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顶夸克和希格斯玻色子玻色子质量与电弱真空的稳定性

The top quark and Higgs boson masses and the stability of the electroweak vacuum

S. Alekhin, A. Djouadi, S. Moch

备注：
12 pages, 1 figure. v2: lapsus corrected in the abstract. v3: typos corrected, updated (and 2 figures added) with most recent data
发表信息：
Phys. Lett. B716 (2012) 214
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摘要：

ATLAS和CMS实验在大型强子对撞机上观测到一个质量为$\approx 126$ GeV的粒子，这与标准模型中的希格斯玻色子是相容的。一个关键的问题是，如果对于这样一个希格斯质量值，人们可以将模型外推到高尺度，同时保持破坏电弱对称性的标量势的最小值稳定。真空稳定性确实要求希格斯玻色子玻色子的质量是$M_H \gsim 129 \pm 1$ GeV，但精确的值关键取决于输入的顶夸克极质量，通常采用在Tevatron上测量的质量，即$m_t^{\rm exp}=173.2 \pm 0.9$ GeV。然而，为了明确和理论上定义明确的确定顶夸克质量，我们应该使用强子对撞机上顶夸克对产生的总截面。根据Tevatron实验测量的最新结果，我们确定$p \bar p \to t\bar t +X$-方案中的运行质量为$m_t^{\bar{\rm MS}}(m_t) = 163.3 \pm 2.7$ GeV，从而给出顶夸克极质量为$m_t^{\rm pole}= 173.3 \pm 2.8$ GeV.这导致了真空稳定性约束$M_H \geq 129.8 \pm 5.6$ GeV，当不确定性很大时，$\approx 126$ GeV希格斯玻色子遵守该真空稳定性约束。只有在未来的高能正负电子对撞机上才能对电弱真空的稳定性进行非常精确的评估，在那里顶夸克极质量可以以几百MeV的精度确定。

英文摘要：

The ATLAS and CMS experiments observed a particle at the LHC with a mass $\approx 126$ GeV, which is compatible with the Higgs boson of the Standard Model. A crucial question is, if for such a Higgs mass value, one could extrapolate the model up to high scales while keeping the minimum of the scalar potential that breaks the electroweak symmetry stable. Vacuum stability requires indeed the Higgs boson mass to be $M_H \gsim 129 \pm 1$ GeV, but the precise value depends critically on the input top quark pole mass which is usually taken to be the one measured at the Tevatron, $m_t^{\rm exp}=173.2 \pm 0.9$ GeV. However, for an unambiguous and theoretically well-defined determination of the top quark mass one should rather use the total cross section for top quark pair production at hadron colliders. Confronting the latest predictions of the inclusive $p \bar p \to t\bar t +X$ cross section up to next-to-next-to-leading order in QCD to the experimental measurement at the Tevatron, we determine the running mass in the $\bar{\rm MS}$-scheme to be $m_t^{\bar{\rm MS}}(m_t) = 163.3 \pm 2.7$ GeV which gives a top quark pole mass of $m_t^{\rm pole}= 173.3 \pm 2.8$ GeV. This leads to the vacuum stability constraint $M_H \geq 129.8 \pm 5.6$ GeV to which a $\approx 126$ GeV Higgs boson complies as the uncertainty is large. A very precise assessment of the stability of the electroweak vacuum can only be made at a future high-energy electron-positron collider, where the top quark pole mass could be determined with a few hundred MeV accuracy.

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