The fluctuational region on the phase diagram of lattice Weinberg - Salam model

Abstract

The lattice Weinberg - Salam model without fermions is investigated numerically for the realistic choice of bare coupling constants correspondent to the value of the Weinberg angle $\theta_W \sim 30^o$, and the fine structure constant $\alpha \sim {1/100}$. On the phase diagram there exists the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase, where the fluctuations of the scalar field become strong. The classical Nambu monopole can be considered as an embryo of the unphysical symmetric phase within the physical phase. In the fluctuational region quantum Nambu monopoles are dense and, therefore, the perturbation expansion around trivial vacuum cannot be applied. The maximal value of the cutoff at the given values of coupling constants calculated using the lattices of sizes $8^3\times 16$, $12^3\times 16$, and $16^4$ is $\Lambda_c \sim 1.4 \pm 0.2$ Tev. As the lattice sizes used are rather small we consider this result as preliminary.