Fixed points in the evolution of neutrino mixings

Abstract

We derive the renormalization group equations for the neutrino masses and mixing angles in explicit form and discuss the possible classes of their solutions. We identify fixed points in the equations for mixing angles, which can be reached during the evolution for several mass patterns and give ${\sin }^{2}2{\theta }_{sol}={\sin }^{2}2{\theta }_{atm}{\sin }^2{\theta }_3/({\sin }^2{\theta }_{atm}{\cos }^2{\theta }_3+{\sin }^2{\theta }_3{)}^2$, consistently with the present experimental information. Further experimental test of this relation is of crucial interest. Moreover, we discuss the stability of quantum corrections to neutrino mass squared differences. Several interesting mass patterns show stability in the presence of fixed point solutions for the angles.

Comments: 17 pages, 2 figures. References added and comments concerning the two-flavour case changed