Possible revelation of a seesaw mass pattern in solar and atmospheric neutrino data.

Assuming the solar and atmospheric neutrino deficits to be due to neutrino oscillations, it is shown that the 3× 3 mass matrix spanning νe, νμ, and ντ may have already revealed a seesaw mass pattern. Also, this matrix is the natural reduction of a simple 5 × 5 seesaw mass matrix with one large scale, the 4 × 4 reduction of which predicts that a fourth neutrino would mix with νe and νμ in such a way that νμ → νe oscillations may occur just within the detection capability of the LSND (Liquid Scintillator Neutrino Detector) experiment. Whether or not neutrinos have mass is clearly a fundamental issue in particle physics and astrophysics. There is now a good deal of indirect evidence from measurements of the solar νe flux[1, 2, 3, 4] and the atmospheric νμ/νe ratio[5, 6] that neutrinos oscillate from one to another. This means that νe and νμ are not mass eigenstates; each is rather an admixture of two or more mass eigenstates. Under the simplifying assumption that only two neutrinos are involved in each case, probable central values for the mass-squared difference and the mixing angle are ∆m ≃ 4× 10 eV, sin 2θ ≃ 0.01, (1) from analyzing[7] solar data, assuming the small-angle, nonadiabatic solution, and ∆m ≃ 10 eV, sin 2θ ≃ 0.5, (2) from analyzing[8] atmospheric data. Given only the above information, it is clearly not possible to reconstruct unambiguously the underlying 3× 3 neutrino mass matrix. However, if a certain empirical relationship can be found among the four parameters listed above, an important insight may be gained as to the form of this mass matrix. Such an example is already very well-known in the case of the quark mass matrix. It was pointed out many years ago[9] that the empirical relationship sin θC ≃ md/ms (3) may be obtained with a 2× 2 mass matrix of the form M = 