Neutrino masses and mixing angles in a predictive theory of fermion masses.

In the extension of the Dimopoulos–Hall–Raby model of the fermion mass matrices to the neutrino sector, there is an entry in the up-quark and neutrino Dirac mass matrices which can be assumed to arise from the Yukawa coupling of a 120, instead of a 10 or a 126, of SO(10). Although this assumption leads to an extra undetermined complex parameter in the model, the resulting lepton mixing matrix exhibits the remarkable feature that the ντ does not mix with the other two neutrinos. Making a reasonable assumption about the extra parameter, we are able to fit the large-mixing-angle MSW solution of the solarneutrino problem, and we obtain mντ ∼ 10 eV, the right mass range to close the Universe. Other possibilities for explaining the solar-neutrino deficit are also discussed. This is a Comment on the paper of Ref. [1]. In that paper, the Dimopoulos–Hall–Raby (DHR) [2] model of the quark and charged-lepton mass matrices in a SUSY GUT, which is in fact a revival of the old Georgi–Jarlskog [3] scheme, has been extended, with the help of some assumptions, to yield also the form of the neutrino mass matrices, thus predicting the neutrino mass ratios and the lepton mixing. In this Comment, we show that, if one of the assumptions is relinquished, a different form of the neutrino Dirac mass matrix can be obtained, which leads to a very interesting prediction for the lepton mixing, namely, that the τ neutrino is an eigenstate of mass. The DHR model requires a small number of SO(10) Higgs representations to give mass to the fermions. It requires one 10 and one 126 to give mass to the down-type quarks and to the charged leptons, and one 126 and one other representation to give mass to the up-type quarks and to the neutrinos. For this other representation, DHR have used either a 126 — obtaining results which agree only marginally with the MSW solution of the solar-neutrino problem — or a 10 — obtaining results which do not agree with that solution. We remark in this Comment that the quarkand charged-lepton-sector predictions are the same if one uses instead a 120 as that representation. In looking for predictions for the neutrino sector, ∗On leave of absence from Universidade Técnica de Lisboa, Lisbon, Portugal