The present paper is based on the assumption that heavy quarks bound states exist in the Standard Model (SM). Considering New Bound States (NBS) of top–antitop quarks (named T-balls) we have shown that: (1) there exists the scalar 1S-bound state of
; (2) the forces which bind the top-quarks are very strong and almost completely compensate the mass of the twelve top–antitop-quarks in the scalar NBS; (3) such strong forces are produced by the Higgs–top-quarks interaction with a large value of the top-quark Yukawa coupling constant gt≃1. Theory also predicts the existence of the NBS
, which is a color triplet and a fermion similar to the t'-quark of the fourth generation. We have also considered the "b-quark-replaced" NBS, estimated the masses of the lightest fermionic NBS: MNBS≳300 GeV, and discussed the larger masses of T-balls. We have developed a theory of the scalar T-ball's condensate and predicted the existence of three SM phases. Searching for heavy quark bound states at the Tevatron and LHC is discussed. We have constructed the possible form-factors of T-balls, and estimated the charge multiplicity coming from the T-ball's decays.