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+6\bar 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_t\simeq 1. Theory also predicts the existence of the NBS 6t + 5\bar
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 + 6\bar t -
n_b t) and n'_b b + (6t + 5\bar 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-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. The
searching for the Higgs boson H and T-balls at the Tevatron and LHC is
discussed.Comment: 43 pages, 20 figure