LHCb-INT-216-36 August 19, 216 Impact of the Velo 2 half misalignment on physical quantities Matej Roguljić 1, Silvia Borghi 2, Lucia Grillo 2,3, Giulio Dujany 2. 1 CERN, Geneva, Switzerland 2 The University of Manchester, Manchester, United Kingdom 3 Milano Bicocca, Milan, Italy Abstract The impact of the misalignment of the Vertex Locator of the LHCb experiment on the physical quantities of the decay D + (D K π + )π + is studied in this note. Different misalignments of the 2 halves are applied to Monte Carlo data and the variations of the physical quantities with respect to the case without misalignment are evaluated. The results show the importance of the VELO 2 half alignment which can significantly affect the physics performance in the large misalignment case. A misalignment equal to the precision of the real-time alignment of the Vertex Locator is found to have a negligible effect on the studied physical quantities.
1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 1 Introduction The LHCb silicon strip VErtex LOcator (VELO) is composed of two halves, each half contains 21 modules and each module contains two semi-circular silicon strip sensors (R and φ sensors) [1]. The alignment is a key ingredient for all detectors for achieving the best possible physics performance. For example, Figure 1 shows the improvement of the impact parameter 1 resolution using different alignments. During data-taking, it is located 7 mm away from the beam, however, during the injection of the beam, the two halves of the VELO are retracted by 3 cm and once the beam is declared stable, the halves are centered around the beam by a mechanical system. The reproducibility of the position has been measured to be better than 1 µm [2]. This procedure can lead to a spatial misalignment of the VELO, usually within its accuracy. Since Run 2 of the LHC, the alignment of the LHCb detector is performed in real-time at the beginning of each fill, allowing the trigger to benefit from the final alignment. The goal of this study is to quantify the effect of the current accuracy of the VELO 2 half alignment procedure on the physical quantities. 1 Impact parameter (IP) of a particle is the distance between the primary vertex and the point of the particle track closest to the vertex. 1
16 17 18 19 2 21 22 The alignment of the VELO can be divided into 3 different categories: Sensor, Module and 2 half alignment. Sensor alignment is the one between the R and φ sensors on a module and is very stable. Module alignment is the relative spatial configuration of the 21 modules in each half and it results to be stable within the alignment accuracy. The last category is the alignment between the 2 VELO halves, that varies fill-by-fill, and is considered in this note. Figure 1: Impact parameter resolution as a function of the inverse transverse momentum. Improving the alignment of the VELO subdetector improves the resolution of the impact parameter. 23 24 25 26 27 28 29 3 This study is performed on the Monte Carlo data sample of D + (D K π + )π + decay (and its charge conjugate), with and without misalignment. Figure 2 shows its topology. This decay is chosen because it is a typical decay studied by the LHCb experiment. The method of evaluating misalignment effect and data samples used are presented in Section 2. The results obtained are presented in Section 3 and all the plots are in the Appendix A.1. Conclusions are summarized in Section 4. 