthgeneration. We have also considered "b-replaced" NBSs: n_b b + (6t + 6\bar t -n_b t) and n'_b b + (6t + 5\bar t - n'_b t), etc. We have estimated the massesof the lightest "b-replaced" NBS: M_{NBS}\simeq (300 - 400) GeV, and discussedthe larger masses of the NBSs. We have developed a theory of the scalarT-ball's condensate, and predicted the existence of the three SM phases,calculating the top-quark Yukawa coupling constant at the border of two phases(with T-ball's condensate and without it) equal to: g_t \approx 1. Thesearching for the Higgs boson H and T-balls at the Tevatron and LHC isdiscussed.

New Bound States of Top-anti-Top Quarks and T-balls Production at Colliders (Tevatron, LHC, etc.)