Signatures of $\tilde{R}_2$ class of Leptoquarks at the upcoming $ep$ colliders

We explore the signatures of the $\tilde{R}_2$ class of leptoquark (LQ) models at the proposed $e^- p$ and $e^+p$ colliders. We carry out an analysis for the proposed colliders LHeC and FCC-eh with center of mass (c.m.) energy 1.3 TeV and 3.46 TeV, respectively. For $\tilde{R}_2$ class of LQ models, there are a number of final states that can arise from LQ production and its subsequent decay. In this report we do a detailed cut-based analysis for the $l^{\pm}j$ final state. We also discuss the effect of polarized electron and positron beams on LQ production and in turn on $l^{\pm}j$ production. At LHeC, the final state $l^+j$ has very good discovery prospect. We find that, only 100 $\text{fb}^{-1}$ of data can probe LQ mass upto 1.2 TeV with $5\sigma$ significance, even with a generic set of cuts. On the contrary, at FCC-eh, one can probe LQ masses upto 2.2 TeV (for $e^-$ beam) and 3 TeV (for $e^+$ beam), at more than $5\sigma$ significance with luminosity $1000\,\text{fb}^{-1}$ and $500\,\text{fb}^{-1}$, respectively.