Create a workflow for using the ZDC SMDs as a local polarimeter by recreating the results from "Analysis of STAR ZDC SMD Data for Polarimetry" by M.B. Bitters and D.P.Grosnick. The data used is from pp 2004, runs 5115003, 5115004, 5115005, 5115007, and 5115008.

The ZDC detector consists of SMD modules on the West and the East end. Each side has 7 vertical (X) and 8 horizontal (Y) SMD slats. The following plots show the raw ADC counts for each slat.

Fig. 1 - Raw ADC counts East X	Fig. 2 - Raw ADC counts East Y
Fig. 3 - Raw ADC counts West X	Fig. 4 - Raw ADC counts West Y

Figure 5 shows all the raw ADC slat counts. Bins 1-7 correspond for the East X, 9-16 for East Y, 17-23 West X, and 25-32 for West Y. When determining the pedestal for each slat, the width of the gaussian fit was ~1 bin wide. The highest ADC count was used as the pedestal value.

Fig. 6 - Pedestal corrected ADC counts East X	Fig. 7 - Pedestal corrected ADC counts East Y
Fig. 8 - Pedestal corrected ADC counts West X	Fig. 9 - Pedestal corrected ADC counts West Y

Figure 10 shows all the pedestal corrected ADC slat counts. For gain correcting each slat, a power equation (Eq. 1) was fitted to the decay region for each slat. A power equation better described the decay region compared to an exponential equation at higher ADC values. Fit parameter P₀ is fixed to the pedestal count value for the slat. To maximize the fit range, the starting range position was varied from 1 to 30 bins after the pedestal value while the end range is static. The reduced chi-square value for the fit is placed on the starting range position. The plots below show the reduced chi-square values for each fit range. Slat 8 is left empty for East X and West X because it only has 7 slats.

Fig. 11 - Reduced chi-square for fit starting at bin for East X	Fig. 12 - Reduced chi-square for fit starting at bin for East Y
Fig. 13 - Reduced chi-square for fit starting at bin for West X	Fig. 14 - Reduced chi-square for fit starting at bin for West Y

Similar process was done to determine the end fit range.

Fig. 15 - Reduced chi-square for fit ending at bin for East X	Fig. 16 - Reduced chi-square for fit ending at bin for East Y
Fig. 17 - Reduced chi-square for fit ending at bin for West X	Fig. 18 - Reduced chi-square for fit ending at bin for West Y

Averaging the reduced chi-square value from all slats, the starting fit range condition was set so that each slat should start the fit range below a reduced chi-square value of 300. The reduced chi-square values for end fit range position was set to be the minimum value. The average reduced chi-square values for all slats will be used later.

Fig. 19 - Averaged reduced chi-square for fit starting at bin

Fig. 20 - Difference of averaged reduced chi-square from previous bin

Fig. 21 - Averaged reduced chi-square for fit ending at bin

The table below has the fit ranges used for each slat.

Slat Fit Ranges
Slat #	Start Range	End Range
1	4	58
2	3	69
3	4	63
4	7	56
5	3	44
6	3	54
7	3	62
8	0	0
9	3	38
10	3	43
11	4	46
12	3	46
13	3	38
14	3	48
15	6	61
16	3	48
17	3	77
18	4	94
19	3	91
20	3	83
21	3	60
22	3	90
23	3	82
24	0	0
25	3	75
26	3	61
27	5	65
28	3	61
29	3	56
30	6	77
31	4	76
32	3	62

Fitting parameter, P₂, varies between the slats. P₂ describes the decay rate seen on the ADC signals.

Fig. 22 - Gain Fit East X	Fig. 23 - Gain Fit East Y
Fig. 24 - Gain Fit West X	Fig. 25 - Gain Fit West Y

To normalize the gains, the slower decaying slat was set as reference (West X2).

Fig. 26 - Gain Correction East X	Fig. 27 - Gain Correction East Y
Fig. 28 - Gain Correction West X	Fig. 29 - Gain Correction West Y

Figure 30 shows all the gain corrected ADC slat counts.

Gain corrected ADCs are assumed to behave similarly. Using Figures 19-21, the average fitting range for all slats is determined to be 6-54. The gain corrected ADCs are once again fitted using the averaged fit range. The fitting parameter, P₂, is much closer for each slat.

Fig. 31 - Gain fit for gain corrected East X	Fig. 32 - Gain fit for gain corrected East Y
Fig. 33 - Gain fit for gain corrected West X	Fig. 34 - Gain fit for gain corrected West Y

Using the procedure to determine the fitting range as described before, the average reduced chi-square value for the gain corrected ADCs is used in order to determine the threshold which an ADC signal is considered good.

