Year: 2005
Type: article
Abstract: We further study the ``complementary'' ansatz, $\mathrm{Tr}({M}_{\ensuremath{\nu}})=0$, for a prediagonal light Majorana type neutrino mass matrix. Previously, this was studied for the $CP$ conserving case and the case where the two Majorana type $CP$ violating phases were present but the Dirac type $CP$ violating phase was neglected. Here we employ a simple geometric algorithm which enables us to ``solve'' the ansatz including all three $CP$ violating phases. Specifically, given the known neutrino oscillation data and an assumed two parameter (the third neutrino mass ${m}_{3}$ and the Dirac $CP$ phase $\ensuremath{\delta}$) family of inputs we predict the neutrino masses and Majorana $CP$ phases. Despite the two parameter ambiguity, interesting statements emerge. There is a characteristic pattern of interconnected masses and $CP$ phases. For large ${m}_{3}$ the three neutrinos are approximately degenerate. The only possibility for a mass hierarchy is to have ${m}_{3}$ smaller than the other two. A hierarchy with ${m}_{3}$ largest is not allowed. Small $CP$ violation is possible only near two special values of ${m}_{3}$. Also, the neutrinoless double beta decay parameter is approximately bounded as $0.020\text{ }\text{ }\mathrm{eV}<|{m}_{ee}|<0.185\text{ }\text{ }\mathrm{eV}$. As a by-product of looking at physical amplitudes we discuss an alternative parametrization of the lepton mixing matrix which results in simpler formulas. The physical meaning of this parametrization is explained.
Language: Latvian
Topic: Neutrino Physics Research
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1976002571