# Difference: TkAlignmentPerformanceMid18 (1 vs. 7)

#### Revision 72019-09-03 - MarcoMusich

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 META TOPICPARENT name="CMS.TkAlignment"

# CMS Tracker Alignment Performance Results 2018

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Contact: The CMS Tracker DPG conveners (cms-dpg-conveners-tracker@cernNOSPAMPLEASE.ch)
and the CMS Tracker Alignment Performance hypernews (hn-cms-tk-alignment@cernNOSPAMPLEASE.ch).

#### Revision 62018-12-12 - MarcoMusich

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 META TOPICPARENT name="CMS.TkAlignment"
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Contact: cms-dpg-conveners-tracker_AT_cern.ch.
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Contact: The CMS Tracker DPG conveners (cms-dpg-conveners-tracker@cernNOSPAMPLEASE.ch)
and the CMS Tracker Alignment Performance hypernews (hn-cms-tk-alignment@cernNOSPAMPLEASE.ch).
Public CDS Record: CMS DP-2018/061
The following figures show the performance of the alignment of the CMS tracker with data taken during 2018. The results were obtained for an alignment with cosmic tracks, and an alignment performed with data taken until the beginning of August 2018. A global alignment is performed, in which alignment constants for the individual sensors and for the large scale structures are derived simultaneously. The alignment constants for the individual sensors are the same throughout the data-taking period, while those for the large scale structures are allowed to vary between shorter time periods. The exact alignment constants are therefore time-dependent. As such the results shown for the alignment constants derived with data collected until the beginning of August 2018 refer to selected time slices; they are a good representation of the average performance.

#### Revision 52018-11-26 - MarcoMusich

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 META TOPICPARENT name="TkAlignment"
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 META TOPICPARENT name="CMS.TkAlignment"

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 The RMS of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The red points show the results with the alignment constants used during data taking, the blue points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker reduces the RMS.

### Z$\rightarrow\mu\mu$ validation

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Distortions of the tracker geometry can lead to a bias in the reconstructed track curvature $\kappa \propto \pm\frac{1}{p_{T}}$. These are investigated using the reconstructed Z$\rightarrow\mu\mu$ mass as a function of the muon direction and separating $\mu^{+}$ and $\mu^{-}$ as the curvature bias has an opposite effect on their $p_{T}$. The invariant mass distribution is fitted to a Breit-Wigner convolved with a Crystal Ball function, thus taking into account the finite track resolution and the radiative tail, for the signal plus an exponential background. The fit range is 75-105 GeV/$c^{2}$ and the Z width is fixed to the PDG value of 2.495 GeV/$c^{2}$. Note that this does not show the CMS muon reconstruction and calibration performance. Additional muon momentum calibrations are applied on top of this in physics analyses.
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Distortions of the tracker geometry can lead to a bias in the reconstructed track curvature $\kappa \propto \pm\frac{1}{p_{T}}$. These are investigated using the reconstructed Z$\rightarrow\mu\mu$ mass as a function of the muon direction and separating $\mu^{+}$ and $\mu^{-}$ as the curvature bias has an opposite effect on their $p_{T}$. The invariant mass distribution is fitted to a Breit-Wigner convolved with a Crystal Ball function, thus taking into account the finite track resolution and the radiative tail, for the signal plus an exponential background. The fit range is 75-105 CMS.GeV/$c^{2}$ and the Z width is fixed to the PDG value of 2.495 CMS.GeV/$c^{2}$. Note that this does not show the CMS muon reconstruction and calibration performance. Additional muon momentum calibrations are applied on top of this in physics analyses.

Figure in PNG format (click on plot to get PDF) Description
The Z-peak mass as a function of $\phi$ and $\eta$ of the positively charged muon. In these figures data from throughout 2018 are used, instead of only shorter time periods. The result with the alignment constants used in data taking is shown here. After aligning the tracker the large variations in the peak Z mass visible with the alignment constants used during data taking are reduced.
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 META TOPICMOVED by="musich" date="1543220079" from="CMS.TkAlignmentPerformanceMid18" to="CMSPublic.TkAlignmentPerformanceMid18"

#### Revision 42018-11-21 - AdeWit

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 META TOPICPARENT name="TkAlignment"
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 Mean track-vertex impact parameter in the transverse plane as a function of track azimuth $\phi$. The impact parameters are obtained by recalculating the vertex position after removing the track being studied from it, and considering the impact parameter of this removed track. The red points show the results with the alignment constants as used during data taking, the blue points show the results using the alignment constants obtained in the alignment procedure. The alignment constants are time-dependent, those used here were obtained for data taken from 30 to 31 May 2018. Modulations visible in this distribution with the alignment constants considered during data-taking are improved with the aligned tracker.

