Cancellations in Neutrinoless Double Beta Decay and the Neutrino Mass Matrix

Abstract

In a degenerate scheme with mass m_0 a complete analysis of the allowed range of the effective electron neutrino Majorana mass <m> is performed. Special attention is paid to effects of cancellations caused either by intrinsic CP parities of the eigenstates (CP invariance) or by complex mixing matrix elements (CP violation). We investigate all possibilities and give in each case constraints on the phases, the relative CP parities or the neutrino mass scale. A solar mixing angle \sin^2 2 \theta smaller than 0.7 jeopardizes the degenerate mass scheme. A key value of <m>/m_0 is identified, which is independent on the solar solution and would rule out certain schemes. Also it would answer the question regarding the presence of CP violation. Even if a total neutrino mass scale and an effective mass is measured, the value of the phases or parities is not fixed, unless in some special cases. The resulting uncertainty in the other mass matrix elements is at least of the same order than the one stemming from nuclear matrix elements calculations.