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arXiv 1409.3489hep-ph
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多标量场有效势的多尺度重整化群方法

Multi-scale Renormalization Group Methods for Effective Potentials with Multiple Scalar Fields

T. G. Steele, Zhi-Wei Wang, D. G. C. McKeon

备注：
13 pages, 3 figures. References updated and explanations added
发表信息：
Phys. Rev. D 90, 105012 (2014)
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摘要：

回顾了多尺度重整化群（RG）方法，并将其应用于多个标量场辐射对称性破缺的有效势分析，从而将Gildener & Weinberg（GW）方法推广到弱耦合极限之外.一个包含两个相互作用的实标量场的模型被用来说明多尺度RG方法，并且该模型的多尺度RG函数被计算为$β$函数的单圈阶和反常质量维度的双圈阶。通过引入一个额外的重整化标度，可以将模型中的有效势映射到一个具有O（2）对称结构的RG等价形式上，沿着多重整化标度空间中的一个特定轨迹，从而得到一个简化形式的有效势。它表明，在原始模型中的有效势的物理内容，参考一个单一的传统重整化尺度，可以从一个特定的RG-轨迹，连接到这个多尺度O（2）对称形式的有效势提取。本文还讨论了这些多尺度方法在含有多个标量的$O(M)\times O(N)$对称性模型中的推广。

英文摘要：

Multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the Gildener & Weinberg (GW) method beyond the weak coupling limit. A model containing two interacting real scalar fields is used to illustrate multi-scale RG methods and the multi-scale RG functions of this model are calculated to one-loop order for the $β$ function and two-loop order for the anomalous mass dimension. The introduction of an extra renormalization scale allows the mapping of the effective potential in this model onto an RG-equivalent form with an O(2) symmetric structure along a particular trajectory in the multiple renormalization-scale space, leading to a simplified form of the effective potential. It is demonstrated that the physical content of the effective potential in the original model, referenced to a single conventional renormalization scale, can be extracted from a particular RG-trajectory that connects to this multi-scale O(2)-symmetric form of the effective potential. Extensions of these multi-scale methods for effective potentials in models containing multiple scalars with $O(M)\times O(N)$ symmetry are also discussed.

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