Sterile Neutrinos in a 6x6 Matrix

An early study of neutrino mixing within the see-saw framework considered random mass matrices in what is now known as the sterile sector[1]. The mixing angles in the lepton sector were found to be closely distributed about the CKM angles that were assumed. In that work, rank 3 was assumed for the weak isospin zero Majorana mass matrix in the sterile neutrino sector. We report here on the character of new results using a reduced rank (``singular'') sterile matrix. We find that an additional flavor misalignment in the sterile sector can produce several interesting effects, including: 1) mass eigenstates that lead to very large flavor mixing among active neutrinos, and 2) small values for the 1-3 mixing angle parameter[2]. We also discuss the limits that current observations place on the mass scale of light sterile neutrinos in this model. [1]T.\ Goldman and G.\ J.\ Stephenson, Jr., ``How Large Are the Neutrino Mixing Angles?'' {\it Phys.\ Rev.\ D} {\bf 24}, 236 (1981). [2]G.\ J.\ Stephenson, Jr.\ , T.\ Goldman, B.\ H.\ J.\ McKellar and M.\ Garbutt, ``Large Mixing from Small: Pseudo-Dirac Neutrinos and the Singular Seesaw,'' {\it Int.\ J.Mod.Phys.}{\bf A20} (2005) 6373; [hep-ph/0404015].