Neutrino oscillation experiments and limits on lepton-number and lepton-flavor violating processes

Abstract

Using a three neutrino framework we investigate bounds for the effective Majorana neutrino mass matrix. The mass measured in neutrinoless double beta decay is its 11 element. Lepton-number and -flavor violating processes sensitive to each element are considered and limits on branching ratios or cross sections are given. Those processes include µ − e + conversion, K + → π − µ + µ + or recently proposed highenergy scattering processes at HERA. Including all possible mass schemes, the three solar solutions and other allowed possibilities, there is a total of 80 mass matrices. The obtained indirect limits are up to 14 orders of magnitude more stringent than direct ones. It is investigated how neutrinoless double beta decay may judge between different mass and mixing schemes as well as solar solutions. Prospects of detecting processes depending on elements of the mass matrix are also discussed.

Cancellations in neutrinoless double beta decay and the neutrino mass matrix

“…have branching ratios or cross section far too small to be measured [14]. All numerical analyses indicate a hierarchy in the mass squared differences of solar and atmospheric experiments:…”

“…Even worse numbers hold for the other elements of the mass matrices and the respective processes they govern, see [14] for a compilation. The closer the measuredm value gets to the minimal value (0.1205 for our specific example) the smaller gets the allowed area or curve in α-β space and therefore the resulting range for the other matrix elements.…”

“…The variation within a factor of roughly 3 between different calculations of the required nuclear matrix elements has to be kept in mind. Results of oscillation experiments can be used to restrict the value of m in different mass schemes and for the different solutions of the solar neutrino problem [7,8,9,10,11,12,13,14,15,16,17]. Typical key scales for m are 0.1 and 0.005 eV, thus lying in the range of current and forthcoming projects.…”

“…The other entries are clearly needed to distinguish between different discussed models. The only information about the phases or parities can come from neutrinoless double beta decay: All other mass matrix entries are impossible to measure directly, since the respective branching ratios or cross sections they govern are way beyond experimental access [14]. Apart from the obvious aspect that fundamental parameters of a model need to be measured, other interesting application of the phases exist: In [18] it was found that the Majorana phases play a crucial role in the stability of the mixing angles against quantum corrections.…”

Neutrino mass matrix: Inverted hierarchy andCPviolation

“…Then, the condition cos 2σ x = 0 implies (see Eqs. (11,13)) sin σ ≈ 0.56 or ≈ 0.83. The present solar neutrino data admit ρ = π/2 (σ = π/4, 3π/4).…”