Beamtime test with PROTO60
2.3 Analysis
2.3.6 Position resolution
Energy / MeV
1000 1500 2000 2500 3000
/ % Eσ
2.4 2.5 2.6 2.7 2.8 2.9 3 3.1
Figure 2.29: Energy resolution for a matrix of6×6crystals with a summation thresh-old1.6 MeVand data from run1. Fit function with reference to Eq. 2.25.
to be strongly dependent on the number of rings. Additionally, the energy resolution for different shaping parameter values of M and L are compared (see Fig. 2.31).
Finally, the energy resolutions for the two tagger configurations are compared in Fig. 2.32. Here, the energy resolution obtained for energies below around1.5GeV are similar, but differ significantly at energies above2 GeVdepending on the tagging version.
Energy / MeV
1000 1500 2000 2500 3000
/ % Eσ
2.6 2.8 3 3.2 3.4
Figure 2.30: Energy resolution for a matrix of3×3crystals. Data from run1 with a summation threshold of1.6 MeV.
low intensity of the beam. Further information about the cluster finding procedure is given by Ferguson [49] and about the bump splitting in thePANDAEMC technical design report [30].
A photon is completely described with a four-vector. For the four-vector not only energy information but also the momentum component is needed. The spatial reso-lution is basically given by the granularity of the detector (σx/y = 1/√
12). It can be improved significantly below the size of the individual modules with many dif-ferent methods. All methods use the observed division of energy among the crystals to estimate the impact position (xpos, ypos) depending on the Molière radiusRM of the individual modules. In case of the PROTO60 with crystals of a diameter compa-rable to RM, most of the energy is deposited in the central crystal, but some of the energy escapes from the central crystal. Due to the narrow distribution in transverse dimensions, for an improved position resolution an extra weight is associated to the energies that are deposited in the outer crystals. This method is described in the next paragraph. The method is also applied for positions when the beam was not directed
Energy / GeV
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
/ % Eσ
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
Figure 2.31: Energy resolution for the shaping parametersM = 440 ns,L = 220 ns (red) compared with M = 560ns, L = 140 ns(green) and withM = 400 ns, L = 80 ns(blue). Data from run1 with a summation threshold of1.6 MeV.
at the center of a crystal. These positions were shown in Fig. 2.22.
Impact position for the weighted mean
Various algorithm developed by Brabson [48] have been considered to determine the impact position(xpos, ypos)of a photon initiating an electromagnetic shower within the PWO-II array. Each of these methods is based on the weighted mean
xc= PN
J wJ(EJ)·xJ PN
J wJ(EJ) . (2.26)
Here,xcis the calculated x-position of where the photon hits the detector. The same formula holds for the y-position. The sum is carried out over all the crystals within an array. The weight,wJ(EJ), is a function of the energy of the Jth crystal. In this
Energy / GeV
0.5 1 1.5 2 2.5 3
/ % Eσ
2 2.2 2.4 2.6 2.8 3 3.2 3.4
Figure 2.32: Energy resolution for a matrix of6×6crystals with tagger configuration
"three regions" (red) compared with "8 energies" (green). Data from run1 with a summation threshold of1.6 MeV.
thesis only the well established logarithmic weighting function wJ(EJ) = Max
0, a0+ ln EJ Etot
, (2.27)
is considered whereEtotis the total energy in all crystals anda0an energy dependent factor. The PANDA EMC technical design report states that a0 varies from2.1for low energies to3.6for high energies [30].
Results on the position resolution
For the analysis of the beamtime test in Bonn the energy dependent factor a0 = 4.4 was chosen. The factor was optimized for the energy range. A still gaussian dis-tribution was required at low energies. The reconstructed impact positions with a logarithmic weighting function (see Eq. 2.27) for run1 are shown in Fig. 2.33 for 8 different photon energies. The beamspot has been reconstructed in Fig. 2.34. The actual beamsize ofσ ≈ 5 mmhas been measured with a photocamera. The position resolution is obtained by fitting a Gaussian to the distribution of the reconstructed
XPosLog01 Entries 131502 Mean 11.01 RMS 4.518
Pos / mm
-100 -50 0 50 100
Counts
0 2000 4000 6000 8000 10000
XPosLog01 Entries 131502 Mean 11.01 RMS 4.518 XPosLog01
XPosLog02 Entries 72439 Mean 10.95 RMS 4.332
Pos / mm
-100 -50 0 50 100
Counts
0 1000 2000 3000 4000 5000 6000
XPosLog02 Entries 72439 Mean 10.95 RMS 4.332 XPosLog02
XPosLog03 Entries 45590 Mean 10.92 RMS 4.176
Pos / mm
-100 -50 0 50 100
Counts
0 500 1000 1500 2000 2500 3000 3500 4000
XPosLog03 Entries 45590 Mean 10.92 RMS 4.176 XPosLog03
XPosLog04 Entries 26044 Mean 10.85 RMS 4.108
Pos / mm
-100 -50 0 50 100
Counts
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
2400 XPosLog04
Entries 26044 Mean 10.85 RMS 4.108 XPosLog04
XPosLog05 Entries 12694 Mean 10.87 RMS 4.015
Pos / mm
-100 -50 0 50 100
Counts
0 200 400 600 800 1000 1200
XPosLog05 Entries 12694 Mean 10.87 RMS 4.015 XPosLog05
XPosLog06 Entries 8372 Mean 10.89 RMS 4.003
Pos / mm
-100 -50 0 50 100
Counts
0 100 200 300 400 500 600 700
800 XPosLog06
Entries 8372 Mean 10.89 RMS 4.003 XPosLog06
XPosLog07 Entries 17711 Mean 10.84 RMS 3.961
Pos / mm
-100 -50 0 50 100
Counts
0 200 400 600 800 1000 1200 1400 1600
XPosLog07 Entries 17711 Mean 10.84 RMS 3.961 XPosLog07
XPosLog08 Entries 11299 Mean 10.75 RMS 3.893
Pos / mm
-100 -50 0 50 100
Counts
0 200 400 600 800 1000
XPosLog08 Entries 11299 Mean 10.75 RMS 3.893 XPosLog08
Figure 2.33: Reconstructed impact position in x-direction with a logarithmic weight-ing function for run1.
