$\tau$ lepton will decay leptonically or hadronically and a small portion of it will give opposite sign dilepton and will increase the signal strength. As $\tau$ decays, eventually we get a final state signal which consist of opposite sign electron ($e^{\pm}$) or muon ($\mu^{\pm}$) or di-jet. For simulation, we consider Yukawa couplings $\lambda^{\prime}_R$, that are allowed by neutrino oscillation data.

Since we are interested in the opposite sign dilepton ($l^{+} l^{-}$) and missing energy ($\cancel{E}_{T}$) signal in the final state, the corresponding SM dominant backgrounds are as follows,

1.  At the time of electron positron collision, opposite sign dilepton and missing energy can be produced as $e^+ e^- \rightarrow l^+ l^- Z\, (\rightarrow \nu_{l} \bar{\nu_{l}})$. This includes both the $ZZ$ and the virtual photon contribution.

2.  Another dominant background is the $W^+ W^-$ pair production and its further leptonic decay. This can mimic the signal as $ e^+ e^- \rightarrow W^{+} W^{-} \, \rightarrow l^+ l^- \nu_{l}\, \bar{\nu_{l}}$.

3.  Moreover, $t \bar{t}$ final state production and its subsequent decay will also affect the signal as background in the following manner: $e^{+} e^{-} \rightarrow t(\rightarrow b\, l^{+} \nu_{l})\, \bar{t} (\rightarrow \bar{b}\, l^{-} \bar{\nu_{l}})$.

We do not put any veto on the 