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There are four neutrino-related flavor parameters that have been measured:The three mixing angles s_{23}, s_{12}, s_{13}, and the ratio of mass-squareddifferences r_{23}. Of these, the first two are order one. On the other hand,s_{13} and r_{23} can be either order-one parameters that are accidentallysomewhat small, or they are small for a reason, for example, they vanish in thelimit of a symmetry that is broken by small parameters. We show that in thelatter case, the Froggatt-Nielsen mechanism could explain the smallness ofs_{13} and r_{23} only if some order-one coefficients are as small as thesymmetry-breaking parameters. It is thus very unlikely that an Abelian symmetryis responsible for the smallness of s_{13} and r_{23}.

Abelian symmetries as the source of the small neutrino-related flavor parameters