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A tale of three diagonalizations
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abstract
In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications -- the singular value decomposition and the Autonne-Takagi factorization. In these pedagogical notes, we carry out each of these diagonalization procedures for the most general $2\times 2$ matrices for which the corresponding diagonalization is possible and provide explicit analytical results in each of the three cases.
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Correlating Resonant Di-Higgs and Tri-Higgs Production to $H\to VV$ in the 2HDM
In the decoupling limit of the 2HDM, a heavy Higgs boson's decays to two Higgs bosons and to Z/W pairs are predicted to have a fixed ratio of about 9.5, independent of Yukawa and scalar-potential parameters.
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