Detector Resolution

Using the full chain of the detector simulation, track reconstruction and $V_0$ selection, the resolution of the kinematic variables can be estimated. Fig. 6.5 shows residuals for kinematical variables $x_F$ and $p_t^2$ for $K^0_S ,\, \Lambda$ and $\bar \Lambda$. The Feynman scaling variable ($x_F$) describes the longitudinal momentum $P_z$ of the scattering product, expressed in terms of the maximally possible momentum $P_{zmax}$,

$$x_F=\frac{P_z}{P_{z max}}\: .$$ (6.1)

The quoted resolutions are from fits of Gaussians to the residual distributions (see Fig. 6.5), they are summarized below:

$$\sigma_{x_F(K^0_S)} =(0.32 \pm 0.01)\,\,\,\,\,\, \, \,\,\,\, \, \, \sigma_{p_t^2(K^0_S)} =(2.5 \pm 0.1)\,\,\,MeV^2/c^2$$ (6.2)

$$\sigma_{x_F(\Lambda)} =(0.47 \pm 0.01)\,\,\,\,\,\, \, \,\,\,\, \, \, \sigma_{p_t^2(\Lambda)} =(3.2 \pm 0.2)\,\,\,MeV^2/c^2$$ (6.3)

$$\sigma_{x_F(\bar \Lambda)} =(0.46 \pm 0.01)\,\,\,\,\,\, \, \,\,\,\, \, \, \sigma_{p_t^2(\bar \Lambda)} =(4.7 \pm 0.3)\,\,\,MeV^2/c^2$$ (6.4)

Figure 6.5: Top: Resulting residual distributions $X_{gen}$- $X_{rec}$ for the $x_F$ variable of $K^0_S ,\, \Lambda ,\, \bar \Lambda$. Bottom: Resulting residual distributions $X_{gen}$-$X_{rec}$ for the $p_t^2$ variable of $K^0_S ,\, \Lambda ,\, \bar \Lambda$. Only $V_0$ candidates which were selected by the same analysis algorithm are used for these plots.

The bin widths are chosen 0.015 for $x_F$ variable and 0.2 $\rm {MeV^2/c^2}$ for $p_t^2$.