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arXiv 1604.03039hep-ph
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太阳轻子混合和规则的辐射修正

Radiative Corrections to the Solar Lepton Mixing Sum Rule

Jue Zhang, Shun Zhou

摘要:

轻子味混合角$(θ^{}_{12}, θ^{}_{13}, θ^{}_{23})$与轻子Dirac CP破坏相$δ$之间的简单关联通常被称为轻子味混合求和规则,它可以从一类具有味对称性的中微子质量模型中导出.本文考虑太阳轻子混合求和规则$θ^{}_{12} \approx θ^ν_{12} + θ^{}_{13} \cos δ$,其中$θ^ν_{12}$源于中微子扇区中的常数混合模式,对于双峰混合(BM)取$θ^ν_{12} = 45^\circ$,对于三双峰混合(TBM)取$θ^ν_{12} = \tan^{-1}(1/\sqrt{2}) \approx 35.3^\circ$,对于黄金比例混合(GR)取$θ^ν_{12} = \tan^{-1}\left[2/(\sqrt{5} + 1)\right] \approx 31.7^\circ$,并研究了在超高能尺度下,当这种求和规则被假定时,重整化群(RG)运行对轻子味混合参数的影响。为了说明,我们在最小超对称标准模型(MSSM)的框架内工作,并实施贝叶斯方法来探索低能量尺度下$δ$的后验分布,当RG运行效应显着时,该后验分布变得相当广泛。此外,我们还讨论了上述三种混合方案与当前中微子振荡数据的兼容性,并观察到辐射修正可以增加BM方案的兼容性,导致对TBM和GR方案的偏好较弱。

英文摘要:

The simple correlation among three lepton flavor mixing angles $(θ^{}_{12}, θ^{}_{13}, θ^{}_{23})$ and the leptonic Dirac CP-violating phase $δ$ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the solar lepton mixing sum rule $θ^{}_{12} \approx θ^ν_{12} + θ^{}_{13} \cos δ$, where $θ^ν_{12}$ stems from a constant mixing pattern in the neutrino sector and takes the value of $θ^ν_{12} = 45^\circ$ for the bi-maximal mixing (BM), $θ^ν_{12} = \tan^{-1}(1/\sqrt{2}) \approx 35.3^\circ$ for the tri-bimaximal mixing (TBM) or $θ^ν_{12} = \tan^{-1}\left[2/(\sqrt{5} + 1)\right] \approx 31.7^\circ$ for the golden-ratio mixing (GR), and investigate the renormalization-group (RG) running effects on lepton flavor mixing parameters when this sum rule is assumed at a superhigh-energy scale. For illustration, we work within the framework of the minimal supersymmetric standard model (MSSM), and implement the Bayesian approach to explore the posterior distribution of $δ$ at the low-energy scale, which becomes quite broad when the RG running effects are significant. Moreover, we also discuss the compatibility of the above three mixing scenarios with current neutrino oscillation data, and observe that radiative corrections can increase such a compatibility for the BM scenario, resulting in a weaker preference for the TBM and GR ones.

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