31 32 33 34 35 36 37 38 39 4 2 Misalignment study The precison of the alignment procedure, both for the modules and for the 2 half alignment, has been evaluated using both data and Monte Carlo samples [3]. The misalignment is shown to be of the order of a few µm for the translations and of the order of 1 µrad for the rotations, as summarized in Table 1. The study of the stability of the VELO alignment on Run 1 and Run 2 data shows an average variation of 3 µm amongs fills, with a maximum variation of 1 µm for translations in x and y direction (Tx,Ty) while the module alignment is stable within the precision of the procedure. For this reason, this study is focusing only on the misalignment of the two halves. 2
Figure 2: Topology of D + (D K π + )π + decay Table 1: Accuracy of the alignment procedure for each degree of freedom of the 2 VELO half alignment. T i stands for translational misalignment in i direction and R i for rotational misalignment in the i direction. DOF Precision alignment procedure Max variation between fills T x T y [µm] 1.5 1 T z [µm] 5 1 R x, R y [µrad] 4 1 R z [µrad] 3 5 41 42 43 44 45 46 47 48 49 5 51 52 53 54 55 The effect of the misalignment is studied on five phyisical quantities of the D + (D K π + )π + decay (and charge conjugate): D mass, D momentum, D transverse momentum, D impact parameter and D cτ. cτ is the proper decay time of the particle multiplied by the speed of light. It is expected that the 2 VELO half misalignment has a larger effect on the cτ and impact parameter than on the mass and momentum because the magnetic field in the VELO is negligible thus the momentum and the mass mainly depend on the tracker alignment. In order to evaluate the effect of the misalignment, the data are reconstructed with and without misalignment. This procedure can be repeated using different orders of misalignment. The data samples are analysed by comparing the chosen physical quantities and by looking at the distributions of the relative difference between them and the pull, evaluated per-candidate. The relative difference is defined as xm x x, where x m is the value of the chosen variable in the data with the misalignment and x without misalignment. x The pull is defined as m x σ where σ 2 xm +σx 2 xm and σ x are the errors of the variable in the 3
56 57 58 59 6 61 62 63 64 65 data with and without misalignment, respectively. The studied misalignments are listed in the Table 2. Small misalignments are similar to the accuracy of the alignment procedure, while larger misalignments are applied to determine the limit to trigger a warning in the data quality (DQ) procedure. The misalignment is applied separately for each degree of freedom (DOF) to see the individual impact of each dof on the data. Additionaly, to evaluate the effect of the residual misalignment of the 2 halves of the real-time alignment procedure, 5 samples of data are generated with a Gaussian distributed misalignment applied to all DOFs and with a sigma equal to the alignment precision for each DOF, as reported in Table 1. Table 2: Studied misalignment, applied individually to each DOF. Tx [µm] Ty [µm] Tz [µm] Rx [µrad] Ry [µrad] Rz [µrad] 1.5 1.5 5 4 4 3 5 5 1 1 1 6 1 1 2 25 25 1 3 3 6 75 75 3 66 67 68 69 7 71 72 73 74 75 76 77 78 79 8 81 82 83 84 85 86 87 88 89 3 Results 3.1 Separate degrees of freedom As pointed out in section 2, the degrees of freedom are separately studied. In Figure 3 we can see the relative difference of D mass and D impact parameter for several values of translation misalignemnt in the x-direction (Tx). As expected, misalignment has a greater effect on the impact parameter than on the mass