A general formula by LDL^T decomposition for the type-I seesaw mechanism
A general formula by LDL^T decomposition for the type-I seesaw mechanism
复制标题
I型跷跷板机制的LDL^T分解通式
DOI：
10.1093/ptep/ptac060
复制
发表时间：
2022
影响因子：
3.5
通讯作者：
Masaki J.S. Yang
中科院分区：
文献类型：
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作者：
Yusuke Izumi;Takayoshi Tsutsumi;Kenji Ishikawa;Hiroki Kondo;Makoto Sekine and Masaru Hori;Masaki J.S. Yang
通过对右手中微子M−1的逆质量矩阵进行近似谱分解，我们得到了与基无关的I型跷跷板机制的公式。在数学上，它是基于对称矩阵M−1=LDLT的广义乔列斯基分解，其中对角矩阵D和下单位角矩阵L。由于L的对角化不需要求解三次方程即可逆，因此该公式将有助于研究该机制的一般性质，如风味对称性、广义CP对称性和微调。
By performing an approximate spectral decomposition on the inverse mass matrix of the right-handed neutrinosM−1, we obtain a basis-independent formula for the type-I seesaw mechanism. Mathematically, it is based on the generalized Cholesky (orLDLT) decomposition of the symmetric matrixM−1=LDLT, with a diagonal matrixDand a lower unitriangular matrixL. Since the diagonalization ofLcan be inverted without solving cubic equations, the formula will be useful in investigating the general properties of the mechanism, such as flavor symmetries, generalizedCPsymmetries, and fine-tunings.