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arXiv 1408.5548hep-ph
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引力对普朗克尺度下Higgs势消失的影响

Gravitational effects on vanishing Higgs potential at the Planck scale

Naoyuki Haba, Kunio Kaneta, Ryo Takahashi, Yuya Yamaguchi

备注：
12 pages, 4 figures, version accepted for publication in PRD: typo corrected, references added
发表信息：
Phys. Rev. D 91, 016004 (2015)
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摘要：

我们调查所谓的多点临界原理（MPCP）在普朗克尺度的引力效应。MPCP需要两个简并真空，其必要条件用Higgs四次耦合$λ(M_{\rm Pl})=0$和$β$函数$β_λ(M_{\rm Pl})=0$的消失表示.我们讨论的情况下，一个特定形式的引力修正被假定为有助于$β$功能的耦合常数，虽然它是公认的引力修正不改变运行的标准模型（SM）的耦合。为了满足普朗克尺度下的上述两个边界条件，我们发现顶极质量和希格斯质量应该分别为$170.8\,{\rm GeV} \lesssim M_t\lesssim 171.7\,{\rm GeV}$和$M_h=125.7\pm0.4\,{\rm GeV}$，并包括适当大小的引力效应（引力贡献系数为$|a_λ| > 2$）。然而，在这种情况下，由于希格斯四次耦合$λ$在普朗克尺度以下变为负值，两个真空不简并。我们发现，$M_h \gtrsim 131.5\,{\rm GeV}$与$M_t \gtrsim 174\,{\rm GeV}$是实现MPCP所必需的。因此，普朗克尺度下的MPCP不能在SM中实现，也不能在有引力的SM中实现，因为$M_h \gtrsim 131.5\,{\rm GeV}$被实验排除。

英文摘要：

We investigate gravitational effects on the so-called multiple point criticality principle (MPCP) at the Planck scale. The MPCP requires two degenerate vacua, whose necessary conditions are expressed by vanishing Higgs quartic coupling $λ(M_{\rm Pl})=0$ and vanishing its $β$ function $β_λ(M_{\rm Pl})=0$. We discuss a case that a specific form of gravitational corrections are assumed to contribute to $β$ functions of coupling constants although it is accepted that gravitational corrections do not alter the running of the standard model (SM) couplings. To satisfy the above two boundary conditions at the Planck scale, we find that the top pole mass and the Higgs mass should be $170.8\,{\rm GeV} \lesssim M_t\lesssim 171.7\,{\rm GeV}$ and $M_h=125.7\pm0.4\,{\rm GeV}$, respectively, as well as include suitable magnitude of gravitational effects (a coefficient of gravitational contribution as $|a_λ| > 2$). In this case, however, since the Higgs quartic coupling $λ$ becomes negative below the Planck scale, two vacua are not degenerate. We find that $M_h \gtrsim 131.5\,{\rm GeV}$ with $M_t \gtrsim 174\,{\rm GeV}$ is required by the realization of the MPCP. Therefore, the MPCP at the Planck scale cannot be realized in the SM and also the SM with gravity since $M_h \gtrsim 131.5\,{\rm GeV}$ is experimentally ruled out.

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