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Imperfections of the acceptance correction and the effects thereof

Due to inaccuracies of our knowledge of the geometrical positions of the equipment in the hall and of the magnitude and configuration of the magnetic field, the acceptance correction is imperfect. It is less reliable on the edges. Typically, when looking at either $\,dN/\,dy$ or $k_T$ spectra from a single setting with sufficiently fine binning one sees points on the edges of acceptance that deviate sharply from the overall pattern. These points must not be included in the fiducial cut area. A sharp non-constancy of $\,dN/\,dy$, inconsistent between different settings, would indicate that a wrong $T(m_T)$ was used.

Acceptance correction to the $m_T$ or $p_T$ spectra includes information about shape of the $\,dN/\,dy$ distribution. Therefore any uncertainty in the $\,dN/\,dy$ shape results in an uncertainty of the slope. In quantifying the uncertainty, the first step was to derive the error propagation factor to convert the uncertainty of the $\,dN/\,dy$ width into uncertainty of the inverse slope $T$. I describe the $\,dN/\,dy$ with a Gaussian whose width I denote by $\sigma_G$. MC was run with two widths of input $\,dN/\,dy$: $\sigma_{G1} = 1.1$ and $\sigma_{G2} = 0.5$. The slopes were extracted in the two cases and compared, the error-propagation factor was found to be

$$\,dT/\,d W = (T(\sigma_{G1}) - T(\sigma_{G2}))/(\sigma_{G1}-\sigma_{G2})$$

It is : for 8 GeV/c high angle: $-52 MeV$, for 4 GeV/c high angle: $-117 MeV$. The problem however is to characterize the uncertainty of our knowledge of the $W$. This has been done in the following (somewhat arbitrary !) way: I say that with ``3$\sigma$'' (99.7%) confidence level, the Gaussian kaon $\,dN/\,dy$ distribution has $W$ parameter between 0.8 and 1.4. Then, one can derive and propagate the ``1$\sigma$'' uncertainty. The resulting uncertainty in the inverse slope can be found in Table 5.1. It dominates the total systematic error, even though smaller additional uncertainties are possible due to other sources.