MC and Data Comparison

In order to understand differences between MC and data, a comparison of the main kinematical variables is performed. For each bin an invariant mass distribution for the corresponding $V_0$ candidate is produced. All obtained distributions are fitted by a Gaussian plus a polynominal of second order to describe the background. Finally in order to simplify the comparison, distributions of kinematical variables for data and MC are normalized to the same area.

The following kinematical variables are compared:

1. azimuthal angle ($\Phi$) of the $V_0$ candidate,
2. polar angle ($\Theta$) of the $V_0$ candidate,
3. Feynman $x$ ($x_F$) of the $V_0$ candidate in the center of mass system,
4. rapidity (y) of the $V_0$ candidate in the center of mass system,

   $$y=\frac{1}{2}ln\frac{E+p_z}{E-p_z}\: ,$$ (6.17)

   
   

5. squared transverse momentum ($p_t^2$) of the $V_0$ candidate in the laboratory frame,

   $$p_t^2=p_x^2+p_y^2 \: ,$$ (6.18)

   
   

6. momentum ($p$) of the $V_0$ candidate in the laboratory frame,

7. flight path ($flight$) of the $V_0$ candidate in the rest frame,

Figure 6.11: Comparison of $K^0_S$ properties in MC and data. (filled triangles: MC, empty triangles: data.)

Figure 6.12: Comparison of $\Lambda$ properties in MC and data. (filled triangles: MC, empty triangles: data.)

Figure: Comparison of $\bar \Lambda$ properties in MC and data. (filled triangles: MC, empty triangles: data.)

The distributions of $x_F$ and $p_t^2$ are of special interest for this analysis. In case of $K^0_S$ MC and data show an agreement on the level of 10-20%. The simulated distribution of $x_F$ for $\Lambda$ is within 25% in agreement with data, $p_t^2$ distribution within 30%. The $x_F$ distribution of $\bar \Lambda$ demonstrated a better agreement, the maximum reached difference is o f the order of 15%, in case of $p_t^2$ distribution it is 30%.

Above a $p_t^2$ of about 0.8 $GeV^2/c^2$ the distributions for all three particles show large differences between MC and data. Such behaviour is due to a simplified model used in MC, $p_t^2$ spectra is simulated with one exponential. Data distributions indicate that it is better described by two exponentials. This behavior is well known and was mentioned already by [#!Mple!#].