and on the momentum, by 2 orders of magnitude. Momentum, mass and transverse momentum are effected by a sub-permile scale. Mean and RMS values of the relative difference distribution of the IP and cτ for different misalignments are shown in Tables 3 to 1. The mass and momentum results are illustrated in the appendix A.1. In case of expected small misalignment, the bias of IP is relatively small, where the Tz misalignment is the main contribution up to a few per-mill level. In the case of large translational (Tx, Ty, Tz) misalignments, the effect could be at a few percent level. An effect of 1 to few % level on the IP resolution RMS is observed even at low Tx and Ty misalignment, while the large misalignment has a major contribution of the order of 1%. The Rx and Ry have an effect that is one order of magnitude smaller than the translation and the Rz misalignment does not affect the IP RMS. Figure 6 and the figures in the Appendix C.1 summarize the mean and the RMS as functions of the misalignment considered. One can note that there is an almost linear dependency on the effect on the RMS and the misalignment applied. The bias does not show this effect, except in the case of Tz misalignment (as shown in 23). The pull of the IP shows that the effect is significant only for Tx and Ty misalignment greater than 5 micron. Figure 4 shows the pull distribution for the case of Tx misalignment, while appendix B contains the pull distributions for all the considered misalignment sets. 4
9 91 92 93 94 95 96 97 98 99 1 The proper time is affected primarily by the translations (Tx, Ty, Tz): the bias is mainly affected by Tx up to per mill level and the RMS increases by few per-mill, in the case of the expected misalignment. A large misalignment of both the translations and the rotations could have an effect of up to 1-2% both on the bias and on the RMS. The rotations have a much smaller effect, up to a per mill level even with large misalignment. The dependency of the mean and RMS as a function of the misalignment is shown in Figure 6 and in the figures in Appendix C.3. For all considered misalignments the RMS has an almost linear dependency on the misalignment size. The bias has no dependence except in the case of Tx and Ry, as can been seen in Figures 21 and 25. The pull of the proper time shows that the variations due to the misalignment (even in the case of large misalignment) are not significant as they are below the error on this variable. 5
Table 3: Mean and mean errors of the relative difference distributions, in percentages, for translational misalignments IP (%) cτ (%) Mis.[µm] Tx Ty Tx Ty 1.5 (.2 ±.1) (.1 ±.1) (.161 ±.2) (.4 ±.2) 5 (.8 ±.3) (.3 ±.2) (.532 ±.7) (.9 ±.6) 1 (.23 ±.6) (.2 ±.4) ( 1. ±.1) (.5 ±.11) 3 (.7 ±.2) (1.4 ±.1) ( 1.7 ±.2) (.1 ±.2) Table 4: Mean and mean errors of the relative difference distributions, in percentages, for translational misalignments IP (%) cτ (%) Mis.[µm] Tz Tz 5 (.241 ±.2) (.13 ±.1) 1 (.485 ±.5) (.27 ±.3) 2 (.97 ±.1) (.52 ±.5) 6 (2.98 ±.3) (.13 ±.1) Table 5: Mean and mean error of the relative difference distributions, in percentages, for rotational misalignments IP (%) cτ (%) Mis.