在格点Weinberg-Salam模型中如何处理连续介质物理
How to approach continuum physics in lattice Weinberg - Salam model
摘要：
本文对无费米子的格点Weinberg-Salam模型进行了数值计算，以确定与Weinberg角$θ_W \sim 30^o$相对应的耦合常数和$α\sim 1/150$附近的裸精细结构常数.我们考虑了对应于希格斯粒子质量$M_H \sim 100, 150, 270$ GeV的标量自耦合值。已经发现，非微扰效应变得重要，而接近连续物理的晶格模型。当紫外截止$Λ= \fracπ{a}$（其中$a$是晶格间距）增加并达到约1 TeV的值时，会遇到波动区域（在晶格模型的相图上），其中标量场的波动变得很强。经典的南部对称可以看作是物理相内的非物理对称相的胚胎。在波动区域量子Nambu单极是密集的，因此，在这个区域中的平凡真空周围的微扰展开的使用是有限的。截止值的进一步增加伴随着到相图区域的过渡，在该区域标量场不凝聚（对于所考虑的晶格尺寸，这发生在$Λ$的值约为1.4 TeV处）。在这个区域内，截止值的进一步增加是可能的，尽管由于规范玻色子相关器的强烈波动，我们没有详细观察到这一点。上面提到的两个区域看起来都是非物质的。由此我们得出结论：格点电弱理论所允许的截止最大值不能超过1 TeV量级。
英文摘要：
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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