  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
$\epsilon_{\alpha \beta}$'s are much more constrained than in the
operator-based model-independent approach. Typically the $\epsilon_{\alpha
\beta}$'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 $\epsilon_{\tau\tau}$ to be as large as
$\sim0.1$, or one of $\epsilon_{ee}$, $\epsilon_{\mu\mu}\sim0.01$. We discuss
the interplay between neutrino physics and leptoquark searches at the LHC.