[µrad] Rx Ry Rx Ry 1.5 (.2 ±.1) (.3 ±.3) (.1 ±.6) (.22 ±.1) 5 (.7 ±.4) (.11 ±.7) (.1 ±.11) (.14 ±.4) 1 (.12 ±.9) (.2 ±.2) (.2 ±.3) (.14 ±.4) 3 (.8 ±.2) (.7 ±.4) (.6 ±.7) (.39 ±.1) 11 12 13 14 15 16 17 18 19 3.2 Current residual misalignment The effect of the current residual misalignment is studied, generating 5 different misalignments with Gaussian distributed misalignments in all DOFs where the sigmas are the current alignment precisions for each DOF, as quoted in Table 1. The results of integrating the 5 data samples for D mass and the D IP are shown in Figure 7 and summarized in Table 11. No bias is observed in any of the physical quantities. The effect on the mass and momentum RMS is negligible. A small increase of 1 percent of the IP resolution and of 4 per-mil on the proper time is observed. This effect is small considering the error on these measurements, as shown by the pull distribution in Figure 8. 6
Table 6: Mean and mean error of the relative difference distributions, in percentages, for rotational misalignments IP (%) cτ (%) Mis.[µrad] Rz Rz 3 (.154 ±.8) (.7 ±.5) 6 (.32 ±.2) (.8 ±.9) 1 (.53 ±.3) (.9 ±.13) 3 (.156 ±.6) (.17 ±.25) Table 7: RMS mean and error of the relative difference distributions, in percentages, for translational misalignments IP (%) cτ (%) Mis.[µm] Tx Ty Tx Ty 1.5 (1.14 ±.1) (.837 ±.5) (.297 ±.2) (.245 ±.1) 5 (3.7 ±.2) (2.65 ±.1) (.947 ±.5) (.785 ±.4) 1 (7.3 ±.4) (5.18 ±.3) (1.7 ±.1) (1.48 ±.1) 3 (19.7 ±.1) (13.68 ±.7) (2.75 ±.2) (3.3 ±.2) 11 111 112 113 114 115 116 117 118 119 12 121 122 123 4 Conclusion The effect of the VELO 2 half misalignment is quantified by looking at its effect on the Monte Carlo data in the decay D + (D K π + )π + and its charge conjugate. Misalignments of different sizes are considered for each DOF to determine a limit above which the DQ would be affected by the VELO 2 half misalignment. From the study of this decay, one can conclude that the 2 half alignment should be better than (5 µm, 1 µm, 6 µm,,, 6 µrad for Tx, Ty, Tz, Rx, Ry and Rz, respectively) to not affect any physical quantities considered. Considering the expected misalignments, the accuracy of the real-time alignment procedure shows that the alignment accuracy has an effect which goes up to the order of a permil for the D IP and cτ, while mass and momentum are effected on a sub-per-mill level. In conclusion, the 2 half VELO alignment accuracy has a negligible effect on the physical quantites. 7
Table 8: RMS mean and error of the relative difference distributions, in percentages, for translational misalignments IP (%) cτ (%) Mis.[µm] Tz Tz 5 (.321 ±.2) (.164 ±.1) 1 (.665 ±.4) (.335 ±.2) 2 (1.271 ±.7) (.64 ±.3) 6 (3.51 ±.2) (1.77 ±.1) Table 9: RMS mean and error of the relative difference distributions, in percentages, for rotational misalignments IP (%) cτ (%) Mis.[µrad] Rx Ry Rx Ry 4 (.188 ±.1) (.453 ±.2) (.749 ±.4) (.1321 ±.7) 1 (.535 ±.3) (.945 ±.5) (.1511 ±.8) (.247 ±.1) 25 (1.128 ±.6) (2.8 ±.1) (.357 ±.2) (.579 ±.3) 75 (3.8 ±.2) (5.4 ±.3) (.877 ±.4 (1.44 ±.8) Table 1: RMS mean and error of the relative difference distributions, in percentages, for rotational misalignments IP (%) cτ (%) Mis.[µrad] Rz Rz 5 (.186 ±.5) (.668 ±.4) 1 (.251 ±.1) (.1141 ±.6) 2 (.332 ±.2) (.167 ±.1) 6 (.767 ±.4) (.331 ±.2) 5 4 3 2 1 1. 1 µm 3 µm.1.5.5.1.2.2 Relative difference of D* M Relative difference of D IP Figure 3: Relative difference between the data with and without Tx misalignment for D mass (left) and D impact parameter (right). The dotted lines represent the results of the same misalignment value as their corresponding color in the legend, but of the opposite sign (VELO being more closed ) and this is the same on all plots. 45 4 35 3 25 2 15 1 5 1. 1 µm 3 µm 8
