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基于CP破坏双对中微子混合的Pontecorvo-Maki-Nakagawa-Sakata混合矩阵参数化

Parameterization of Pontecorvo-Maki-Nakagawa-Sakata mixing matrix based on CP-violating bipair neutrino mixing

Jun Iizuka, Teruyuki Kitabayashi, Yuki Minagawa, Masaki Yasue

备注：
7 pages, 3 figures, version to appear in Modern Physics Letters A
发表信息：
Mod. Phys. Lett. A, Vol. 30, No. 5 (2015) 1550019
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摘要：

中微子相互作用中的CP破坏由Pontecorvo-Maki-Nakagawa-Sakata混合矩阵（$U_{PMNS}$）中包含的三个相描述。我们认为，如果按照双对中微子混合方案构造$U_{PMNS}$，即要求$ | U_{12} | = | U_{32} | {\rm and} | U_{22} | = | U_{23} | (\rm case 1)$和$ | U_{12} | = | U_{22} | {\rm and} | U_{32} | = | U_{33}| (\rm case 2)$，其中$U_{ij}$代表$U_{PMNS}$的$i$-$j$矩阵元，则可以得到狄拉克CP破坏的唯象一致的结果.结果表明，太阳、大气和反应堆中微子混合角$θ_{12}$、$θ_{23}$和$θ_{13}$分别满足$\cos 2{θ_{12}} = \sin^2θ_{23} - \tan^2θ_{13}$（情况1）或$\cos 2{θ_{12}} = \cos^2θ_{23} - \tan^2θ_{13}$（情况2）.此外，如果观察到狄拉克CP破坏是最大的，则$θ_{23}$由$θ_{13}$确定为：$\sin^2θ_{23} \approx ({\sqrt 2 - 1})({\cos^2θ_{13} + \sqrt 2 \sin^2θ_{13}})$（情况1）或$\cos^2θ_{23} \approx ({\sqrt 2 - 1})({\cos^2θ_{13} + \sqrt 2 \sin^2θ_{13}})$（情况2）。对于非最大Dirac CP破坏的情形，我们通过数值计算给出了CP破坏的Dirac相位与混合角之间的关系。

英文摘要：

CP violation in neutrino interactions is described by three phases contained in Pontecorvo-Maki-Nakagawa-Sakata mixing matrix ($U_{PMNS}$). We argue that the phenomenologocally consistent result of the Dirac CP violation can be obtained if $U_{PMNS}$ is constructed along bipair neutrino mixing scheme, namely, requiring that $ | U_{12} | = | U_{32} | {\rm and} | U_{22} | = | U_{23} | (\rm case 1)$ and $ | U_{12} | = | U_{22} | {\rm and} | U_{32} | = | U_{33}| (\rm case 2)$, where $U_{ij}$ stands for the $i$-$j$ matrix element of $U_{PMNS}$. As a results, the solar, atmospheric and reactor neutrino mixing angles $θ_{12}$, $θ_{23}$ and $θ_{13}$, respectively, are correlated to satisfy $\cos 2{θ_{12}} = \sin^2θ_{23} - \tan^2θ_{13}$ (case 1) or $\cos 2{θ_{12}} = \cos^2θ_{23} - \tan^2θ_{13}$ (case 2). Furthermore, if Dirac CP violation is observed to be maximal, $θ_{23}$ is determined by $θ_{13}$ to be: $\sin^2θ_{23} \approx ({\sqrt 2 - 1})({\cos^2θ_{13} + \sqrt 2 \sin^2θ_{13}})$ (case 1) or $\cos^2θ_{23} \approx ({\sqrt 2 - 1})({\cos^2θ_{13} + \sqrt 2 \sin^2θ_{13}})$ (case 2). For the case of non-maximal Dirac CP violation, we perform numerical computation to show relations between the CP-violating Dirac phase and the mixing angles.

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