arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1408.3141hep-thhep-lathep-ph
收藏

关于$λ(\vecϕ^2)^2_4$理论Beta函数的紫外零点问题

On the Question of an Ultraviolet Zero of the Beta Function of the $λ(\vecϕ^2)^2_4$ Theory

Robert Shrock

备注：
16 pages latex with four figures
发表信息：
Phys. Rev. D90, 065023 (2014)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们调查的可能性，紫外线（UV）零的$n$环β函数的$λ(\vecϕ^2)^2$场论与$N$分量标量场，$\vecϕ$，在四个时空维度，$n=5$循环的水平。虽然双回路β函数有一个UV零点，但我们发现$n=3, \ 4, \ 5$的$n$ -回路β函数要么没有UV零点，要么在值为$λ$时没有UV零点，这与双回路计算近似一致。在将格式变换应用于β函数和通过计算Padé逼近后，得到了类似的结果。因此，我们的结论是，在$λ$的范围内的$n$ -环β函数的微扰计算是可靠的，该理论没有表现出强大的证据UV零的水平$n=5$循环。

英文摘要：

We investigate the possibility of an ultraviolet (UV) zero in the $n$-loop beta function of a $λ(\vecϕ^2)^2$ field theory with an $N$-component scalar field, $\vecϕ$, in four spacetime dimensions, up to the level of $n=5$ loops. Although the two-loop beta function has a UV zero, we find that the $n$-loop beta function for $n=3, \ 4, \ 5$ either does not have a UV zero or does not have one at a value of $λ$ in approximate agreement with the two-loop calculation. Similar results are obtained after application of scheme transformations to the beta function and via calculation of Padé approximants. We thus conclude that in the range of $λ$ where the perturbative calculation of the $n$-loop beta function is reliable, the theory does not exhibit robust evidence of a UV zero up to the level of $n=5$ loops.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