  In this letter we introduce a new variable $\xi$, namely the number of tracks
associated with the primary vertex, which are not parts of reconstructed
objects such as jets/isolated leptons etc. We demonstrate its usefulness in the
context of new physics searches in the channel monojet$+$missing transverse
momentum (MET). In models such as in compressed supersymmetry, events are often
characterized by a rather large number of soft partons from the cascade decays,
none of which result in reconstructed objects. We find that $\xi$, binned in
$p_T$, can discriminate these new physics events from events due to
$Z+\text{jets}$, that is, the main background in the channel monojet+ MET. The
information contained in soft tracks is largely uncorrelated with traditional
variables such as the effective mass, MET, $p_T$ of the jet, etc. and,
therefore, can be combined with these to increase the discovery potential by
more than $200\%$ (depending on the spectra, of course). In fact, we find that
simple cuts on $\xi(p_T)$ along with cuts on MET, and the effective mass
outperforms sophisticated optimized MultiVariate Analyses using all
conventional variables. One can model the background distribution of $\xi(p_T)$
in an entirely data-driven way, and make these robust against pile-up by
identifying the primary vertex.
