The determination of the RCAL position is somewhat more difficult as it is not possible to use the module cracks due the non-projectiveness of the RCAL. As a result only a few of the cracks are visible. In addition, those which are visible are not very pronounced, leading to large uncertainties in the calculation of the calorimeter position. Therefore a different approach has to be chosen where the most obvious one uses the calorimeter position together with the position information from a CTD track associated with the electron. However, this approach has the disadvantage that it relies on the calorimeter-position reconstruction which is heavily biased as we shall see later. This method also implies, due to the limited CTD acceptance, that only electrons hitting the RCAL at a radius r 70 cm can be used for this analysis, resulting in limited statistics. Here, the CTD acceptance is defined by tracks that pass at least 4 superlayers of the CTD, corresponding to a minimum radius of 45 cm at the CTD end-plate. Extrapolating the line going through this point and the nominal IP up to the electron-position reconstruction plane of the RCAL atz=−153.03 cm, yields the mentioned minimum radius of r ≈70 cm.
Figures A.3 a–c, already depicted in Fig. 4.3, show the mean difference between calorimeter and track position in x (y) as a function of thex (y) position in the calorimeter, where in the case of y, the RCAL is split into its left and right half. Module 12 is always excluded as it can be moved iny independently from the rest of the RCAL. All plots show strong fluctuations in the
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xcal [cm]
xcal− xtrk[cm]
RCAL total
Module 12 always excluded
ycal [cm]
ycal− ytrk[cm]
RCAL left half
Module 12 always excluded
ycal [cm]
ycal− ytrk[cm]
RCAL right half
Module 12 always excluded
a)
b)
c)
Data Monte Carlo
Figure A.3: (a) Difference in x between calorimeter position xcal and track position xtrk as a function of xcal. (b) Difference in y between calorimeter position ycal and track position ytrk as a function of ycal for left RCAL half. (c) Difference in y between calorimeter position ycal and track position ytrk as a function of ycal for right RCAL half. Dark points are data and light points are MC. The vertical lines indicate the cell boundaries. The thickness of the lines connecting the points represent the error on the measured differences.
differences between the calorimeter and track positions, which are correlated with the physical structure of the calorimeter and appear both in MC and data. In the x direction (Fig. A.3 a) this fluctuation has a periodicity of 20 cm, the width of a module, and an amplitude of up to 2 cm. In y (Fig. A.3 b and c) the fluctuations have a periodicity of only 10 cm, reflecting the subdivision of the EMC section within a tower into two cells. Due to the lack of a flat area which could be used as an unbiased position information, the calorimeter position is not suitable for aligning the RCAL.
As an alternative the position information of the RHES is used. This has the advantage that, in contrast to the calorimeter, the signals are already produced in a plane, which simplifies the spatial position reconstruction. The RHES plane runs parallel to the RCAL surface and
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0 20 40 60 80 100 120 140 160
xHES [cm]
yHES− ytrk[cm]
RHES left half
xHES [cm] yHES− ytrk[cm]
RHES right half a)
b)
Data Monte Carlo
Module 12 always excluded
Figure A.4: Difference in y between HES position yHES and track position ytrk as a function of xHES for left (a) and right (b) RHES half. Common offsets of skis in individual modules show displacements in y. Dark points are data and light points are MC.
is located 7.1 cm inside the RCAL. The x-y position for a track in this plane is obtained by a linear extrapolation of the track from the calorimeter reconstruction plane to the RHES plane (∆z= 2.0 cm). The following parameters are determined for each half of the RHES: shift iny for the skis in each module, rotation about thezaxis, shift inzand shift inx. As both the upper and the lower half of module 12 can be moved independently relative to the corresponding RCAL half, additional shifts inxandyrelative to the corresponding RCAL half have been determined.
Figure A.4 shows the difference between HES and track position in y as a function ofx for the left (a) and right (b) RHES half. The dashed vertical lines indicate the module boundaries. This kind of plot is supposed to show shifts inyof the skis in one module. These common shifts are possible as the skis of a module are inserted from the top of the calorimeter independently from the other modules. For data the different module offsets are clearly visible in the plots, whereas the MC points have a rather flat distribution. The offsets for data are obtained by fitting a constant for each module. The resulting values are listed in Fig. A.13 a.
