arXiv 1405.60062014-05hep-ph

轻子CP破坏位相的预测

Predicting the Values of the Leptonic CP Violation Phases

S. T. Petcov

备注：: 30 pages, results unchanged, title modified, text (including the Introduction) streamlined, with exception of a few added references version to be published in Nuclear Physics B
DOI：: 10.1016/j.nuclphysb.2015.01.011

摘要：

利用中微子混合矩阵$U = U^\dagger_{e}U_ν$（其中$U_{e}$和$U_ν$是由带电轻子和中微子质量矩阵对角化得到的）这一事实，我们考虑了与各种味对称性有关的$U_ν$的一些形式：i）双峰（BM）和ii）三双峰（TBM）形式，该形式对应于iii）轻子电荷$L' = L_e - L_μ- L_τ$（LC）的守恒，iv）黄金比例A型（GRA）混合，v）黄金比例B型（GRB）混合，和iii）六方（HG）混合。采用$U_e$的最小形式，可以提供必要的修正$U_ν$，使反应堆，大气和太阳中微子混合角$θ_{13}$，$θ_{23}$和$θ_{12}$的值与当前的数据兼容，包括可能的相当大的偏差$θ_{23}$从$π/4$，我们讨论了可能性，以获得预测的CP破坏阶段的中微子混合矩阵。按照文献[1]中提出的方法，我们在$U_ν$的GRA、GRB和HG形式的情况下得到了狄拉克相位$δ$和再定相不变量$J_{\rm CP}$的预言（文献[1]中得到了TBM和BM（LC）形式的结果）。我们还表明，在相当一般的条件下，在计划内考虑的PMNS矩阵中的马约拉纳阶段的值可以预测的$U_ν$讨论的每一种形式。我们给出了这些预测的例子和它们对无中微子双β衰变的影响。在GRA，GRB和HG的情况下，在TBM的一个，相对较大的CP破坏中微子振荡的影响进行了预测（$|J_{CP}| \sim (0.031 - 0.034)$）。区分$U_ν$的TBM、BM（LC）、GRA、GRB和HG形式需要测量$\cosδ$或相对高精度的测量$J_{\rm CP}$。

英文摘要：

Using the fact that the neutrino mixing matrix $U = U^\dagger_{e}U_ν$, where $U_{e}$ and $U_ν$ result from the diagonalisation of the charged lepton and neutrino mass matrices, we consider a number of forms of $U_ν$ associated with a variety of flavour symmetries: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding iii) to the conservation of the lepton charge $L' = L_e - L_μ- L_τ$ (LC), iv) to golden ratio type A (GRA) mixing, v) golden ratio type B (GRB) mixing, and iii) to hexagonal (HG) mixing. Employing the minimal form of $U_e$ that can provide the requisite corrections to $U_ν$ so that reactor, atmospheric and solar neutrino mixing angles $θ_{13}$, $θ_{23}$ and $θ_{12}$ have values compatible with the current data, including a possible sizable deviation of $θ_{23}$ from $π/4$, we discuss the possibility to obtain predictions for the CP violation phases in the neutrino mixing matrix. Following the approach developed in [1] we derive predictions for the Dirac phase $δ$ and the rephasing invariant $J_{\rm CP}$ in the cases of GRA, GRB and HG forms of $U_ν$ (results for the TBM and BM (LC) forms were obtained in [1]). We show also that under rather general conditions within the scheme considered the values of the Majorana phases in the PMNS matrix can be predicted for each of the forms of $U_ν$ discussed. We give examples of these predictions and of their implications for neutrinoless double beta decay. In the GRA, GRB and HG cases, as in the TBM one, relatively large CP violation effects in neutrino oscillations are predicted ($|J_{CP}| \sim (0.031 - 0.034)$). Distinguishing between the TBM, BM (LC), GRA, GRB and HG forms of $U_ν$ requires a measurement of $\cosδ$ or a relatively high precision measurement of $J_{\rm CP}$.

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摘要：

英文摘要：

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