Systematic Errors

The following sources of systematic errors are considered in the analysis:

• In order to understand the errors in the efficiency estimation, the selection criteria were varied within their measured resolution. As well, a dependence of the $V_0$ reconstruction on the event multiplicity was investigated. These two effects are summed into the efficiency estimation systematic error $\sigma_{eff}$ of 5%.

• The limited MC statistic contributes into systematic error $\sigma_{stat}$ 2%.

• The bias which is coming from the not proper described data behavior in simulated events is estimated by re-weighting the MC $p_t^2$ and $x_F$ distributions, this results into a 10% systematic error $\sigma_{mc}$

• For the background fitting of the invariant mass distributions different functions were used and also bin sizes in $x_F$ and $p_t^2$ were varied. This results in a change of the cross section in the order of 3% $\sigma_{fit}$ .

• The integrated luminosity was determined with 3 different methods, the obtained results differ within 5-10%. Conservatively an error of $\sigma_{Lumi}$=10% is included in the total systematic uncertainty.

• In order to extract $\mathrm{d} \sigma /\mathrm{d}p_t^2$ the differential cross section is extrapolated to the full $x_F$ range with the equation

  $$\frac{\mathrm{d}^2 \sigma}{\mathrm{d}p_t^2\mathrm{d}x_F}=C\,(1-\vert x_F\vert)^n \, exp(-B\,p_t^2)$$ (6.21)

  
  
  where the parameter $n$ is determined experimentally [#!Adam!#]. By varying the parameter n the induced systematic error of the extrapolation $\sigma_{extrap}$ is estimated to be in the order of 15% for $K^0_S$, $\Lambda$ and $\bar \Lambda$ .

To obtain the total systematic error, the errors are combined in the following way

$$\sigma_{tot}^{sys}=\sqrt{ \sigma_{eff}^2 \, + \, \sigma_{stat}^2 ... ...mc}^2 \, + \, \sigma_{fit}^2 \, + \, \sigma_{Lumi}^2 \, + \, \sigma_{extrap}^2}$$ (6.22)

The presented analysis is clearly dominated by systematic errors. A systematic error due to the deviations in the $p_t^2$ and $x_F$ can be reduced by improving the kinematical model used for $V_0$ generation, for example by introducing two slopes into the $p_t^2$ distribution, as was mentioned above. A further improvement of the detector description in simulated events is needed. All sources of the systematic errors are listed in the Table 6.12.

Table 6.12: Sources of the systematic errors contributed to the final systematic error.

Source of systematic error	error, %
Selection criteria	5.
Limited MC statistic	2.
Not proper described behaviour of $p_t^2$ and $x_F$	10.
Bin size and fit function	3.
Luminosity determination	10.
Extrapolation to the full $x_F$ range	15.