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Background subtraction

Our final goal is correcting the average power spectrum components (PSC) for the background contribution. Let me first introduce the basic notions and notation. I will denote the total amplitude from the analyzed part of the detector as $x$, and distinguish three kinds of probability density distribution:

• $F(x)$ - non-interactions. $F(x)$ is found in the empty target run.
• $G(x)$ - minimum bias sample of $PbPb$ interactions. This distribution can be only obtained by on-line or off-line discrimination. The NA44 design emphasized triggering on central events with high rates, with no attention paid to obtaining unbiased $G(x)$ in a broad range of $x$. This has been discussed at length in Section 4.2.
• $P(x)$ - ``valid beam'' ($VB$) sample. It consists of two fractions:
  1. minimum bias sample of interactions. Their fraction in the sample equals the interaction probability $\alpha \ll 1$ (Section 3.3).
  2. non-interactions - the predominant majority, fraction $1-\alpha$.

For definiteness, let's talk about one certain direction mode and one certain scale of PSC, and use notation ${\mathcal{P}}_F$, ${\mathcal{P}}_G$, ${\mathcal{P}}_P$ for the PSCs in the respective trigger modes. It turns out, that under reasonable assumptions, for all multiplicity bins except the one which contains 0, the following formula can be justified:

$${\mathcal{P}}_{G,x} = {\mathcal{P}}_{P,x} - {\mathcal{P}}_{F,0}$$ (92)

The justification of this intuitive formula is given in Appendix B.

As is clear from the Appendix, this approach is not perfect because it ignores large amplitude events in the empty target sample. Such events, although rare, do occur there. Moreover, those events are often dominated by the correlated noise (already discussed in Subsection 6.7.1) with pronounced large scale texture features. In terms of multiplicity, these effects are localized not in the zero bin (between and -5 MeV and +5 MeV), but rather, spread over the range of total ionizations 10-40 MeV (counting only the $\delta$-free side of the detector). The method of correction is empty target background subtraction according to formula 6.39. The zero bin had to be extended to include the affected multiplicity range, as shown in Fig.7.1. The same zero bin was used in the physics and empty target runs.

Events with negative total amplitude get into bins with ``negative'' values of $\,dN/\,d\eta$. Such events happen in non-central trigger runs due to the fact that the low-amplitude behaviour of the detector is dominated by the noise which has inherent correlations of purely instrumental nature.