".... Quite unusually, my last instantiation of the periodic posting of "The Say of the Week" resulted in some constructive criticism and in some insightful comments. Due to the usual care in documenting his comments, Tony Smith deserves to be quoted here - to the benefit of whomever wants to read more on the subject, and to the intrigue of who wants to know about Tony's own "unconventional" model of neutrino masses:
In his book Journeys Beyond the Standard Model (Perseus 1999) Pierre Ramond says: " the standard model must be extended to accommodate massive neutrinos the extensions do not put in question the nature of the standard model, but rather add more parameters to it To preserve lepton number and massive neutrinos we need to introduce new fermions to serve as the Dirac partners of the left handed neutrinos. These new fermion degrees of freedom can have any electroweak quantum numbers Electroweak breaking then generates a neutrino Dirac mass of the order of 245 x Y(0) GeV The experimental limits on neutrino masses imply that the Y(0) cuopling constants must themselves be very small, in the range of Y(0) less than or equal to ( 10^(-10) - 10^(-4) ). If one accepts such tiny couplings (after all, we already have m_e = 10^(-6) M_W ), this represents a viable extension of the standard model ".
To me, that sounds like Dirac mass for neutrinos would indeed be much like Tommaso's "say of the week": " a rearrangement of the furniture in the kids' room forced by the arrival of a new baby". To verify the "say" in that way, the question is: Are neutrino mass states Dirac mass states?
In a Particle Data Group review NEUTRINO MASS, MIXING, AND FLAVOR CHANGE, Revised September 2005, B. Kayser (Fermilab) says: " In the Standard Model (SM), neutrinos are assumed to be massless. Now that we know they do have masses, it is straightforward to extend the SM to accommodate these masses in the same way that this model accommodates quark and charged lepton masses. if the cosmological assumptions are correct, then 0.04 eV is less than [ the mass of the heaviest neutrino ] is less than (0.2 - 0.4) eV To accommodate the nu mass in the same manner as quark masses are accommodated, we add nu_R to the Model. Then we may construct the "Dirac mass term" Suppose the right-handed neutrinos required by Dirac mass terms have been added to the SM. If we insist that this extended SM conserve [lepton number] L, then, of course, Majorana mass terms are forbidden. One approach that shows great promise is the search for neutrinoless double beta decay ( 0 nu beta beta ). This process manifestly violates L conservation, so we expect it to be suppressed. Are the neutrino mass eigenstates Majorana particles? The confirmed observation of neutrinoless double beta decay would establish that the answer is "yes." If there are only three nu_i, knowledge that the spectrum is inverted and a definitive upper bound on the "effective Majorana mass for neutrinoless double beta decay" that is well below 0.01 eV would establish that it is "no" ".
In hep-ph/0611243 ( Lecture notes at TASI2006, Boulder, CO, June 2006 ) Petr Vogel says: " [in] the Heidelberg-Moscow experiment no obvious peak at the [ 0 nu beta beta ] expected position can be seen Nevertheless, a subset of members of the Heidelberg-Moscow collaboration reanalyzed the data (and used additional information, e.g. the pulse-shape analysis and a different algorithm in the peak search) and claimed to observe a positive signal corresponding to the effective mass of 0.39 +0.17 -0.28 eV That report has been followed by a lively discussion the next generation of experiments will, among other things, test this recent claim. let me briefly comment on the most advanced of the forthcoming experiments CUORE, GERDA, EXO, and MAJORANA These four experiments are in various stages of funding and staging. First results are expected in about 3 years, and substantial results within 3-5 years in all of them ".
So here too we have a drama of a collaboration with one view of experimental results and a subgroup of the collaboration holding a very different view, and the prospect that bigger/better experiments may resolve the matter within 3 to 5 years. This is the sort of thing that, to me, is the heart of physics, and what makes physics fun.
PS - Based on my own (unconventional) physics model, my bet is on no Majorana masses, and for Dirac masses of two of the three neutrino states nu_2 and nu_3, at around 0.009 eV and 0.054 eV, with nu_1 being massless. Very roughly my physical picture is of a 4+4=8-dim Kaluza-Klein structure in which the higher (massive neutrino) generations have interactions related to all 8 dimensions while the first (massless neutrino) generation lives in 4-dim physical spacetime. It is somewhat like the overall structure of the model of Arkani-Hamed, Cheng, Dobrescu and Hall in hep-ph/0006238 (Phys. Rev. D62, 096006 (2000)), but differing in details. ...".