Summary of Used Cuts

The following selection criteria were used in the analysis to reject background and to ensure a reliable event reconstruction:

1. for the reconstruction of each track, at least 5 hits in the Vertex Detector System (VDS) and 5 hits in the Main Tracker (MT) have to be used,

2. tracks have to be marked by the clone removal algorithm as not being clones,

3. only opposite charged track pairs are considered,

4. for a quick rejection of track pairs a cut on the DCA between two $V_0$ candidate tracks is applied, cut at $\le$ 0.12 cm.

5. for every track pair, three mass hypotheses are checked:
   1. first the $K^0_S$ mass hypothesis is checked, with a cut at the calculated invariant mass $0.428\,\, GeV/c^2\,\, \le\,\, m_{K^0_S}\,\, \le\,\, 0.568\,\, GeV/c^2$. It corresponds to approximately 10$\sigma$ of the signal mass width (see table 6.3),

   2. at the next step $\Lambda$ and $\bar \Lambda$ hypotheses are examined, taking into account the charge of the track with dominant momentum (in order to correctly assign the masses of decay products), with invariant mass cut
      $1.10\,\, GeV/c^2\,\, \le\,\, m_{\Lambda / \bar \Lambda}\,\, \le\,\, 1.13\,\, GeV/c^2$. It corresponds to approximately 8 $\sigma$ of the signal mass width (see table 6.3)

6. impact parameter cut of the $V_0$ candidate to the closest primary vertex, cut at $\le$ 0.06 cm. This criteria is used also to select a primary vertex for the $V_0$'s flight path calculation.

7. the most powerful cut is the cut on the flight path ($c\tau$) of the $V_0$ candidate in the $V_0$ rest frame, cut at $\ge$ 0.13 cm for $K^0_S$ and cut at $\ge$ 0.39 cm for $\Lambda ,\, \bar \Lambda$ candidates.

8. all $\Lambda$ and $\bar \Lambda$ candidates which fulfill the $K^0_S$ mass hypothesis in the mass region $0.48\,\, GeV/c^2\,\, \le\,\, m_{K^0_S}\,\, \le\,\, 0.515\,\, GeV/c^2$ are removed

Table: Cuts applied to the minimum bias data sample, efficiency and rejection for each cut for $K^0_S ,\, \Lambda$ and $\bar \Lambda$.

	$K^0_S$		$\Lambda$		$\bar \Lambda$
Cut	$\varepsilon_{\rm {Sg}}$, %	$\varepsilon_{\rm {Bg}}$, %	$\varepsilon_{\rm {Sg}}$, %	$\varepsilon_{\rm {Bg}}$, %	$\varepsilon_{\rm {Sg}}$, %	$\varepsilon_{\rm {Bg}}$, %
Opposite charge requirement	100.0	-	100.0	-	100.0	-
Clone removal requirement	91.6	-	86.7	-	86.5	-
DCA $\le$ 0.12 cm	97.2	15.1	94,9	18.2	96.0	17.6
Mass hypothesis	99.8	0.0	100.0	0.0	99.5	0.0
Impact Parameter $\le$ 0.06 cm	93.3	51.6	90.8	47.1	89.5	49.
$c\tau~\ge~$0.13 cm	90.6	98.7	91.6	94.9	89.8	95.2
$K^0_S$ indistinguishable from
$\Lambda$ and $\bar \Lambda$ removal	88.8	7.3	86.9	12.1	89.9	12.7
Over all	66.7	99.5	59.5	98.1	59.7	98.2