Armenteros-Podolanski Plot

The kinematic properties of the $V_0$ candidates can be illustrated by the Armenteros-Podolanski plot. This is a two dimensional plot, of transverse momentum $p_t$ of the oppositely charged decay products with respect to the $V_0$ versus the longitudinal momentum asymmetry $\alpha =\frac{p_l^+-p_l^-}{p_l^++p_l^-}$. The obtained distribution (see Fig.6.4) can be explained by the fact that decay products of the $K^0_S\, \rightarrow\pi^+ \pi^-$ have the same mass and therefore their momenta are distributed symmetrically on average, while for decays $\Lambda\, \rightarrow p \pi^- (\bar \Lambda\, \rightarrow \bar p \pi^+)$ the proton (antiproton) takes on average a larger part of the momentum and as a result the distribution is asymmetric.

$K^0_S$ are kinematically indistinguishable from $\Lambda / \bar \Lambda$ in the area where the corresponding bands of the Armenteros-Podolanski plot overlap and contribute to the background in the invariant mass distributions. A simple cut allows to remove these overlaps: all $\Lambda$ and $\bar \Lambda$ candidates are removed that fulfill a $K^0_S$ mass hypothesis in the mass range $0.48\,\, GeV/c^2\,\, \le\,\, m_{K^0_S}\,\, \le\,\, 0.515\,\, GeV/c^2$. The loss of $V_0$ signals due to the cut at the Armenteros-Podolanski plot is approximately 10-15%. The bands in the Armenteros-Podolanski plot can be explained by the applied mass cut.

Figure: On the left, the Armenteros-Podolanski plot for $K^0_S ,\, \Lambda ,\, \bar \Lambda$ candidates reconstructed in run 20677. Right, the Armenteros-Podolanski plot after removal of overlap in the masses.