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-anti-top quarks (named T-balls) we have shown that: 1) there exists the scalar 1S--bound state of $6t+6bar t$; 2) the forces which bind the top-quarks are very strong and almost completely compensate the mass of the twelve top-anti-top-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 $g_tsimeq 1$. 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 the b-quark-replaced NBS, estimated the masses of the lightest fermionic NBS: $M_{NBS}gtrsim 300$ GeV, and discussed the larger masses of T-balls. We have developed a theory of the scalar T-balls 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-balls decays.
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