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$θ_{13} = 0$附近中微子混合参数的重整化群演化和高尺度下$θ_{13}$消失模型

Renormalization group evolution of neutrino mixing parameters near $θ_{13} = 0$ and models with vanishing $θ_{13}$ at the high scale

Amol Dighe, Srubabati Goswami, Shamayita Ray

备注：
24 pages, 6 figures, revtex4
发表信息：
Phys.Rev.D79:076006,2009
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摘要：

中微子质量矩阵的重整化群演化可能使混合角$θ_{13}$的值非常接近于零，或者使其为零。另一方面，从高尺度的$θ_{13}=0$开始，可以辐射地生成非零的$θ_{13}$。在最一般的情况下，与非零CP违反狄拉克和马约拉纳阶段，我们探讨了在$θ_{13}=0$附近的演变，在其结构的复杂${\cal U}_{e3}$平面。这使我们能够解释在$θ_{13}=0$的狄拉克CP相位$δ$的演变中的明显的奇异性。我们还介绍了一种形式主义，用于计算RG的中微子参数的演变，使用Jarlskog不变量，自然避免了这种奇异行为。我们发现，参数需要非常微调，以获得完全消失的$θ_{13}$在进化过程中。对于一类高尺度下具有$θ_{13}=0$的中微子质量模型，当低能有效理论是标准模型或其最小超对称扩展时，我们计算了RG演化能在多大程度上产生非零的$θ_{13}$.我们发现相关的限制$θ_{13}$，最轻的中微子质量$m_0$，有效的马约拉纳质量$m_{ee}$测量的中微子双β衰变，和超对称参数$\tanβ$。

英文摘要：

Renormalization group (RG) evolution of the neutrino mass matrix may take the value of the mixing angle $θ_{13}$ very close to zero, or make it vanish. On the other hand, starting from $θ_{13}=0$ at the high scale it may be possible to generate a non-zero $θ_{13}$ radiatively. In the most general scenario with non-vanishing CP violating Dirac and Majorana phases, we explore the evolution in the vicinity of $θ_{13}=0$, in terms of its structure in the complex ${\cal U}_{e3}$ plane. This allows us to explain the apparent singularity in the evolution of the Dirac CP phase $δ$ at $θ_{13}=0$. We also introduce a formalism for calculating the RG evolution of neutrino parameters that uses the Jarlskog invariant and naturally avoids this singular behaviour. We find that the parameters need to be extremely fine-tuned in order to get exactly vanishing $θ_{13}$ during evolution. For the class of neutrino mass models with $θ_{13}=0$ at the high scale, we calculate the extent to which RG evolution can generate a nonzero $θ_{13}$, when the low energy effective theory is the standard model or its minimal supersymmetric extension. We find correlated constraints on $θ_{13}$, the lightest neutrino mass $m_0$, the effective Majorana mass $m_{ee}$ measured in the neutrinoless double beta decay, and the supersymmetric parameter $\tanβ$.

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