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arXiv · 2112.14402

A general formula by $LDL^{T}$ decomposition for the type-I seesaw mechanism

Masaki J. S. Yang
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Abstract

By performing an approximate spectral decomposition to the inverse mass matrix of the right-handed neutrinos $M^{-1}$, we obtain a basis-independent formula for the type-I seesaw mechanism. Mathematically, it is based on the generalized Cholesky (or $LDL^{T}$) decomposition of the symmetric matrix $M^{-1} = L D L^{T}$, with a diagonal matrix $D$ and a lower unitriangular matrix $L$. Since the diagonalization of $L$ can be inverted without solving cubic equations, the formula will be useful to investigate general properties of the mechanism, such as flavor symmetries, generalized $CP$ symmetries, and fine-tunings.

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Masaki J. S. Yang. 2021-12-29. A general formula by $LDL^{T}$ decomposition for the type-I seesaw mechanism. https://doi.org/10.1093/ptep%2Fptac060

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