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arXiv 2008.04310hep-phgr-qchep-th
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中微子质量、真空稳定性与顶夸克质量的量子引力预言

Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark

Guillem Domènech, Mark Goodsell, Christof Wetterich

AI总结:

本文研究渐近安全量子引力对顶夸克质量的预言,发现引入解释中微子质量的 SU(2) 三重态标量和右手中微子后,顶夸克质量预言可升至约172.5 GeV,并在适当Yukawa耦合范围内缓解真空稳定性问题。

摘要:

渐近安全量子引力给出的一个一般性预言是:在普朗克尺度之外的紫外固定点,所有四次标量耦合近似为零。希格斯双重态四次耦合在普朗克尺度附近趋于零,可转化为希格斯玻色子质量 $M_H$ 与顶夸克质量 $M_t$ 之比的预言。如果普朗克质量以下只有标准模型粒子参与耦合跑动,则观测到的 $M_H\sim125\\,{\rm GeV}$ 会给出顶夸克质量预言 $M_t\sim 171\\,{\rm GeV}$,与近期测量结果一致。本文研究渐近安全对顶夸克质量的预言如何受到可能存在的中间尺度物理的影响。我们考察了 $SU(2)$ 三重态标量和右手中微子的效应,它们是为解释左手中微子的微小质量所必需的。对于纯 seesaw II 机制,即没有右手中微子或右手中微子非常重的情形,当三重态质量为 $M_Δ\sim 10^8{\rm GeV}$ 时,顶夸克质量可增大到 $M_t\sim 172.5\\,{\rm GeV}$。处于中间尺度的右手中微子质量会增大 $M_t$ 预言的不确定性,原因在于右手中微子的未知 Yukawa 耦合以及标量势中的三次相互作用。在适当的 Yukawa 耦合范围内,真空稳定性问题将不再存在。

英文摘要:

A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson $M_H$ and the top quark $M_t$. If only the standard model particles contribute to the running of couplings below the Planck mass, the observed $M_H\sim125\,{\rm GeV}$ results in the prediction for the top quark mass $M_t\sim 171\,{\rm GeV}$, in agreement with recent measurements. In this work, we study how the asymptotic safety prediction for the top quark mass is affected by possible physics at an intermediate scale. We investigate the effect of a $SU(2)$ triplet scalar and right-handed neutrinos, needed to explain the tiny mass of left-handed neutrinos. For pure seesaw II, with no or very heavy right handed neutrinos, the top mass can increase to $M_t\sim 172.5\,{\rm GeV}$ for a triplet mass of $M_Δ\sim 10^8{\rm GeV}$. Right handed neutrino masses at an intermediate scale increase the uncertainty of the predictions of $M_t$ due to unknown Yukawa couplings of the right-handed neutrinos and a cubic interaction in the scalar potential. For an appropriate range of Yukawa couplings there is no longer an issue of vacuum stability.

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