Fig. 35 - Averaged reduce chi-square for start range on gain corrected ADCs

Fig. 36 - Difference of averaged reduce chi-square from previous bin

Fig. 37 - Averaged reduce chi-square for end range on gain corrected ADCs

Using Figures 35-37, the minimum ADC value for a good hit was chosen to be 10. Figure 38 shows the slats with good hits fitted for ADC range 10-87.

Fig. 38 - Threshold cut East X	Fig. 39 - Threshold cut East Y
Fig. 40 - Threshold cut West X	Fig. 41 - Threshold cut West Y

Figure 42 shows all the threshold cut ADC slat counts. The red line is the reference parameter value P_{2 ref} = 0.023931. Parameter₂ from gain corrected slats are closer together, giving the slats a more uniform behavior.

Fig. 43 - Slope fit parameter

Fig. 44 - Slope fit parameter after gain correction

Fig. 45 - Slope fit parameter after threshold

Figure 46 shows the total number of ADC counts per slat after pedestal correction. Gain correcting and placing a minimum ADC threshold cut to be considered a good hit help level the total counts per slats as shown on Figure 47.

Fig. 46 - Sum of pedestal corrected ADC counts for each slat

Fig. 47 - Sum of good ADC counts for each slat

The following figures show the number of events which had at least 1 vertical and 1 horizontal slat above threshold after gain correction for each bunch crossing on the East and West detector.

Fig. 48 - East events per bunch crossing

Fig. 49 - West events per bunch crossing

Bunch crossings events from polarized protons.

Fig. 50 - East events per polarized bunch crossing

Fig. 51 - West events per polarized bunch crossing

The plots below show the number of multiple particle hits above threshold a slat receives per event. This is done by counting the perpendicular slats with ADC values above threshold for slats above ADC threshold per event. The multiplicity plots contain empty bins because the slats cross multiple perpendicular slats and the combinations of certain multiplicity counts are therefore suppressed. An event could only have hit counts with multiples from 1-8. Looking at Figure 52, single count events per slat gave a large number of events with hit counts from 1-8. Events with 5 or 7 counts are smaller because its less likely to have 5 or 7 slats crossed with one perpendicular slat compared to 2 or 3 slats. Counts with 4, 6, 8, and 9 are larger than 5 and 7 because they have multiples of 2, 3, 4 which increase their overall counts. Prime numbers above 7 like event counts 11, 13, 17, 19 are nonexistent because they can't be combined with a single perpendicular slat. Events counts created with larger multiples are also suppressed because its more likely a large multiple slat count is crossed with a smaller perpendicular slat count.

Fig. 53 - East number particle hits per event

Fig. 54 - West number particle hits per event

Half of the events have 1-3 hits on both West and East end.

East Multiplicity
# of Hits	Events	Percent of Total Events	Cum. Percent of Total Events
1	159537	25.8	25.8
2	137718	22.3	48.1
3	26546	4.3	52.4
4	93565	15.1	67.5
5	374	0.1	67.6
6	82880	13.4	81.0
7	4	0.0	81.0
8	17790	2.9	83.9
9	39646	6.4	90.3
10	2572	0.4	90.7
12	31174	5.0	95.7
14	48	0.0	95.7
15	7251	1.2	96.9
16	8761	1.4	98.3
18	1137	0.2	98.5
20	5632	0.9	99.4
21	145	0.0	99.4
24	1267	0.2	99.6
25	1171	0.2	99.8
28	169	0.0	99.9
30	605	0.1	100.0
32	16	0.0	100.0
35	95	0.0	100.0
36	102	0.0	100.0
40	5	0.0	100.0
42	40	0.0	100.0
48	2	0.0	100.0
49	3	0.0	100.0

 

West Multiplicity
# of Hits	Events	Percent of Total Events	Cum. Percent of Total Events
1	136145	24.5	24.5
2	127701	23.0	47.5
3	23469	4.2	51.7
4	89835	16.2	67.9
5	301	0.1	67.9
6	76662	13.8	81.7
7	6	0.0	81.7
8	15117	2.7	84.4
9	36797	6.6	91.0
10	2019	0.4	91.4
12	27324	4.9	96.3
14	28	0.0	96.3
15	5378	1.0	97.3
16	7451	1.3	98.6
18	755	0.1	98.8
20	4380	0.8	99.6
21	98	0.0	99.6
24	883	0.2	99.7
25	852	0.2	99.9
28	102	0.0	99.9
30	379	0.1	100.0
32	10	0.0	100.0
35	61	0.0	100.0
36	67	0.0	100.0
40	3	0.0	100.0
42	21	0.0	100.0
48	1	0.0	100.0
49	3	0.0	100.0

Particles had to hit the following blue area in order to be considered for Left-Right asymmetry. Figures with the red hits were denied.

