Effective theory and simple completions for neutrino interactions

We consider all the dimension-six operators as well as some simple extensions of the standard model that give new contributions to neutrino interactions with matter. Such interactions are usually parametrized by ε_αβ, where α and β are neutrino flavor indices taking the values e, μ, and τ. In the simple models we consider the ε_αβ's are much more constrained than in the operator-based model-independent approach. Typically the ε_αβ's are restricted to be smaller in magnitude than around 10^-3. In some of the leptoquark models, a specific pattern for the leptoquark Yukawa couplings allows the diagonal element ε_ττ to be as large as ~0.1, or one of εₑₑ, ε_μμ~0.01. We discuss the interplay between neutrino physics and leptoquark searches at the LHC.