Is polarization effect visible in leptonic SUSY searches?

On-shell effective theory approach has been widely used in search of various supersymmetric signals, in particular, gluino/squark pairs with long cascade decay chains in which complete matrix element calculations may encounter over-20 dimensional integrations. On the other hand, leptons from polarized chargino decays may show significant boost or anti-boost effect in some scenarios and simulation without polarization information may underestimate or overestimate the lepton $p_{T}$ cut efficiencies in the first place. We study the polarization effects in supersymmetry searches of multi-jets plus leptons final states. We find it justifiable for first two generations to only use on-shell effective theories. While for measurements related to third generation squarks, for instance, polarization effect of charginos from stop may reduce the lepton $p_{T}$ cut efficiencies in cross section measurements by $25\%$ when slepton contributions dominate in chargino decay or $W$ are on-shell. The signal is then underestimated if only on-shell effective theory approach is taken in simulation of signal and the real bound on squark/gluino should be more stringent.