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 The mean of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker improves the mean of this distribution. Outliers in the trend are understood as degraded tracking performance caused by suboptimal pixel local reconstruction calibration input. The RMS of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker reduces the RMS.
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 The mean of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The red points show the results with the alignment constants used during data taking, the blue points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker improves the mean of this distribution. Outliers in the trend are understood as degraded tracking performance caused by suboptimal pixel local reconstruction calibration input. The RMS of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The red points show the results with the alignment constants used during data taking, the blue points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker reduces the RMS.

### Z$\rightarrow\mu\mu$ validation

Distortions of the tracker geometry can lead to a bias in the reconstructed track curvature $\kappa \propto \pm\frac{1}{p_{T}}$. These are investigated using the reconstructed Z$\rightarrow\mu\mu$ mass as a function of the muon direction and separating $\mu^{+}$ and $\mu^{-}$ as the curvature bias has an opposite effect on their $p_{T}$. The invariant mass distribution is fitted to a Breit-Wigner convolved with a Crystal Ball function, thus taking into account the finite track resolution and the radiative tail, for the signal plus an exponential background. The fit range is 75-105 GeV/$c^{2}$ and the Z width is fixed to the PDG value of 2.495 GeV/$c^{2}$. Note that this does not show the CMS muon reconstruction and calibration performance. Additional muon momentum calibrations are applied on top of this in physics analyses.

#### Revision 32018-11-03 - AdeWit

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 META TOPICPARENT name="TkAlignment"
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Contact: cms-dpg-conveners-tracker_AT_cern.ch.
Changed:
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The following figures show the performance of the alignment of the CMS tracker with data taken during 2018. The results were obtained for an alignment with cosmic tracks, and an alignment performed with data taken until the beginning of August 2018.
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The following figures show the performance of the alignment of the CMS tracker with data taken during 2018. The results were obtained for an alignment with cosmic tracks, and an alignment performed with data taken until the beginning of August 2018. A global alignment is performed, in which alignment constants for the individual sensors and for the large scale structures are derived simultaneously. The alignment constants for the individual sensors are the same throughout the data-taking period, while those for the large scale structures are allowed to vary between shorter time periods. The exact alignment constants are therefore time-dependent. As such the results shown for the alignment constants derived with data collected until the beginning of August 2018 refer to selected time slices; they are a good representation of the average performance.
The definition and general interpretation of the figures shown in the following are explained in more detail in reference [3]. The coordinate systems, including the definition of the primed coordinates, used in the following figures are also defined in this reference.
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### Comparison of module positions

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 Difference in the positions of the modules between the alignment constants used during data taking and the alignment constants obtained after aligning the tracker. The change in the z coordinate between the constants obtained after aligning the tracker and the alignment constants used during data taking is shown as a function of the coordinate r in the alignment constants used during data taking. Each point represents a module. The colours correspond to the different sub-detectors of the tracker, and match the colours used in the tracker layout shown above. The alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The large spread in movements in the tracker endcaps is due to noise. This module position comparison shows that the alignment procedure shifts the position of the barrel pixel detector.
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 Difference in the positions of the modules between the alignment constants used during data taking and the alignment constants obtained after aligning the tracker. The change in the z coordinate between the constants obtained after aligning the tracker and the alignment constants used during data taking is shown as a function of the coordinate r in the alignment constants used during data taking. Each point represents a module. The colours correspond to the different sub-detectors of the tracker, and match the colours used in the tracker layout shown above. The alignment constants are time-dependent, those used here were obtained for data taken from 18 to 19 May 2018. The large spread in movements in the tracker endcaps is a feature of the algorithm used for the alignment. The algorithm cannot constrain the positions of modules far away from the interaction point along the longitudinal axis as tightly as for modules which are closer to the interaction point along the longitudinal axis. This module position comparison shows that the alignment procedure shifts the position of the barrel pixel detector.

