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arXiv 2005.05171hep-phhep-ex
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关于最小中微子质量和Majorana CP相的双圈辐射起源

On the two-loop radiative origin of the smallest neutrino mass and the associated Majorana CP phase

Zhi-zhong Xing, Di Zhang

摘要:

给定一个超高能标度的无质量中微子$Λ$(例如,在仅有两个重的Majorana中微子的最小跷跷板模型中),利用标准模型中的双圈重整化群方程(RGE)和最新的中微子振荡数据,计算了在费米尺度$Λ^{}_{\rm F}$下,对初始消失的质量$m^{}_1$(或$m^{}_3$)和伴随的Majorana CP相$ρ$(或$\varrho$)的量子修正.从我们的解析近似得到的数值结果是在良好的协议,通过数值求解两个回路的RGE。特别是,我们确认,一个非零值的$m^{}_1$(或$m^{}_3$)的${\cal O}(10^{-13})$ eV在$Λ^{}_{\rm F}$可以辐射产生的$m^{}_1 =0$(或$m^{}_3 =0$)在$Λ\simeq 10^{14}$ GeV的SM,并发现$ρ$(或$\varrho$)可能相应地获得一个可观的物理值。作为一个非平凡的副产品,大质量中微子的所有其他(最初非零)味参数的演化都是通过分析和数值研究的,只要保持它们的领先(即,单回路)RGE诱导的效应。

英文摘要:

Given a massless neutrino at a superhigh energy scale $Λ$ (e.g., in the minimal seesaw model with only two heavy Majorana neutrinos), we calculate quantum corrections to its initially vanishing mass $m^{}_1$ (or $m^{}_3$) and the associated Majorana CP phase $ρ$ (or $\varrho$) at the Fermi scale $Λ^{}_{\rm F}$ by means of the two-loop renormalization-group equations (RGEs) in the standard model and with the help of the latest neutrino oscillation data. The numerical results obtained from our analytical approximations are in good agreement with those achieved by numerically solving the two-loop RGEs. In particular, we confirm that a nonzero value of $m^{}_1$ (or $m^{}_3$) of ${\cal O}(10^{-13})$ eV at $Λ^{}_{\rm F}$ can be radiatively generated from $m^{}_1 =0$ (or $m^{}_3 =0$) at $Λ\simeq 10^{14}$ GeV in the SM, and find that $ρ$ (or $\varrho$) may accordingly acquire an appreciable physical value. As a nontrivial by-product, the evolution of all the other (initially nonzero) flavor parameters of massive neutrinos is studied both analytically and numerically, by just keeping their leading (i.e., one-loop) RGE-induced effects.

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