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 µ-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. 1. What is wrong with the Seesaw? Needless to say, the seesaw 1,2,3 is the most appealing mechanism of small neutrino mass generation. We admire its simplicity, elegance and naturalness. We (at least some of us) admire, and doubt, and the reasons for doubt can be summarized in the following way. 1). No clear evidence of the seesaw is seen in the observed pattern of neutrino masses and lepton mixing. Such an evidence would be obtained if, e.g., the " HDM + solar SMA MSW " scenario advocated in 90ties is realized. A priory this scenario implied nearly quadratic neutrino mass hierarchy: m ν ∼ m 2 u and small (similar to quark) mixing. The heaviest neutrino was in the eV-range providing the hot component of the dark matter (HDM) in the Universe with substantial contribution to the energy density balance. If this is realized we would agree that the seesaw works, the right handed neutrino masses * Talk given at the Conference " Seesaw Mechanism and Neutrino Masses: 25 Years Later " , 10-11 june 2004, Paris.