Neutrino oscillations: Inevitability of non-standard interactions or a sterile neutrino

We conjecture that the neutrino mixing matrix must be such that in the flavour oscillation process the energy expectation values enjoy flavour independence. Based on this conjecture we present unitarity and energy conservation constraints on neutrino oscillation parameters. In our analysis \theta_{13} depends on the ratio of the mass-squared differences \zeta and on \theta_{12} alone; while \delta_{CP} is completely determined by \zeta, \theta_{12}, and \theta_{23}. The standard neutrino oscillation phenomenology (SNOP) suggests \zeta \approx 30. The resulting prediction for \theta_{13} conflicts with SNOP expectation for all values of \theta_{12}. This leads to the suggestion that some non-standard neutrino interactions may be intervening to invalidate the SNOP inferred \zeta and \theta_{13}. An alternate inference is to go beyond the three flavours of SNOP and incorporate sterile neutrinos in the analysis.