Effective Theory and Simple Completions for Neutrino Interactions

We consider all the dimension 6 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 $\epsilon_{\alpha \beta}$,where$\alpha$and$\beta$ are neutrino flavor indices taking the values $e$, $\mu$ and $\tau$. In the simple models we consider the ${ϵ}_{\alpha \beta }$'s are much more constrained than in the operator-based model-independent approach. Typically the $\epsilon_{\alpha \beta}${}^{\mathrm{\prime }}sarerestrictedtobesmallerinmagnitudethanaround$10^{-3}$. In some of the leptoquark models, a specific pattern for the leptoquark Yukawa couplings allows the diagonal element ${ϵ}_{\tau \tau }$ to be as large as $\sim 0.1$, or one of ${ϵ}_{ee}$, ${ϵ}_{\mu \mu }\sim 0.01$. We discuss the interplay between neutrino physics and leptoquark searches at the LHC.