### DMR validation

Distributions of medians of unbiased track-hit residuals. Each track is refitted using the alignment constants under consideration, and the hit prediction for each module is obtained from all of the other track hits. The median of the distribution of unbiased hit residuals is then taken for each module and is histogrammed. The width of this distribution of the medians of residuals (DMR) is a measure of the local precision of the alignment results; deviations from zero indicate biases.

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 The distribution of median residuals is plotted for the local x’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local y’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local y’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker inner barrel (TIB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker outer barrel (TOB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker inner disks (TID). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker endcaps (TEC). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.
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 The distribution of median residuals is plotted for the local x’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18 to 19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local y’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18 to 19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18 to 19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local y’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18 to 19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker inner barrel (TIB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18 to 19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker outer barrel (TOB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18 to 19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker inner disks (TID). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18 to 19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker endcaps (TEC). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18 to 19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.

### Primary vertex validation

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 Mean track-vertex impact parameter in the transverse plane as a function of track azimuth $\phi$. The impact parameters are obtained by recalculating the vertex position after removing the track being studied from it, and considering the impact parameter of this removed track. The red points show the results with the alignment constants as used during data taking, the blue points show the results using the alignment constants obtained in the alignment procedure. The alignment constants are time-dependent, those used here were obtained for data taken during 30-31 May 2018. Modulations visible in this distribution with the alignment constants considered during data-taking are improved with the aligned tracker.
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 Mean track-vertex impact parameter in the transverse plane as a function of track azimuth $\phi$. The impact parameters are obtained by recalculating the vertex position after removing the track being studied from it, and considering the impact parameter of this removed track. The red points show the results with the alignment constants as used during data taking, the blue points show the results using the alignment constants obtained in the alignment procedure. The alignment constants are time-dependent, those used here were obtained for data taken from 30 to 31 May 2018. Modulations visible in this distribution with the alignment constants considered during data-taking are improved with the aligned tracker.

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 The mean of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker improves the mean of this distribution.
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 The mean of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker improves the mean of this distribution. Outliers in the trend are understood as degraded tracking performance caused by suboptimal pixel local reconstruction calibration input.

 The RMS of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker reduces the RMS.

### Z$\rightarrow\mu\mu$ validation

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#### Revision 22018-10-25 - AdeWit

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 META TOPICPARENT name="TkAlignment"
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The following figures show the performance of the alignment of the CMS tracker with data taken during 2018. The results were obtained for an alignment with cosmic tracks, and an alignment performed with data taken until the beginning of August 2018.
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Schematic of the CMS tracker, showing the different subdetectors (modified from reference [1). Nearest to the interaction point the pixel detector consists of the barrel pixel detector (BPIX or PXB), shown in grey, and the forward pixel detector (FPIX or PXF), shown in red. Surrounding the pixel detector the tracker is made up of a silicon strip detector, divided into the tracker inner barrel (TIB), tracker outer barrel (TID), tracker inner disks (TID) and tracker endcaps (TEC). This figure corresponds to the layout of the tracker until the end of 2016. At the beginning of 2017 an upgraded version of the pixel detector was installed. The global structure of the tracker did not change in this upgrade.

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The definition and general interpretation of the figures shown in the following are explained in more detail in reference [3]. The coordinate systems, including the definition of the primed coordinates, used in the following figures are also defined in this reference.

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The definition and general interpretation of the figures shown in the following are explained in more detail in reference [3. The coordinate systems, including the definition of the primed coordinates, used in the following figures are also defined in this reference.

## DMR validation

Distributions of medians of unbiased track-hit residuals. Each track is refitted using the alignment constants under consideration, and the hit prediction for each module is obtained from all of the other track hits. The median of the distribution of unbiased hit residuals is then taken for each module and is histogrammed. The width of this distribution of the medians of residuals (DMR) is a measure of the local precision of the alignment results; deviations from zero indicate biases.

