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arXiv 1006.5887hep-phhep-th
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重整化群改进的有效势能否用于标准模型共形极限下的Higgs质量估计？

Can the Renormalization Group Improved Effective Potential be used to estimate the Higgs Mass in the Conformal Limit of the Standard Model?

F. A. Chishtie, T. Hanif, J. Jia, R. B. Mann, D. G. C. McKeon, T. N. Sherry, T. G. Steele

备注：
24 pages, 5 figures. Updated version contains new discussion, references, figures, and corrects errors in references
发表信息：
Phys.Rev.D83:105009,2011
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摘要：

我们考虑的有效势$V$在标准模型与一个单一的希格斯偶极子的限制，唯一的质量尺度$μ$目前是辐射产生的。当使用Coleman-Weinberg（CW）重整化方案时，使用已被证明完全根据重整化群（RG）函数确定$V$的技术，我们首先使用与五个耦合相关联的单循环RG函数对$V$的前导对数（LL）贡献求和（顶夸克汤川耦合$x$，希格斯场的四次耦合$y$，SU（3）规范耦合$z$，以及$SU(2) \times U(1)$耦合$r$和$s$）。然后，我们使用具有三个耦合$x$、$y$、$z$的两个循环RG函数来对$V$的下一个前导对数（NLL）贡献求和，然后使用具有一个耦合$y$的三到五个循环RG函数来对$V$的所有$N^2LL...N^4LL$贡献求和。为了计算这些和，有必要将最初在最小减法（MS）方案中显式计算的RG函数转换为CW方案中的形式。希格斯粒子的质量可以由有效势来确定：$LL$的结果是$m_{H}=219\;GeV/c^2$在$N^{2}LL$级减少到$m_{H}=188\;GeV/c^2$，在$N^{4}LL$级减少到$m_{H}=163\;GeV/c^2$。在$V_{NLL}$或$V_{N^3LL}$订单下，无法对$m_H$进行合理估计。这表明这种自发对称破缺的机制实际上是可行的，尽管其中有一个缓慢的收敛到$m_H$的实际值。质量$163\;GeV/c^2$被认为是$m_H$的上限。

英文摘要：

We consider the effective potential $V$ in the standard model with a single Higgs doublet in the limit that the only mass scale $μ$ present is radiatively generated. Using a technique that has been shown to determine $V$ completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg (CW) renormalization scheme, we first sum leading-log (LL) contributions to $V$ using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling $x$, the quartic coupling of the Higgs field $y$, the SU(3) gauge coupling $z$, and the $SU(2) \times U(1)$ couplings $r$ and $s$). We then employ the two loop RG functions with the three couplings $x$, $y$, $z$ to sum the next-to-leading-log (NLL) contributions to $V$ and then the three to five loop RG functions with one coupling $y$ to sum all the $N^2LL...N^4LL$ contributions to $V$. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction (MS) scheme to their form in the CW scheme. The Higgs mass can then be determined from the effective potential: the $LL$ result is $m_{H}=219\;GeV/c^2$ decreases to $m_{H}=188\;GeV/c^2$ at $N^{2}LL$ order and $m_{H}=163\;GeV/c^2$ at $N^{4}LL$ order. No reasonable estimate of $m_H$ can be made at orders $V_{NLL}$ or $V_{N^3LL}$. This is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of $m_H$. The mass $163\;GeV/c^2$ is argued to be an upper bound on $m_H$.

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