Studying superpartner production together with a hard initial state radiation (ISR) jet has been a useful strategy for searches of supersymmetry with a compressed spectrum at the Large Hadron Collider (LHC). In the case of the top squark (stop), the ratio of the missing transverse momentum from the lightest neutralinos and the ISR momentum, defined as $bar{R}_M$, turns out to be an effective variable to distinguish the signal from the backgrounds. It has helped to exclude the stop mass below 590 GeV along the top corridor where $m_{tilde{t}} - m_{tilde{chi}_1^0} approx m_t$. On the other hand, the current experimental limit is still rather weak in the $W$ corridor where $m_{tilde{t}} - m_{tilde{chi}_1^0} approx m_W +m_b$. In this work we extend this strategy to the parameter region around the $W$ corridor by considering the one lepton final state. In this case the kinematic constraints are insufficient to completely determine the neutrino momentum which is required to calculate $bar{R}_M$. However, the minimum value of $bar{R}_M$ consistent with the kinematic constraints still provides a useful discriminating variable, allowing the exclusion reach of the stop mass to be extended to $sim 550$ GeV based on the current 36 fb$^{-1}$ LHC data. The same method can also be applied to the chargino search with $m_{tilde{chi}_1^pm} -m_{tilde{chi}_1^0} approx m_W$ because the analysis does not rely on $b$ jets. If no excess is present in the current data, a chargino mass of 300 GeV along the $W$ corridor can be excluded, beyond the limit obtained from the multilepton search.
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