8 7 6 5 4 3 2 1 1. 1 µm 3 µm 1.5.5 1 1.5.5 1 Pull of D cτ Pull of D IP Figure 4: Distribution of the pull for D impact parameter and cτ. 14 12 1 8 6 4 2 1. 1 µm 3 µm D* M relative difference.6.4.2.2.4.6 1 5 25 2 15 1 5 5 1 15 2 25 3 35 D* PT relative difference 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Tx [µm] Two halves misalignment Tx [µm] Figure 5: Effect of increasing Tx misalignment on the relative difference distribution for D mass and transverse momentum. Dots are the mean values of the relative difference distributions and error bars correspond to the RMS..15.1.5.5.1.15 relative difference D cτ.4.2.2.4 D IP relative difference.2.15.1.5.5.1.15.2 5 25 2 15 1 5 5 1 15 2 25 3 35 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Tx [µm] Two halves misalignment Tx [µm] Figure 6: Effect of increasing Tx misalignment on the relative difference distribution for D IP and cτ. Dots are the mean values of the relative difference distributions and error bars correspond to the RMS of the relative difference distributions. 9
Table 11: Mean and RMS values of the relative difference, in percentages, for chosen variables with the current expected residual misalignment D M% D M% D P T % D IP % D cτ% Mean O(1 5 ) O(1 5 ) O(1 4 ).8.11 RMS O(1 ) O(1 5 ) O(1 2 ) 1.3.4 5 4 3 2 3 25 2 15 1 1 5.2.2.4.2.2.4 D* M relative difference D IP relative difference Figure 7: Relative difference of the 5 data samples with current expected residual misalignment and without misalignment for D mass (left) and D impact parameter (right)..25.2.15 6 1 1 8 6 3 1.1.5 4 2 1.5.5 1 1.5.5 1 D cτ pull D IP pull Figure 8: Pull of the 5 data samples with current expected residual misalignment and without misalignment for D cτ(left) and D impact parameter (right). 1
124 Appendices 125 A Relative difference of the physical quantities 126 A.1 Tx misalignment 5 4 3 2 1 1..1.5.5.1 Relative difference of D* M 1 µm 3 µm 45 4 35 3 25 2 15 1. 1 3 µm 5.1.5.5.1 Relative difference of D* P 1 µm 5 4 3 1. 2 1 1 µm 3 µm 45 4 35 3 25 2 15 1 5.2.1.1.2 Relative difference of D* PT 1. 1 µm 3 µm.2.2.1.5.5.1 Relative difference of D IP Relative difference of D cτ Figure 9: Relative difference between the data with and without Tx misalignment. 8 7 6 5 4 3 2 1 1. 1 µm 3 µm 11
127 A.2 Ty misalignment 5 4 3 2 1 1. 1 µm 3 µm.1.5.5.1.1.5.5.1 Relative difference of D* M Relative difference of D* P 9 8 7 6 5 4 3 2 1 1. 1 µm 3 µm 6 5 4 3 2 1. 1 µm 1 3 µm 45 4 35 3 25 2 15 1 5.2.1.1.2 Relative difference of D* PT 1. 1 µm 3 µm.2.2.1.5.5.1 Relative difference of D IP Relative difference of D cτ Figure 1: Relative difference between the data with and without Ty misalignment. 7 6 5 4 3 2 1 1. 1 µm 3 µm 12
128 A.3 Tz 8 9 7 8 7 6 6 5 1 µm 1 µm 5 4 4 2 µm 3 3 2 µm 2 6 µm 2 6 µm 1 1.1.5.5.1.1.5.5.1 Relative difference of D* M Relative difference of D* P 9 8 7 6 5 4 3 2 1 µm 2 µm 6 µm 1.2.1.1.2 Relative difference of D* PT 12 1 8 6 4 2 1 µm 2 µm 6 µm.2.2.1.5.5.1 Relative difference of D IP Relative difference of D cτ Figure 11: Relative difference between the data with and without Tz misalignment. 7 6 5 4 3 2 1 1 µm 2 µm 6 µm 13
129 A.4 Rx 9 7 8 6 4µrad 7 4µrad 5 6 1 µrad 1 µrad 5 4 4 3 3 2 2 1 1.1.5.5.1.1.5.5.1 Relative difference of D* M Relative difference of D* P 6 5 4 3 2 1 4µrad 1 µrad 9 8 7 6 5 4 3 2 1.2.1.1.2 Relative difference of D* PT 4µrad 1 µrad.2.2.1.5.5.1 Relative difference of D IP Relative difference of D cτ Figure 12: Relative difference between the data with and without Rx misalignment. 9 8 7 6 5 4 3 2 1 4µrad 1 µrad 14
13 A.5 Ry misalignment 5 4 3 2 1 4µrad 1 µrad.1.5.5.1.1.5.5.1 Relative difference of D* M Relative difference of D* P 35 3 25 2 15 1 5 4µrad 1 µrad 6 5 4 3 2 4µrad 1 µrad 1.2.1.1.2 Relative difference of D* PT 8 9 7 8 6 4µrad 4µrad 7 6 5 1 µrad 1 µrad 5 4 4 3 3 2 2 1 1.2.2.1.5.5.1 Relative difference of D IP Relative difference of D cτ Figure 13: Relative difference between the data with and without Ry misalignment. 15
