Generalized Pauli-Gursey transformation and Majorana neutrinos
Generalized Pauli-Gursey transformation and Majorana neutrinos
复制标题
广义泡利-格西变换和马约拉纳中微子
DOI：
10.1016/j.physletb.2018.12.008
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发表时间：
2019
影响因子：
4.4
通讯作者：
Kazuo Fujikawa
中科院分区：
文献类型：
--
作者：
染谷洋二;加藤満也;日渡良爾;坂本宜照;飛田健次;Kazuo Fujikawa
我们讨论了由Auton-Takagi分解引起的Pauli-Gursey变换的推广，它使用U(2n)定义了一般的正则变换，并在特殊情况下对角化对称复Majorana质量矩阵，从而推广到任意n代中微子。Pauli-Gursey变换将粒子和反粒子混合在一起，从而改变了真空和C的定义。我们在由广义Pauli-Gursey变换指定的每个Pauli标架上定义了C、P和CP对称性。然后，通过选择适当的Pauli标架，自然地定义了C和P违反拉锯模型中的Majorana中微子，其中只有Dirac类型的费米子具有明确的C、P和Cp，因此Majorana中微子的C对称性与Dirac类型费米子的C对称性一致。这种完全对称的设置对应于Majorana中微子作为Bogoliubov准粒子的想法。相反，在拉锯模型中，传统的直接构造Majorana中微子的方法遇到了Majorana中微子的C对称性和手征费米子的C对称性的失配，这种失配被认为是手征费米子C对称性的单重态(平凡)表示的必然出现。
We discuss a generalization of the Pauli–Gursey transformation, which is motivated by the Autonne–Takagi factorization, to an arbitrary n number of generations of neutrinos using U (2 n) that defines general canonical transformations and diagonalizes symmetric complex Majorana mass matrices in special cases. The Pauli–Gursey transformation mixes particles and antiparticles and thus changes the definition of the vacuum and C. We define C, P and CP symmetries at each Pauli frame specified by a generalized Pauli–Gursey transformation. The Majorana neutrinos in the C and P violating seesaw model are then naturally defined by a suitable choice of the Pauli frame, where only Dirac-type fermions appear with well-defined C, P and CP, and thus the C symmetry for Majorana neutrinos agrees with the C symmetry for Dirac-type fermions. This fully symmetric setting corresponds to the idea of Majorana neutrinos as Bogoliubov quasi-particles. In contrast, the conventional direct construction of Majorana neutrinos in the seesaw model, where CP is well-defined but C and P are violated, encounters the mismatch of C symmetry for Majorana neutrinos and C symmetry for chiral fermions; this mismatch is recognized as the inevitable appearance of the singlet (trivial) representation of C symmetry for chiral fermions.