Fig. 55 - Accepted hits East Left/Right	Fig. 56 - Accepted hits West Left/Right
Fig. 57 - Denied hits East Left/Right	Fig. 58 - Denied hits West Left/Right

Particles had to hit the following blue area in order to be considered for Top-Bottom asymmetry. Figures with the red hits were denied.

Fig. 59 - Accepted hits East Top/Bottom	Fig. 60 - Accepted hits West Top/Bottom
Fig. 61 - Denied hits East Top/Bottom	Fig. 62 - Denied hits West Top/Bottom

Square root asymmetries results for luminosity, physics, and geometry for Left-Right and Top-Bottom. West Top-Bottom shows a stronger geometry asymmetry. Physics asymmetry can be seen for both East and West for Left-Right but not Top-Bottom.

	Asymmetries
	Luminosity	Geometry	Physics
East Left-Right	-0.09678 ± 0.00072	0.03004 ± 0.00073	0.01549 ± 0.00073
East Top-Bottom	-0.09677 ± 0.0008	0.07681 ± 0.0008	0.00123 ± 0.00081
West Left-Right	-0.09447 ± 0.00076	0.03826 ± 0.00077	0.0129 ± 0.00077
West Top-Bottom	-0.09359 ± 0.00086	0.13449 ± 0.00085	0.00586 ± 0.00087

Vertical single slat physics asymmetries show a noticeable asymmetry. Horizontal slats though they tend to zero, the West end slats show an incremental increase.

The following figures show the accepted particles for the East φ distribution asymmetries. Each color group describes a phi angle used.

Fig. 64 - Accepted hits East φ Distribution	Fig. 65 - Accepted hits East Group 1	Fig. 66 - Accepted hits East Group 2
Fig. 67 - Accepted hits East Group 3	Fig. 68 - Accepted hits East Group 4	Fig. 69 - Accepted hits East Group 5
Fig. 70 - Accepted hits East Group 6	Fig. 71 - Accepted hits East Group 7	Fig. 72 - Accepted hits East Group 8

The following figures show the accepted particles for the West φ distribution asymmetries. Each color group describes a phi angle used.

Fig. 73 - Accepted hits West φ Distribution	Fig. 74 - Accepted hits West Group 1	Fig. 75 - Accepted hits West Group 2
Fig. 76 - Accepted hits West Group 3	Fig. 77 - Accepted hits West Group 4	Fig. 78 - Accepted hits West Group 5
Fig. 79 - Accepted hits West Group 6	Fig. 80 - Accepted hits West Group 7	Fig. 81 - Accepted hits West Group 8

Using Equation 2, the plots were fitted to find parameter P₀. Parameter P₁ phase shifts the function which gives a better fit to the measured points because the mapping regions are an approximate φ angle and don't reside on the exact φ value.

Fig. 82 - East physics asymmetry for φ distribution

Fig. 83 - West physics asymmetry for φ distribution

Averaging out P₀ from East and West gives 0.02059 ± 0.0014 and using the beam polarization 0.26 ± 0.03 gives an analyzing power A_N = 0.079 ± 0.02 . The asymmetry values for the West end between 0.2 < φ < 1.25 are higher than the values from the East end. Figures 70, 71, 72 have more pronounced accepted counts on the left side than the right side which can be seen by just observing the plots.

 

Analyzed runs individually and in combinations to see if the shift seen on the West end can be isolated to a specific run. Run 5115003 was too small to have enough statistics when analyzed individually. There was no obvious run to remove or decrease the shift. Run 5115004 has a strange single slat physics asymmetry behavior which doesn't follow the other runs.

Fig. 84 - West physics asymmetry for φ distribution (Single Run)

Fig. 85 - West physics asymmetry for φ distribution (Combination Runs)

More detailed analysis results for single or combination runs.

Fig. 86 - Run 5115004	Fig. 87 - Run 5115005	Fig. 88 - Run 5115007
Fig. 89 - Run 5115008	Fig. 90 - Runs 5115003-5115005	Fig. 91 - Runs 5115003-5115007
Fig. 92 - Runs 5115003-5115005, 5115008	Fig. 93 - Runs 5115003, 5115005, 5115008	Fig. 94 - Runs 5115003-5115008

Half of the events have 1-3 hits. Single hit events have a better correlation to the initial neutral particle from the collision. This might remove the shift seen on the West end because the correlation between the secondary particles detected in multiple hit events is not taken into account.

More detailed analysis results for varying Hit/Event configurations. Physics φ distribution asymmetry values for 1-2 Hits/Events are similar to single hit events. The West end shift couldn't be isolated using this method.

Fig. 96 - Run 5115003-5115008 (1 Hit/Event)	Fig. 97 - Run 5115003-5115008 (2-56 Hits/Event)
Fig. 98 - Run 5115003-5115008 (1-2 Hits/Event)	Fig. 99 - Run 5115003-5115008 (1-3 Hits/Event)