usually thought of as a finite cutoff theory. For small Higgs masses (less than about $350$ GeV) the correspondent energy scale $\Lambda_c^{0}$ calculated within the perturbation theory is much larger, than $1$ Tev. In particular, for $M_H \sim 300$ GeV we have $\Lambda_c^{0}\sim 1000$ TeV. It is worth mentioning that for $\lambda
\rightarrow \infty$ the perturbation expansion in $\lambda$ cannot be used. In this case Higgs mass approaches its absolute upper bound[^1], and both triviality and Hierarchy scales approach each other.

From the previous research we know that the phase diagram in the $\beta$ - $\gamma$ plane of the lattice $SU(2)$ Gauge - Higgs for any fixed $\lambda$ resembles the phase diagram for the lattice Weinberg - Salam model. The only difference is that in the $SU(2)$ Gauge - Higgs model the confinement-deconfinement phase transition corresponding to the $U(1)$ constituents of the model is absent. The direct measurement of the renormalized coupling $\beta_R$ shows [@1; @2; @3; @4; @5; @6; @7; @8; @9; @10; @11; @12; @13; @14] that the line of constant renormalized coupling constant (with the value close to the experimental one) intersects the phase transition line. Also we know from the direct measurements of $M_W$ in the 