非等级中微子的辐射破缺对称性
Radiatively broken symmetries of nonhierarchical neutrinos
摘要：
基于对称性的思想，如夸克-轻子互补原理（QLC）和三双峰混合（TBM）方案，已被提出来解释所观察到的中微子混合模式。我们认为，这样的对称关系需要施加在一个高尺度$Λ\sim 10^{12}$ GeV的特征大质量的右手中微子需要实施的跷跷板机制。对于非等级中微子，重整化群演化到实验室能量尺度$λ\sim 10^3$ GeV往往会在显著水平上辐射破坏这些对称性，并破坏它们预测的混合模式。然而，对于马约拉纳中微子，适当的额外阶段$α_{2,3}$的限制，使这些高尺度混合模式在实验室的能量保留。我们在最小超对称标准模型（MSSM）中研究了这个问题，并证明了上述两个版本的QLC和两个版本的TBM的事实。对这四种情况都提出了相应的约束条件。具体地，在每种情况下出现对$α_2 \approx π$（即$m_1 \approx -m_2$）的偏好。我们还展示了如何在未来的精确测量$θ_{13}$可能使这四种情况下，尽管重整化群演化之间的一些歧视。
英文摘要：
Symmetry-based ideas, such as the quark-lepton complementarity (QLC) principle and the tri-bimaximal mixing (TBM) scheme, have been proposed to explain the observed mixing pattern of neutrinos. We argue that such symmetry relations need to be imposed at a high scale $Λ\sim 10^{12}$ GeV characterizing the large masses of right-handed neutrinos required to implement the seesaw mechanism. For nonhierarchical neutrinos, renormalisation group evolution down to a laboratory energy scale $λ\sim 10^3$ GeV tends to radiatively break these symmetries at a significant level and spoil the mixing pattern predicted by them. However, for Majorana neutrinos, suitable constraints on the extra phases $α_{2,3}$ enable the retention of those high scale mixing patterns at laboratory energies. We examine this issue within the Minimal Supersymmetric Standard Model (MSSM) and demonstrate the fact posited above for two versions of QLC and two versions of TBM. The appropriate constraints are worked out for all these four cases. Specifically, a preference for $α_2 \approx π$ (i.e. $m_1 \approx -m_2$) emerges in each case. We also show how a future accurate measurement of $θ_{13}$ may enable some discrimination among these four cases in spite of renormalization group evolution.
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