Large gauge invariant non-standard neutrino interactions
  Theories beyond the Standard Model must necessarily respect its gauge symmetry. This implies strict constraints on the possible models of non-standard neutrino interactions, which we analyze. The focus is set on the effective low-energy dimension six and eight operators involving four leptons, decomposing them according to all possible tree-level mediators, as a guide for model building. The new couplings are required to have sizeable strength, while processes involving four charged leptons are required to be suppressed. For non-standard interactions in matter, only diagonal tau-neutrino interactions can escape these requirements and can be allowed to result from dimension six operators. Large non-standard neutrino interactions from dimension eight operators alone are phenomenologically allowed in all flavour channels and shown to require at least two new mediator particles. The new couplings must obey general cancellation conditions both at the dimension six and eight levels, which result from expressing the operators obtained from the mediator analysis in terms of a complete basis of operators. We illustrate with one example how to apply this information to model building. 
M. B. Gavela, D. Hernandez, T. Ota, W. Winter