# Alignment constants derived with cosmic tracks

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 Difference in impact parameter in the transverse plane between the top and bottom halves of cosmic tracks recorded with the CMS magnet at 3.8T. A comparison is made between the alignment constants obtained in the final alignment using 2017 data, and the alignment constants obtained by aligning the tracker using cosmic tracks recorded with the CMS magnet at 0T and at 3.8T before the start of proton-proton collisions in 2018. The mean and width of the distribution are significantly improved after the alignment with cosmic tracks. Difference in impact parameter in the longitudinal plane between the top and bottom halves of cosmic tracks recorded with the CMS magnet at 3.8T. A comparison is made between the alignment constants obtained in the final alignment using 2017 data, and the alignment constants obtained by aligning the tracker using cosmic tracks recorded with the CMS magnet at 0T and at 3.8T before the start of proton-proton collisions in 2018. The mean and width of the distribution are significantly improved after the alignment with cosmic tracks.
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# Alignment constants derived with data collected until the beginning of August 2018

Performance figures of the tracker alignment for the first part of the 2018 data-taking period are presented. The alignment constants are compared with those used at the time of data taking.
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The alignment constants used at the time of data taking were obtained with cosmic-ray data taken prior to pp operation and collision data at the beginning of the 2018 data taking period. Time- dependent movements of the large scale structures of the pixel detector are corrected by an automated "prompt calibration loop"-procedure, described in more detail in reference [2.
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The alignment constants used at the time of data taking were obtained with cosmic-ray data taken prior to pp operation and collision data at the beginning of the 2018 data taking period. Time- dependent movements of the large scale structures of the pixel detector are corrected by an automated "prompt calibration loop"-procedure, described in more detail in reference [2].
The alignment constants obtained using data taken during the 2018 data-taking period until the beginning of August 2018 were derived using cosmic tracks, minimum-bias pp collision events, pp collision events with isolated muons and pp collision events with Z$\rightarrow\mu\mu$ decays. Time-dependent effects are taken into account.
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### Tracker layout

Schematic of the CMS tracker, showing the different subdetectors (modified from reference [1]). Nearest to the interaction point the pixel detector consists of the barrel pixel detector (BPIX or PXB), shown in grey, and the forward pixel detector (FPIX or PXF), shown in red. Surrounding the pixel detector the tracker is made up of a silicon strip detector, divided into the tracker inner barrel (TIB), tracker outer barrel (TID), tracker inner disks (TID) and tracker endcaps (TEC). This figure corresponds to the layout of the tracker until the end of 2016. At the beginning of 2017 an upgraded version of the pixel detector was installed. The global structure of the tracker did not change in this upgrade.

### Comparison of module positions

Figure in PNG format (click on plot to get PDF) Description
Difference in the positions of the modules between the alignment constants used during data taking and the alignment constants obtained after aligning the tracker. The change in the z coordinate between the constants obtained after aligning the tracker and the alignment constants used during data taking is shown as a function of the coordinate r in the alignment constants used during data taking. Each point represents a module. The colours correspond to the different sub-detectors of the tracker, and match the colours used in the tracker layout shown above. The alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The large spread in movements in the tracker endcaps is due to noise. This module position comparison shows that the alignment procedure shifts the position of the barrel pixel detector.

### DMR validation

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Distributions of medians of unbiased track-hit residuals. Each track is refitted using the alignment constants under consideration, and the hit prediction for each module is obtained from all of the other track hits. The median of the distribution of unbiased hit residuals is then taken for each module and is histogrammed. The width of this distribution of the medians of residuals (DMR) is a measure of the local precision of the alignment results; deviations from zero indicate biases.

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 The distribution of median residuals is plotted for the local x’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local y’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local y’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker inner barrel (TIB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker outer barrel (TOB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker inner disks (TID). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker endcaps (TEC). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.
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 The distribution of median residuals is plotted for the local x’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local y’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local y’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker inner barrel (TIB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker outer barrel (TOB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker inner disks (TID). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation. The distribution of median residuals is plotted for the local x’ -direction in the tracker endcaps (TEC). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations $\sigma$; are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.

### Primary vertex validation

Figure in PNG format (click on plot to get PDF) Description
Mean track-vertex impact parameter in the transverse plane as a function of track azimuth $\phi$. The impact parameters are obtained by recalculating the vertex position after removing the track being studied from it, and considering the impact parameter of this removed track. The red points show the results with the alignment constants as used during data taking, the blue points show the results using the alignment constants obtained in the alignment procedure. The alignment constants are time-dependent, those used here were obtained for data taken during 30-31 May 2018. Modulations visible in this distribution with the alignment constants considered during data-taking are improved with the aligned tracker.
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 The mean of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker improves the mean of this distribution. The RMS of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker reduces the RMS.