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yHES [cm]
x HES− x trk[cm]
DATA: δφ = (2.4±0.1) mrad MC: δφ = (0.7±0.06) mrad
RHES left half
yHES [cm]
x HES− x trk[cm]
DATA: δφ = (0.7±0.12) mrad MC: δφ = (0.7±0.06) mrad
RHES right half a)
b)
Data Monte Carlo
Module 12 always excluded
Figure A.5: Difference in x between HES position xHES and track position xtrk as a function ofyHES for left (a) and right (b) RHES half. Slopes in the distributions indicate a rotation about the z axis. Dark points are data and light points are MC.
Figure A.5 displays the difference inx between RHES and track position as a function of y for the left (a) and right (b) RHES half. To first order a rotation about thezaxis results in a slope in these diagrams. As can be seen from the plots all slopes correspond to rotations below 1 mrad, except for that of the left RHES half in data which yields a rotation of 2.4 mrad. Note that the errors given are only statistical, whereas the final errors will also contain systematic errors, which will be discussed in the next section. The fact that even the MC has a non vanishing slope suggests that the reconstruction method has a slight bias which would imply that for data the right RHES half is not rotated about the z axis. Therefore, the final shifts/rotations for data will be calculated relative to those of the MC.
The following plots already contain the previous corrections for data, i.e. a rotation about thez axis by 1.7 mrad for the left RHES half and they shifts of the individual modules. No rotation for the right half is applied as the difference between data and MC is 0.0 mrad.
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y
HES[ cm ] y
HES− y
trk[ cm ]
DATA: δz = (1.8±0.12) mm MC: δz = (-0.4±0.08) mm
RHES left half
y
HES[ cm ] y
HES− y
trk[ cm ]
DATA: δz = (-0.8±0.14) mm MC: δz = (-0.5±0.08) mm
RHES right half a)
b)
Data Monte Carlo
Module 12 always excluded
Figure A.6: Difference in y between HES position yHES and track position ytrk as a function ofyHES for left (a) and right (b) RHES half. Slopes in the distributions indicate a shift in z. Dark points are data and light points are MC.
Figure A.6 shows the difference iny between HES and track position as a function ofy. A slope in these plots indicates a shift in z. All shifts are below 1 mm except for the data of the left RHES half, where the fit yields az shift of 1.8 mm away from the IP. The fit was restricted to
±100 cm as the data shows a non-linear behavior in the outer parts of the calorimeter. This feature is not yet understood and needs further investigations.
For the following plotsz shifts of −2.2 mm for the left and 0.3 mm for the right RHES half in data are included.
Figure A.7 a displays the difference inx as a function ofx indicating shifts of the RHES halves in x. As in the case of the calorimeter (Fig. A.3) the structure of the HES is clearly visible.
However, in contrast to the RCAL the RHES has a flat region between two module gaps which
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xHES [cm]
x HES− x trk[cm]
RHES total
xHES [cm]
x HES− x trk[cm]
DATA (left half): δx = (-1.3±0.06) mm DATA (right half): δx = (-1.1±0.07) mm MC (left half): δx = (0.3±0.04) mm MC (right half): δx = (-0.2±0.04) mm
RHES total a)
b)
Data Monte Carlo
Module 12 always excluded
Figure A.7: Difference in x between HES position xHES and track position xtrk as a function of xHES. (a) shows all x positions whereas in (b) the mean value for each module is shown, obtained from fitting a constant to the central region of the corresponding module. Offsets are caused by shifts inx. The left and right halves were fitted separately.
Dark points are data and light points are MC. The thickness of the lines connecting the points repesents the error on the measured differences.
can be used to fit a constant and take the offset as thexposition in this module (the fit excludes 5 cm to either edge of the module). The results of these fits are displayed in Fig. A.7 b. The MC distribution is flat and has offsets less than 0.5 mm, whereas the data show offsets of more than 1 mm for both RHES halves. The offset values are determined by fitting a constant to the five inner modules of each RHES half. The offsets in data are 1.3 mm (left half) and 1.1 mm (right half) which leads to corrections in x for the data of 1.6 mm and 0.9 mm, respectively.
Figures A.8–A.11 show the previous plots after applying all corrections to the data. Ignoring the non-linear behavior in the outer regions of Fig. A.10, all data distributions agree very well with those of the MC.