131 A.6 Rz misalignment 7 6 5 4 3 2 1 3µrad 6 µrad 1 µrad 3 µrad.1.5.5.1 Relative difference of D* M 1 8 6 4 2 9 8 7 6 5 4 3 2 1 7 6 5 4 3 2 1.2.1.1.2 Relative difference of D* PT 3µrad 6 µrad 1 µrad 3 µrad 3µrad 6 µrad 1 µrad 3 µrad.1.5.5.1 Relative difference of D* P.2.2.1.5.5.1 Relative difference of D IP Relative difference of D cτ Figure 14: Relative difference between the data with and without Rz misalignment. 9 8 7 6 5 4 3 2 1 3µrad 6 µrad 1 µrad 3 µrad 3µrad 6 µrad 1 µrad 3 µrad 16
132 B Pull distributions of the physical quantities 133 B.1 Tx misalignment 8 7 6 5 4 3 2 1 1. 1 µm 3 µm 1.5.5 1 1.5.5 1 Pull of D cτ Pull of D IP Figure 15: Distributions of the pull for Tx misalignment scenarios. 14 12 1 8 6 4 2 1. 1 µm 3 µm 134 B.2 Ty misalignment 7 2 6 18 5 1. 16 1. 14 4 12 3 1 µm 1 8 1 µm 2 6 1 3 µm 4 3 µm 2 1.5.5 1 1.5.5 1 Pull of D cτ Pull of D IP Figure 16: Distributions of the pull for Ty misalignment scenarios. 17
135 B.3 Tz misalignment 8 7 6 5 4 3 2 1 1 µm 2 µm 6 µm 1.5.5 1 1.5.5 1 Pull of D cτ Pull of D IP Figure 17: Distributions of the pull for Tz misalignment scenarios. 7 6 5 4 3 2 1 1 µm 2 µm 6 µm 136 B.4 Rx misalignment 9 8 7 6 5 4 3 2 1 4 µrad 1 µrad 1.5.5 1 1.5.5 1 Pull of D cτ Pull of D IP Figure 18: Distributions of the pull for Rx misalignment scenarios. 7 6 5 4 3 2 1 4 µrad 1 µrad 18
137 B.5 Ry misalignment 1 8 6 4 4 µrad 1 µrad 5 4 3 2 4 µrad 1 µrad 2 1 1.5.5 1 1.5.5 1 Pull of D cτ Pull of D IP Figure 19: Distributions of the pull for Ry misalignment scenarios. 138 B.6 Rz misalignment 9 8 7 6 5 4 3 2 1 4 µrad 1 µrad 1.5.5 1 1.5.5 1 Pull of D cτ Pull of D IP Figure 2: Distributions of the pull for Rz misalignment scenarios. 7 6 5 4 3 2 1 4 µrad 1 µrad 19
139 14 C Dependency of the misalignment effect as a function of the considered misalignment 141 C.1 Tx misalignment 1 1 D* M relative difference.6.4.2.2.4.6 D* P relative difference.4.2.2.4 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Tx [µm] 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Tx [µm] D* PT relative difference.15.1.5.5.1.15 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Tx [µm] D IP relative difference.2.15.1.5.5.1.15.2 relative difference D cτ.4.2.2.4 5 25 2 15 1 5 5 1 15 2 25 3 35 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Tx [µm] Two halves misalignment Tx [µm] Figure 21: Effect of increasing Tx misalignment on the relative difference distribution. Dots are the mean values of the relative difference distributions and error bars correspond to the RMS. 2
142 C.2 Ty misalignment D* M relative difference.4.3.2.1.1.2.3.4 1 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Ty [µm] D* P relative difference 1.15.1.5.5.1.15 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Ty [µm] D* PT relative difference.8.6.4.2.2.4.6.8 1 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Ty [µm] D IP relative difference.15.1.5.5.1.15 5 25 2 15 1 5 5 1 15 2 25 3 35 relative difference D cτ 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Ty [µm] Two halves misalignment Ty [µm] Figure 22: Effect of increasing Ty misalignment on the relative difference distribution..3.2.1.1.2.3 21
