Scaling in the neutrino mass matrix

In an attempt to uncover any underlying structure in the neutrino mass matrix, we discuss the possibility that the ratios of elements of its Majorana mass matrix are equal. We call this “strong scaling Ansatz” for neutrino masses and study its phenomenological implications. Of three possible independent scale invariant possibilities, only one is allowed by current data, predicting in a novel way the vanishing of U_e3$U_{e3}$ and an inverted hierarchy with the lightest neutrino having zero mass. The Ansatz has the additional virtue that it is not affected by renormalization running. We also discuss explicit models in which the scaling Ansatz is realized.