arXiv 1306.51382013-06-29hep-th

有效势奇异性结构的重整化群分析

Renormalization group analysis of the singularity structure of effective potentials

T. Hanif, N. Ishtiaque

备注：: 25 pages, added reference, typos corrected

摘要：

使用重整化群技术，它以前表明，在$\mathcal{O}(N)$对称$ϕ^4$理论，无质量标量电动力学以及在标准模型的共形极限的微扰有效势可以唯一地确定在已知的MS方案重整化群功能。此外，再加总的首阶修正加上部分的这些高阶贡献的有效势在$\mathcal{O}(N)$对称$ϕ^4$理论显示了一个特殊的转变，在通常的“朗道奇异性”明显的个人首阶修正。在这项工作中，我们已经进一步研究了这种转变，通过扩展的结果，具有多重耦合的理论。我们已经表明，通过对任何有限$P$的部分$V_{N^{P+n}LL}$求和所看到的有效势的奇异性结构，当这些微扰贡献被求和到所有阶时，如预期的那样被改变，但更重要的是，我们发现这种奇异性的转变完全由一个和两个圈β函数决定。我们认为，这是一个一般的结果，适用于共形不变的标准模型。

英文摘要：

Using the renormalization group techniques it was previously shown that the perturbative effective potential in the $\mathcal{O}(N)$ symmetric $ϕ^4$ theory, massless scalar electrodynamics as well as in the conformal limit of the standard model can be uniquely determined in terms of the known MS scheme renormalization group functions. Furthermore, re-summation of the leading order corrections plus portions of these higher order contributions to the effective potential in the $\mathcal{O}(N)$ symmetric $ϕ^4$ theory shows a peculiar shift in the usual "Landau singularity" apparent in the individual leading order corrections. In this work, we have further investigated this shift by extending the result for theories having multiple couplings. We have shown that the singularity structure of the effective potential as seen by summing up portions of the $V_{N^{P+n}LL}$ for any finite $P$ is altered as expected when these perturbative contributions are summed to all orders but more significantly we found that this shift in the singularity is completely determined by the one and two loop beta functions only. We argue that this is a general result which applies to the conformally invariant standard model.

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英文摘要：

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