Studies of Non-standard Particle Mixings Through Singular Values

Singular values provide a method to study mixing matrices in particle physics. The methods of unitary dilations and the cosine–sine matrix decomposition are discussed in the framework of the Standard Model neutrinos mixing with one non-standard neutrino. We show that the mixings are continuous functions of singular values. It implies that the magnitude of non-standard mixing can be estimated from below and above unambiguously from the experimentally determined interval PMNS mixing matrix