Tests Performed

• HL structure. The first step is a test if the z-rescaling weak mode appears with the high level structure alignment. After the alignment procedure some shifts were observed but with not huge effect. Figure 7.7 shows the comparison between the initial geometry and the geometry obtained after the high level alignment procedure ([30]).

(a) (b) (c)

Figure 7.7: The alignment procedure control plot of the ∆z −z distribution with only position parameters included (a), rotation only (b) and both position and rotation parameters included (c), performed for the high level tracker structure.

This test shows small differences (up to 15µm) between the initial geometry and the geometry obtained after the high level alignment procedure, but they do not have a dependence from

7.4. Z-RESCALING WEAK MODE 87 the z-axis. This effect can be explained by general shifts of the tracker detector parts. It has to be studied carefully, but obviously it is not related to the z-rescaling weak mode and will not be considered in this study. The important point here is that this issue mainly comes from the alignment with position coordinates only (Fig. 7.7(a)) while for the rotation parameters alignment (Fig. 7.7(b)) it does not appear and is slightly reduced in the combination of the position and rotation alignment parameters (Fig. 7.7(c)). The minimum bias sample has a P_T cut on tracks which is greater than 1 GeV. All other tests are carried out with the module level alignment.

• Fixed End Caps. The test was performed with fixed End Caps for TID, TEC, with module level alignment.

From figure 7.8 one can see that the z-rescaling effect disappeared but instead some spread of TOB and other detector part modules is present. In this test the end caps for TID and TEC were fixed which means that the corresponding high level parameters are not involved in the alignment procedure and are obtained as relative values to the TPB part.

(a) (b) (c)

Figure 7.8: The alignment procedure with fixed End Caps for the TID, TEC parts. The minimum bias data sample is shown in the plot (a), cosmic data only in (b) and both minimum bias and cosmic data samples are shown for the plot (c).

One can see that for all distributions (Fig. 7.8), the TEC and TID parts are not shifted. In the case with TID some distribution is still present since module shifts are allowed if the average level corresponds to the fixed parameters. One can see that a source of other tracker part shifts is caused by the impact of the cosmic data (Fig. 7.8(b)). But those shifts are relatively small (up to 10 µm) and are not considered in this study. This test shows that the z-rescaling effect could be particularly related to the TID and TEC End Caps.

• P_T dependencies. To collect more information an analysis withP_T dependencies for the minimum bias data sample was performed. This test shows a reduction of the z-rescaling effect if the P_T cut is increased (Fig. 7.9 ).

Figure 7.10 shows that the reduction of the effect is related to the reduction on the number of tracks which are registered in the End Caps. In this case it is not clear if the P_T cut has a real impact to the z-rescaling weak mode. Figure 7.10 shows the occupancy of TEC for the P_T

(a) (b)

(c) (d)

Figure 7.9: The alignment procedure with differentP_T cuts. The minimum bias data sample with standard cut on tracks PT >1 GeV (a), minimum bias data with PT >4 GeV (b) , minimum bias data with P_T cut > 7 GeV (c) and both minimum bias and cosmic data samples are used for the alignment plot (d) with cut on tracks transverse momentum P_T >7 GeV.

(a) (b)

Figure 7.10: Figure shows occupancy of TEC for the two cuts on track P_T : 1 and 7 GeV. Both distributions show dependence r fromz coordinates, where r is quadratic function ofx andy coordi-nates. Both plots show the number of tracks, as rectangles with different size, for mimum bias tracks which were detected by TEC and with cut on P_T >1 GeV (left, (a)) and P_T >1 GeV (right, (b)).

Plots were obtained by [128].

cut on 1 and 7 GeV [128]. Since minimum bias data samples consist of low P_T tracks one can observe a significant reduction of the number of tracks.

• Cosmics as “real data”. For the cosmic data the z-rescaling effect is not observed. In this test we tried to simulate “collision” like data from the cosmic data sample by playing

7.4. Z-RESCALING WEAK MODE 89 with the dZ cut. The idea of this simulation is an observation of the z-rescaling effect with the cosmic data as well.

Cosmic muon tracks are different from the collision tracks because of their straight line tracks which go through the detector and cross it in any random coordinate . In this test the z-coordinate of such tracks is restricted to be close to the interaction point in the sense of the z-axis. This cut will significantly reduce the cosmic data statistics but on other hand it will be a rough simulation of collision data. The cut parameter which was applied to the cosmic muon

(a) (b) (c)

Figure 7.11: This figure shows ∆z−zdistributions in case with no cuts (a), with cut 0.5m (b) and cut 1 m (c) on the z-coordinate of cosmic tracks.

track z-coordinate in this test was chosen as 1 m (Fig. 7.11(c)) and 0.5 (Fig. 7.11(b)). In such an approximation all tracks which have the z-coordinate less than the chosen cut parameter are considered as collision tracks which go in opposite directions. Of course, this is a very rough approximation, but in such a test it can allow us to get more information and helps to understand the z-rescaling effect a bit better. This test shows that with such simulation one does not observe z-rescaling effect by using the cosmic data sample. An important point is that unlike cosmic data we observe this effect for minimum bias. And it is an important part of the work to find out why this effect does not appear for both data samples. Cosmic tracks have special characteristics which make them different from the minimum bias tracks. Cosmic tracks have a higherP_T spectrum, and due to their nature they break the cylindrical symmetry of the detector. With this test collision like tracks were selected and no z-rescaling effect was observed (Fig. 7.11). This could mean that some special characteristics of the cosmic data tracks are indeed creating such a restriction that does not allow z-rescaling to be present. A good start point for future studies could be a careful comparison of all alignment steps which are applied to the cosmic and collision data samples.

• TEC/TID disk constraints. This test was performed to show if it is possible to reduce the z-rescaling effect with introducing an additional alignment constraints for TEC and TID disks. Constraints were prepared as follows: the first disk (which is closest to the interaction point) is allowed to make a movements during the alignment procedure. The remaining disks are moving in the same directions as the first one. The constraints are implemented independly for the “-z” and “+z” directions (Fig. 7.12). In this test an isolated muon sample was used.

(a) (b)

Figure 7.12: Schematicall explanation of how the TID and TEC end cap disks were constrained.

Figure 7.12 shows a TID sketch (a) that has 3 end cap disks in which 2 of them (closest to the interaction point) are allowed to make a movement during the alignment procedure. Other disks are moving in the same direction as the first one from each z-direction. This constraint is separated for the positive and negative direction of the z-axis. At the same time, the same constraint was applied to the TEC disks (Fig. 7.12(b)) with the difference that it has 18 disks instead of 6 for TID. Thus, at the end of the alignment procedure about 20 constraints were applied to the end caps (Fig. 7.13).

(a) (b)

Figure 7.13: The dz−z distribution of the alignment procedure without (a) and with (b) the TID and TEC end cap disks constraints.

Figure 7.13(b) shows the result of the alignment procedure for the isolated muon data sample. Here it has to be mentioned that for the isolated muons data sample the same z-rescaling effect was observed (Fig. 7.13(a)). One can see that the constraints eliminated the z-rescaling effect. A significant spread of the TEC modules is still present. This might be eliminated by adding the cosmic data as was shown in one of the tests above. This test shows again that the z-rescaling effect directly depends from the TEC and TID end caps alignment parameters. For a future study one can start from this idea and make a careful investigation how these parameters are fitted with the alignment procedure and try to find out what is going in the wrong direction.

Other tests were performed and do not make a huge effect on the z-rescaling issue [127].

They are : a “Skyline/Bandwidth option test”, which test a few algorithms of the error

7.4. Z-RESCALING WEAK MODE 91