Softly brokenA4symmetry for nearly degenerate neutrino masses

The leptonic Higgs doublet model of neutrino masses is implemented with an $A_4$ discrete symmetry (the even permutation of four objects or equivalently the symmetry of the tetrahedron) which has four irreducible representations: $\underset{¯}{1},{\underset{¯}{1}}^{\prime },{\underset{¯}{1}}^{″},$ and $\underset{¯}{3}.$ The resulting spontaneous and soft breaking of $A_4$ provides a realistic model of charged-lepton masses as well as a nearly degenerate neutrino mass matrix. The phenomenological consequences at and below the TeV scale are discussed.