Probing Leptoquark and Heavy Neutrino at LHeC

We explore leptoquark production and decay for the $\tilde{R}_{2}$ class of models at the proposed $e^{-} p$ collider LHeC, planned to operate with 150 GeV electron and 7 TeV proton beams. In addition to the coupling of leptoquark with the lepton and jet, the model also has right handed neutrinos, coupled to the leptoquark. We analyse the collider signatures of a number of final states, that can originate from leptoquark decay into the standard model particles, as well as, the final states that originate from further decay of the heavy neutrinos, produced from leptoquark. We find that the final state $\ell^{-}+\text{n-jets}\,(1\leq\text{n} \leq 2)$ has the largest discovery prospect, more than $5\sigma$ with only few fb of data to probe a leptoquark of mass 1.1 TeV, even with a generic set of cuts. The significance falls sharply with increasing leptoquark mass. However, with 100\,$\rm{fb}^{-1}$ of data, a 5$\sigma$ discovery for leptoquarks of mass upto 1.4 TeV is still achieveable. Also for the same luminosity, final state $\bar{b}\ell^{+}\tau^{-}+\text{n-jets}\,(\text{n}\geq 2)+\text{MET}$, resulting from the cascade decay of the leptoquark to an $\bar{t}$ and right handed neutrino, followed by further decays of $\bar{t}$ and the neutrino, is expected to yield a rather large number of events~($\approx 180$).