The present talk is based on the assumption that New Bound States (NBSs) of top-anti-top quarks (named T-balls) exist in the Standard Model (SM): a) there exists the scalar 1S - bound state of 6t+6bar t - the bound state of 6 top-quarks with their 6
anti-top-quarks; b) the forces which bind these top-quarks are very strong and almost completely compensate the mass of the 12 top-anti-top-quarks forming this bound state; c) such strong forces are produced by the interactions of top-quarks via the virtual exchange of the scalar Higgs bosons having the large value of the top-quark Yukawa coupling constant g_tsimeq 1. Theory also predicts the existence of the NBS 6t + 5bar t, which is a color triplet and a fermion similar to the t-quark of the fourth generation. We have also considered b-replaced NBSs: n_b b + (6t + 6bar t - n_b t) and n_b b + (6t + 5bar t - n_b t), etc. We have estimated the masses of the lightest b-replaced NBS: M_{NBS}simeq (300 - 400) GeV, and discussed the larger masses of the NBSs. We have developed a theory of the scalar T-balls 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-balls condensate and without it) equal to: g_t approx 1. The searching for the Higgs boson H and T-balls at the Tevatron and LHC is discussed.
