Search for excited spin-3/2 neutrinos at LHeC
We study the potential of the next $ep$ collider, namely LHeC, with two options $\sqrt{s}=1.3$ TeV $\sqrt{s}=1.98$ TeV, to search for excited spin-1/2 and spin-3/2 neutrinos. We calculate the single production cross section of excited spin-1/2 and spin-3/2 neutrinos according to their effective currents describing their interactions between gauge bosons and SM leptons. We choose the $ν^{\star}\rightarrow eW$ decay mode of excited neutrinos and $W\rightarrow jj$ decay mode of $W$-boson for the analysis. We put some kinematical cuts for the final state detectable particles and plot the invariant mass distributions for signal and the corresponding backgrounds. In order to obtain accessible limits for excited neutrino couplings, we show the $f-f^{\prime}$ and $c_{iV}-c_{iA}$ contour plots for excited spin-1/2 and excited spin-3/2 neutrinos, respectively.