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Correction for the consequences of radiation damage in Si

Radiation damage in Si detectors is known  [42] to result in

• an increase in dark current due to damage to the bulk Si
• a decrease in the collected charge signal due to charge trapping

Both effects make discrimination of particle track signals against the noise and dark current background more difficult. Technically, the problem shows up in the number of hits with signal above the threshold, not associated with particle tracks. These ``fake hits'' affect the multiplicity measurement. The effect calls for evaluation and correction. The correction algorithm (to be described below) deconvolutes the real distribution from the real+noise by sampling events according to the measured distributions of real+noise and noise, and consists of the following steps:

1. In the valid beam run, a sample of ``pure noise'' Si events was selected by cuts on all T0 tubes, combined with a 2D cut on the Si amplitude sum vs Si number of hits, using both sides of the Si detector and vetoing Si events with large total amplitude (but not with large number of hits !). Thus the distribution of the number of hit Si pads (delta-free part only) in these ``pure noise'' events was sampled. It is an asymmetric distribution with maximum around 10 and a mean between 20 and 40, depending on the quality of the detector's performance. (An example can be found in Fig. 4.6, the middle panel, ``Noise Si hits''.) The asymmetry points to a ``collective'' nature of the effect responsible for the fake hits - in accordance with the features of the physics mechanism just discussed.

2. Knowing the ``pure noise'' distribution, and the ``real+noise'' distribution of the Si hits in the central trigger run, it is possible to reconstruct the ``real'' distribution, because the two known pieces of information determine it uniquely. The following ``random purification'' algorithm has been constructed:
   • make up a random number distributed according to the distribution of the number of fake hits. This random number will be called $NFAKE$. Randomly pick $NFAKE$ Si channels.

   • make up a random number distributed according to the distribution of ``real+fake'' hits. This random number will be called $NTOTAL$.

   • make up an integer random number uniformly distributed between 0 and the maximum number of working channels. This random number will be called $NPURE$. Randomly pick $NPURE$ channels.

   • Count channel numbers occupied by $NPURE$ OR $NFAKE$.

   • Compare it with $NTOTAL$.

   • If it equals $NTOTAL$, histogram $NPURE$.

   • Repeat the steps until sufficient statistics is obtained in the histogram of $NPURE$. By construction, the histogram so obtained represents the needed ``rectified'' distribution (with a caveat discussed below).

3. Transform the ``real+noise'' and ``real'' distributions into the Poissonian variable $\mu$ which characterizes multiplicity of tracks. Derive the correction factor, $\mu (real)/\mu(real+noise)$

   Figure 4.6: Illustration of the Si radiation damage correction algorithm in case of the 4GeV negative low angle setting, 4% centrality sample. From left to right, from top to bottom: SI ADC sum vs number of hits for the left and right parts of the detector in the valid beam run, with the non-interaction cut shown by the solid line; non-interaction cut on T0 signals in the valid beam run ; distribution of the number of Si noise hits in the valid beam run with the non-interaction cut; the ``dirty'' number of charged tracks in the physics run; the ``purified'' number of charged tracks. See text of Subsection  4.2.9

   

4. Apply the correction directly to $\,dN/\,dy$

This ends the description of the correction method. Application of the method is illustrated by Fig.  4.6.

Table 4.4 gives the summary of corrections for all settings used in the analysis. The error bars on the correction factors were derived from the scatter of correction factors determined in 3 independent ``random purification'' runs, 1000 successful events each.

Table: Radiation damage correction. The factors listed here are applied directly to $\,dN/\,dy$.

Setting	4% centr.	10% centr	Setting	4% centr.	10% centr
4k-low	0.91 $\pm$ 0.013	0.902 $\pm$ 0.011	4k+low	0.873 $\pm$ 0.002	0.864 $\pm$ 0.007
4k-high	0.943 $\pm$ 0.004	0.951 $\pm$ 0.011	4k+high	0.935 $\pm$ 0.008	0.931 $\pm$ 0.010
4$\pi^-$low	0.92 $\pm$ 0.01	0.921 $\pm$ 0.007	4$\pi^+$low	0.89 $\pm$ 0.02	0.876 $\pm$ 0.005
4$\pi^-$high	0.947 $\pm$ 0.002	0.934 $\pm$ 0.003	4$\pi^+$high	0.937 $\pm$ 0.01	0.934 $\pm$ 0.003
8k-low	0.955 $\pm$ 0.004	0.955 $\pm$ 0.002	8k+low	0.879 $\pm$ 0.013	0.879 $\pm$ 0.010
8k-high	0.930 $\pm$ 0.003	0.926 $\pm$ 0.006	8k+high	0.938 $\pm$ 0.005	0.947 $\pm$ 0.007
8$\pi^-$low	0.956 $\pm$ 0.008	0.948 $\pm$ 0.009	8$\pi^+$low	0.88 $\pm$ 0.016	0.872 $\pm$ 0.009
8$\pi^-$high	0.939 $\pm$ 0.008	0.9333 $\pm$ 0.0004	8$\pi^+$high	0.930 $\pm$ 0.013	0.931 $\pm$ 0.007

Conclusions from the table:

1. Si in the the high angle setting performs better. This is natural, given the radiation damage mechanism of the problem, and the fact that the high angle setting was used earlier in the run.
2. As a general trend, the larger multiplicity bin (4%) needs less of a correction. This is because more real multiplicity leaves less room for the fake hits to contaminate the picture.