Does the LMA MSW solar solution imply the Dirac nature of neutrinos?

Abstract

Operating with the bilarge neutrino mixing, we show that in the option of Dirac neutrinos the fermion universality -- expressed by the proportionality of neutrino masses to charged-lepton masses -- predicts $\Delta m_{21}^2$ of the order $10^{-5} {\rm eV}^2$, consistently with the LMA MSW solar solution. In contrast, in the option of Majorana neutrinos the fermion universality -- introduced as the seesaw proportionality of neutrino masses to charged-lepton masses squared -- predicts $\Delta m_{21}^2$ of the order $10^{-8} {\rm eV}^2$, what is consistent rather with the LOW MSW solar solution. Thus, the favored LMA MSW estimation of $\Delta m_{21}^2$ might be a signal from the Dirac nature of neutrinos.