论文标题
在最小的中微子质量和相关的Majorana CP期的两循环辐射起源上
On the two-loop radiative origin of the smallest neutrino mass and the associated Majorana CP phase
论文作者
论文摘要
给定超高能量尺度的无质量中微子$λ$（例如，在最小的seesaw模型中，只有两个重量的主要中微子），我们将量子校正计算为其最初消失的质量$ m^{} _ 1 $（或$ m^{} _ 3 $）和相关的Majorana cp apep $ $ $ $ $ $ $ cp $ \ vho $λ^{} _ {\ rm f} $通过标准模型中的两环重归于组方程（RGE），并借助最新的中微子振荡数据。从我们的分析近似值获得的数值结果与通过数值求解双环RGE所获得的结果非常吻合。特别是，我们确认$ m^{} _ 1 $（或$ m^{} _ 3 $）的$ {\ cal o}（10^{ - 13}）$ ev at $λ^{} _ {} _ {\ rm f} $可以从$ m^{$ m^{$^$^at = 0 $ 1 = 0 = 0 = 0. $λ\ simeq 10^{14} $ gev在SM中，发现$ρ$（或$ \ varrho $）可以因此获得可观的物理价值。作为一种非平凡的副产品，通过在分析和数值上研究了其他所有其他（最初是非零）的风味参数的演变，仅通过保持其领先（即一环）RGE诱导的影响。
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.
