How to approach continuum physics in the lattice Weinberg-Salam model

Abstract

We investigate lattice Weinberg -Salam model without fermions numerically for the realistic choice of coupling constants correspondent to the value of the Weinberg angle θW ∼ 30 o , and bare fine structure constant around α ∼ 1 150 . We consider the values of the scalar self coupling corresponding to Higgs mass MH ∼ 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 = π 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.

Two- and three-point functions in Landau gauge Yang-Mills-Higgs theory

“…[82]. In this gauge, on each gauge orbit the gauge copy is chosen for which the ϕ a become unit matrices.…”

Zero temperature lattice Weinberg-Salam model for the values of the cutoffΛ∼1 TeV

“…This diagram is obtained, mainly, using the lattice 8 3 Â 16. Some regions ( ¼ 0:009, required about 600 hours), however, were checked using larger lattices (see, for example, [19,20,[22][23][24]). According to our data there is no dependence of the diagram on the lattice size.…”

“…The physical Higgs phase is situated right to the solid transition line. The position of this line was determined using various methods [19,20,[22][23][24]. However, the uncertainty is still present in the final determination of the phase transition points.…”

“…Based on trivial dimensional analysis we may expect that the mentioned scale can be compared to the electroweak scale $250 GeV. In fact, some indications were recently found that this scale might be around 1 TeV (see, for example, [19][20][21][22][23][24][25]). Namely, in the electroweak theory there exist objects that are not described by the first orders of the perturbation theory: Nambu monopoles and the Z-strings [26].…”

“…Namely, in the electroweak theory there exist objects that are not described by the first orders of the perturbation theory: Nambu monopoles and the Z-strings [26]. It has been found that there exists the vicinity of the phase transition [24], where the average distance between the Nambu monopoles is compared to their sizes. This region was called in [22] the fluctuational region (FR).…”