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x
HES[ cm ] y
HES− y
trk[ cm ]
RHES left half
x
HES[ cm ] y
HES− y
trk[ cm ]
RHES right half a)
b)
Data Monte Carlo
Module 12 always excluded
Figure A.8: Difference in x between HES position xHES and track position xtrk as a function of yHES for left (a) and right (b) RHES half after all corrections. Dark points are data and light points are MC.
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y
HES[ cm ] x
HES− x
trk[ cm ]
DATA: δφ = (0.6±0.1) mrad MC: δφ = (0.7±0.06) mrad
RHES left half
y
HES[ cm ] x
HES− x
trk[ cm ]
DATA: δφ = (0.7±0.11) mrad MC: δφ = (0.7±0.06) mrad
RHES right half a)
b)
Data Monte Carlo
Module 12 always excluded
Figure A.9: Difference in y between HES position yHES and track position ytrk as a function of xHES for left (a) and right (b) RHES half after all corrections. Dark points are data and light points are MC.
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y
HES[ cm ] y
HES− y
trk[ cm ]
DATA: δz = (-0.3±0.12) mm MC: δz = (-0.4±0.08) mm
RHES left half
y
HES[ cm ] y
HES− y
trk[ cm ]
DATA: δz = (-0.4±0.14) mm MC: δz = (-0.5±0.08) mm
RHES right half a)
b)
Data Monte Carlo
Module 12 always excluded
Figure A.10: Difference in y between HES position yHES and track position ytrk as a function of yHES for left (a) and right (b) RHES half after all corrections. Dark points are data and light points are MC.
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x
HES[ cm ] x
HES− x
trk[ cm ]
RHES total
x
HES[ cm ] x
HES− x
trk[ cm ]
DATA (left half): δx = (0.2±0.06) mm DATA (right half): δx = (-0.2±0.07) mm MC (left half): δx = (0.3±0.04) mm MC (right half): δx = (-0.2±0.04) mm
RHES total a)
b)
Data Monte Carlo
Module 12 always excluded
Figure A.11: Difference in x between HES position xHES and track position xtrk as a function ofxHES after all corrections. (a) shows all x positions whereas in (b) the mean value for each module is shown, which was obtained from fitting a constant to the central region of the corresponding module. Dark points are data and light points are MC.
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number of events
Data: δx = (2.4±0.17) mm MC: δx = (0.6±0.13) mm
Data: δy = (1.8±0.29) mm MC: δy = (-0.3±0.21) mm
RHES Module 12 upper half
xHES - xtrk at HES
number of events
Data: δx = (-2.6±0.17) mm MC: δx = (-1±0.14) mm
yHES - ytrk at HES
Data: δy = (3.5±0.25) mm MC: δy = (0.3±0.23) mm
RHES Module 12 lower half a)
b)
c)
d)
Data Monte Carlo
Figure A.12: Difference inx andy between HES and track position for RCAL module 12 for upper half (a,b) and lower half (c,d). Data and MC are not normalized to each other.
Both halves of module 12 can be moved inywith respect to the RCAL half they are attached to.
Therefore independent alignment studies inxand yfor these two module halves are performed.
As the number of events is much lower than in the previous studies, the difference between HES and track position is plotted as a histogram. In Fig. A.12 the upper and lower two plots show δx and δy histograms for the upper and lower half of module 12, respectively. As neither MC nor data events are weighted the histograms are not normalized to each other. All shifts for MC are below 1 mm, whereas for data they range from 1.8 mm (upper left plot) to 3.5 mm (lower right plot). Astonishingly enough, for data the fits suggest a shift in x of over 2 mm towards the corresponding RCAL half. The fact that these shifts are also present in MC, though below 1 mm, indicates that the reconstruction method is biased. As a movement of a module by more than 1 mm towards the RCAL half it is attached to seems mechanically impossible, these shifts are ignored. As a result from this study, the upper (lower) half of module 12 is shifted down by 2.1 mm (3.2 mm) in data.
left RCAL half δx (1.6±0.2) mm δz (−2.2±0.4) mm δφ (1.7±0.9) mrad
right RCAL half δx (0.9±0.3) mm δz (0.3±0.7) mm δφ (0.0±0.8) mrad
Table A.1: Table with shifts and rotations for both RCAL halves, where δφ is the rotation about thez axis.