General Determination of Phases in Leptonic Mass Matrices.pdf

ITP-SB-93-63 November, 1993 General Determination of Phases in Leptonic Mass Matrices 3 9 9 1 v o Alexander Kusenko∗ and Robert Shrock∗∗ N 8 1 Institute for Theoretical Physics 1 State University of New York v 7 Stony Brook, N. Y. 11794-3840 0 3 1 1 3 9 / Abstract h p - p We construct new invariants and give several theorems which determine in general (i) the e h number of physically meaningful phases in charged lepton and neutrino mass matrices and (ii) : v which elements of these matrices can be rendered real by rephasings. We illustrate our results with i X simple models. r a ∗email: sasha@max.physics.sunysb.edu ∗∗email: shrock@max.physics.sunysb.edu Understanding fermion masses and mixing remains one of the most important outstanding prob- lems in particle physics. In particular, the issue of possible neutrino masses and associated lepton mixing is of fundamental interest. Although there is no definite direct evidence for nonzero neutrino masses1 they are expected on general grounds: given only the known left-handed neutrino fields 2 and the usual Higgs field(s) , nonzero neutrino masses result generically from higher-dimension operators which would occur at a scale near to that of quantum gravity, suppressed by associated ¯ hc/¯ (8πG ) = 2.4 × 1018 GeV, For exam- inverse powers of the (reduced) Planck ma