Non standard neutrino interactions at LEP2 and the LHC

We consider Non-Standard neutrino Interactions (NSI) connecting two neutrinos with two first-generation fermions ($e,u$ or $d$), which we assume to arise at at dimension eight due to New Physics. The coefficient is normalised as $4 \epsilon G_F/\sqrt{2}$. We explore signatures of NSI-on-electrons at LEP2, and of NSI-on-quarks at the LHC, treating the NSI as contact interactions at both energies. In models where the coefficients of dangerous dimension six operators are suppressed by cancellations, LEP2 provides interesting bounds on NSI operators ($ϵ\text{lsim}{10}^{-2}-{10}^{-3}$), which arise because $\sqrt{s} \sim 200$ GeV, and the cancellation applied at zero momentum transfer. At the LHC, we use the Equivalence Theorem, which relates the longitudinal $W$ to the Higgs, to estimate the rate for $\bar{q}q{W}^{+}{W}^{-}{e}_{\alpha }^{+}{e}_{\beta }^{-}$ induced by NSI. We find that the cross-section is small, but that the outgoing particles have very high $p_T>400$ GeV, which reduces the issue of backgrounds. In a conservative scenario, we find that the LHC at 14 TeV and with 100 fb${}^{-1}$ of data would have a sensitivity to $\epsilon \gsim 3 \times 10^{-3}$.