Theory of neutrino masses and mixing

In spite of enormous experimental progress in determination of the neutrino parameters, theory of neutrino mass and mixing is still on the cross-roads. Guidelines could be (i) the connection between zero neutrino charges (and therefore a possibility to be Majorana particle), smallness of the neutrino mass and large lepton mixing, (ii) joint description of leptons and quarks, (iii) existence of the right handed (RH) neutrinos without special quantum numbers. Properties of the RH neutrinos and the UV completion of the seesaw may turn out to be the key to understand the neutrino mass and mixing. In view of the LHC results minimalistic scenarios like $\nu$MSM look rather plausible. Still the GUT's with additional hidden sector, QLC, high scale flavor symmetries are appealing. Concerning mixing, the main issue is "symmetry or no symmetry" behind the observed pattern. The symmetry group condition is useful tool to study consequences of symmetries and to perform "symmetry building". Sterile neutrinos are challenge but also opportunity for the present theoretical constructions.Comment: 13 pages, Talk given at the "Pontecorvo 100" Symposium, Pisa, Italy, September 18 - 20, 201

Riddle of the Neutrino Mass

We discuss some known approaches and results as well as few new ideas concerning origins and nature of neutrino mass. The key issues include (i) connections of neutrino and charged fermions masses, relation between masses and mixing, energy scale of new physics behind neutrino mass where possibilities spread from the Planck and GUT masses down to a sub-eV scale. The data hint two different new physics involved in generation of neutrino mass. Determination of the CP phase as well as mass hierarchy can play important role in identification of new physics. It may happen that sterile neutrinos provide the key to resolve the riddle.Comment: 6 pages, talk given at the Neutrino Oscillation Workshop, NOW 2014, Conca Specchiulla (Otranto, Lecce, Italy), September 7 - 14, 201

Alternatives to the seesaw mechanism

The observed pattern of lepton mixing does not give an evidence of the seesaw. It is easier to disprove seesaw showing that one of the alternatives gives dominant contribution to the neutrino mass. We consider alternative mechanisms based on (i) small (tree level) effective couplings, (ii) small VEV, (iii) radiative generation of masses, (iv) protection by SUSY breaking scale or by $\mu$-term, (v) small overlap of wave functions of the left and right handed neutrino components in extra dimensions. Seesaw can be the mechanism of suppression of the Dirac mass terms and not dominant mechanism of the neutrino mass giving just a sub-leading contribution.Comment: 16 pages, latex, 5 figures. Talk given at the Conference ``Seesaw Mechanism and Neutrino Masses: 25 Years Later'', 10-11 June 2004, Paris. References added, statement in sec. 6 correcte