How to approach continuum physics in lattice Weinberg - Salam model

We investigate lattice Weinberg - Salam model without fermions numerically for the realistic choice of coupling constants correspondent to the value of the Weinberg angle $θ_W \sim 30^o$, and bare fine structure constant around $α\sim 1/150$. We consider the values of the scalar self coupling corresponding to Higgs mass $M_H \sim 100, 150, 270$ GeV. It has been found that nonperturbative effects become important while approaching continuum physics within the lattice model. When the ultraviolet cutoff $Λ= \fracπ{a}$ (where $a$ is the lattice spacing) is increased and achieves the value around 1 TeV one encounters the fluctuational region (on the phase diagram of the lattice model), 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 use of the perturbation expansion around trivial vacuum in this region is limited. Further increase of the cutoff is accompanied by a transition to the region of the phase diagram, where the scalar field is not condensed (this happens at the value of $Λ$ around 1.4 TeV for the considered lattice sizes). Within this region further increase of the cutoff is possible although we do not observe this in details due to the strong fluctuations of the gauge boson correlator. Both mentioned above regions look unphysical. Therefore we come to the conclusion that the maximal value of the cutoff admitted within lattice Electroweak theory cannot exceed the value of the order of 1 TeV.

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