impact position. Then, the resolution is given by the standard deviation of the Gaus-sian. One example can be seen in Fig. 2.35. The position resolution for impinging the center of the crystal surface (run1) for x- and y-direction is depicted in Fig. 2.36.
For an energy of1 GeV a position resolution of4.8 mmin x-direction and4.1 mm in y-direction was obtained.
The method was applied as well for positions when the beam was not directed at the center of a crystal surface. In particular, the obtained position resolutions for the beam moved vertically (see Fig. 2.37) and horizontally (see Fig. 2.38). Addition-aly, the position resolution for the beam aimed at center of four crystals is shown in Fig. 2.39. The obtained position resolutions are shown in Tab. 2.5.
Position Resolution x inmm Resolution y inmm
2 4.8 3.2
9 3.8 4.2
13 3.9 3.4
Table 2.5: Position resolution for various impact positions at1 GeV.
Reconstructed x position / mm
-50 -40 -30 -20 -10 0 10 20 30 40 50
Reconstructed y position / mm
-50 -40 -30 -20 -10 0 10 20 30 40 50
Entries 12694 Mean x 10.87 Mean y -9.76 RMS x 4.023 RMS y 3.499
0 20 40 60 80 100 120 140 Entries 12694
Mean x 10.87 Mean y -9.76 RMS x 4.023 RMS y 3.499
Figure 2.34: Reconstructed beamspot with a logarithmic weighting function for run1.
For a beam energy of1 GeVthe position resolution improves in all cases compared to the beam aimed in the center of the crystal. For higher photon energies the fluc-tuations in position resolution get very strong since statistics of collected events is very low. It is obvious that in all cases except Position 9 the position resolution in y-direction is significantly better.
XPosLog05 Entries 12694 Mean 10.87 RMS 4.023
Reconstructed x position / mm
-10 0 10 20 30
Counts
0 200 400 600 800 1000 1200
XPosLog05 Entries 12694 Mean 10.87 RMS 4.023
Figure 2.35: Reconstructed impact position in x-direction with a logarithmic weight-ing function for run1 for one energy. Fitted with a Gaussian.
Energy / MeV
1000 1500 2000 2500 3000
/ mmxσ
4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
(a)
Energy / MeV
1000 1500 2000 2500 3000
/ mmyσ
3 3.2 3.4 3.6 3.8 4 4.2 4.4
(b)
Figure 2.36: Position resolution for run1 in x-direction (a) y-direction (b).
Energy / GeV
1 1.5 2 2.5 3
/ mmxσ
4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.8 4.85 4.9
(a)
Energy / GeV
1 1.5 2 2.5 3
/ mmyσ
2.4 2.6 2.8 3 3.2 3.4
(b)
Figure 2.37: Position resolution for run9 (corresponding to postion 2) in x-direction (a) y-direction (b).
Energy / GeV
1 1.5 2 2.5 3
/ mmxσ
3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1
(a)
Energy / GeV
1 1.5 2 2.5 3
/ mmyσ
3.6 3.7 3.8 3.9 4 4.1 4.2 4.3
(b)
Figure 2.38: Position resolution for run16 (corresponding to position 9) in x-direction (a) y-direction (b).
Energy / GeV
1 1.5 2 2.5 3
/ mmxσ
3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1
(a)
Energy / GeV
1 1.5 2 2.5 3
/ mmyσ
2.6 2.8 3 3.2 3.4 3.6
(b)
Figure 2.39: Position resolution for run20 (corresponding to position 13) in x-direction (a) y-x-direction (b).