1306.1890 (Anjan S. Joshipura et al.)

Horizontal symmetries of leptons with a massless neutrino    [PDF]

Anjan S. Joshipura, Ketan M. Patel

Residual symmetry G_\nu\ of neutrino mass matrix with a massless neutrino and embedding of G_\nu\ and the residual symmetry G_l of the charged lepton mass matrix into finite discrete groups G is discussed. Massless neutrino results if G_\nu\ and hence G are subgroups of U(3) rather than of SU(3). Structure of the resulting leptonic mixing matrix U_{PMNS} is discussed in three specific examples based on groups (a) \Sigma(3N^3), (b) \Sigma(2N^2) and (c) S_4(2) = A_4\rtimes Z_4. \Sigma(3N^3) groups are able to reproduce either the second or the third column of U_{PMNS} correctly. \Sigma(2N^2) groups lead to prediction \theta_{13}=0, \theta_{23}=\pi/4 for the reactor and atmospheric mixing angles respectively if neutrino mass hierarchy is inverted. Solar angle remains undetermined in this case. This also gets determined when G=S_4(2) which can give bi-maximal mixing for inverted hierarchy. Examples (b) and (c) provide a good zeroth order approximation to realistic leptonic mixing with a massless neutrino.

View original: http://arxiv.org/abs/1306.1890