143 C.3 Tz misalignment D* M relative difference.15.1.5.5.1.15 1 D* P relative difference.8.6.4.2.2.4.6.8 1 7 6 5 4 2 1 1 2 3 4 5 6 7 Two halves misalignment Tz [µm] 7 6 5 4 2 1 1 2 3 4 5 6 7 Two halves misalignment Tz [µm] D* PT relative difference.2.1.1.2 1 7 6 5 4 2 1 1 2 3 4 5 6 7 Two halves misalignment Tz [µm] D IP relative difference.6.4.2.2.4.6 7 6 5 4 2 1 1 2 3 4 5 6 7 relative difference D cτ 7 6 5 4 2 1 1 2 3 4 5 6 7 Two halves misalignment Tz [µm] Two halves misalignment Tz [µm] Figure 23: Effect of increasing Tz misalignment on the relative difference distribution..2.15.1.5.5.1.15.2 22
144 C.4 Rx misalignment D* M relative difference.2.1.1.2 1 D* P relative difference 1.15.1.5.5.1 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 Two halves misalignment Rx [µrad].15 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 Two halves misalignment Rx [µrad] D* PT relative difference 1.8.6.4.2.2.4.6.8 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 Two halves misalignment Rx [µrad] D IP relative difference.3.2.1.1.2.3 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 relative difference D cτ.1.5.5.1 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 Two halves misalignment Rx [µrad] Two halves misalignment Rx [µrad] Figure 24: Effect of increasing Rx misalignment on the relative difference distribution. 23
145 C.5 Ry misalignment 1 1 D* M relative difference.4.2.2.4 D* P relative difference.4.2.2.4 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 Two halves misalignment Ry [µrad] 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 Two halves misalignment Ry [µrad] D* PT relative difference.15.1.5.5.1.15 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 Two halves misalignment Ry [µrad] D IP relative difference.6.4.2.2.4 D cτ relative difference.2.15.1.5.5.1.15.6.2 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 2 1 1 2 3 4 5 6 7 8 9 Two halves misalignment Ry [µrad] Two halves misalignment Ry [µrad] Figure 25: Effect of increasing Ry misalignment on the relative difference distribution. 24
146 C.6 Rz misalignment D* M relative difference.2.15.1.5.5.1.15.2 1 D* P relative difference.15.1.5.5.1.15 1 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Rz [µrad] 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Rz [µrad] D* PT relative difference.2.15.1.5.5.1.15.2 1 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Rz [µrad] D IP relative difference.1.5.5.1 relative difference D cτ.3.2.1.1.2.3 5 25 2 15 1 5 5 1 15 2 25 3 35 5 25 2 15 1 5 5 1 15 2 25 3 35 Two halves misalignment Rz [µrad] Two halves misalignment Rz [µrad] Figure 26: Effect of increasing Rz misalignment on the relative difference distribution. 25
147 148 D Results on the samples with an expected misalignment 149 D.1 Relative difference of the physical quantities 5 4 3 45 4 35 3 25 2 2 15 1 1 5.2.2 D* M relative difference.1.1 D* P relative difference 25 2 15 1 5.2.2 D* PT relative difference 12 1 8 6 3 25 2 15 4 2 1 5.2.1.1.2.4.2.2.4 D cτ relative difference D IP relative difference Figure 27: Relative difference of the merged data sample with the expected misalignment 26
15 D.2 Pull distributions of the physical quantities.25.2.15 6 1 1 8 6 3 1.1.5 4 2 1.5.5 1 1.5.5 1 D cτ pull D IP pull Figure 28: Pull of the 5 data sample with current expected residual misalignment and without misalignment 27
151 152 153 154 155 156 157 References [1] L. Collaboration, LHCb VELO Upgrade Technical Design Report, Tech. Rep. CERN- LHCC-213-21. LHCB-TDR-13, Nov, 213. [2] LHCb VELO Group, R. Aaij et al., Performance of the LHCb Vertex Locator, J. Instrum. 9 (214) P97. 61 p, Comments: 61 pages, 33 figures. [3] G. Dujany, S. Borghi, and P. C. Study of the accuracy and stability for the VELO real-time alignment procedure, LHCb-INT-216-35. 28