### Cosmic-ray data at 0T

Changed:
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 Unbiased track-hit residuals for 0T tracks in BPIX x'. After the first alignment of the barrel pixel high-level structures (cyan triangles) both the bias and the width of the distribution are strongly reduced with respect to the geometry assumed before performing any alignment (black circles). The width of the distribution is further reduced after aligning the full pixel tracker down to the level of single modules (red squares). The mentioned alignments have been performed using 0T cosmic-ray tracks. Unbiased track-hit residuals for 0T tracks in BPIX y'. After the first alignment of the barrel pixel high-level structures (cyan triangles) both the bias and the width of the distribution are strongly reduced with respect to the geometry assumed before performing any alignment (black circles). The width of the distribution is further reduced after aligning the full pixel tracker down to the level of single modules (red squares). The mentioned alignments have been performed using 0T cosmic-ray tracks. Unbiased track-hit residuals for 0T tracks in FPIX x'. After the first alignment of the forward pixel high-level structures (blue triangles) both the bias and the width of the distribution are strongly reduced with respect to the geometry assumed before performing any alignment (black circles). The width of the distribution is further reduced after aligning the full pixel tracker down to the level of single modules (red squares). The mentioned alignments have been performed using 0T cosmic-ray tracks. Unbiased track-hit residuals for 0T tracks in FPIX y'. After the first alignment of the forward pixel high-level structures (blue triangles) both the bias and the width of the distribution are strongly reduced with respect to the geometry assumed before performing any alignment (black circles). The width of the distribution is further reduced after aligning the full pixel tracker down to the level of single modules (red squares). The mentioned alignments have been performed using 0T cosmic-ray tracks.
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 The mean of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker improves the mean of this distribution. The RMS of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker reduces the RMS.

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### Z$\rightarrow\mu\mu$ validation

Distortions of the tracker geometry can lead to a bias in the reconstructed track curvature $\kappa \propto \pm\frac{1}{p_{T}}$. These are investigated using the reconstructed Z$\rightarrow\mu\mu$ mass as a function of the muon direction and separating $\mu^{+}$ and $\mu^{-}$ as the curvature bias has an opposite effect on their $p_{T}$. The invariant mass distribution is fitted to a Breit-Wigner convolved with a Crystal Ball function, thus taking into account the finite track resolution and the radiative tail, for the signal plus an exponential background. The fit range is 75-105 GeV/$c^{2}$ and the Z width is fixed to the PDG value of 2.495 GeV/$c^{2}$. Note that this does not show the CMS muon reconstruction and calibration performance. Additional muon momentum calibrations are applied on top of this in physics analyses.

Figure in PNG format (click on plot to get PDF) Description
The Z-peak mass as a function of $\phi$ and $\eta$ of the positively charged muon. In these figures data from throughout 2018 are used, instead of only shorter time periods. The result with the alignment constants used in data taking is shown here. After aligning the tracker the large variations in the peak Z mass visible with the alignment constants used during data taking are reduced.
The Z-peak mass as a function of $\phi$ and $\eta$ of the positively charged muon. In these figures data from throughout 2018 are used, instead of only shorter time periods. The result with the alignment constants obtained in the alignment procedure is shown here. After aligning the tracker the large variations in the peak Z mass visible with the alignment constants used during data taking are reduced.

# References

1. CMS Collaboration "The CMS experiment at the CERN LHC" JINST 3 (2018) doi:10.1088/1748-0221/3/08/S08004
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1. CMS Collaboration "Alignment of the CMS tracker with LHC and cosmic ray data " 2014 JINST 9 P06009 doi:10.1088/1748-0221/9/06/P06009

-- AdeWit - 2018-10-25

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# CMS Tracker Alignment Performance Results 2018

Contact: cms-dpg-conveners-tracker_AT_cern.ch.

The following figures show the performance of the alignment of the CMS tracker with data taken during 2018. The results were obtained for an alignment with cosmic tracks, and an alignment performed with data taken until the beginning of August 2018.

Schematic of the CMS tracker, showing the different subdetectors (modified from reference [1). Nearest to the interaction point the pixel detector consists of the barrel pixel detector (BPIX or PXB), shown in grey, and the forward pixel detector (FPIX or PXF), shown in red. Surrounding the pixel detector the tracker is made up of a silicon strip detector, divided into the tracker inner barrel (TIB), tracker outer barrel (TID), tracker inner disks (TID) and tracker endcaps (TEC). This figure corresponds to the layout of the tracker until the end of 2016. At the beginning of 2017 an upgraded version of the pixel detector was installed. The global structure of the tracker did not change in this upgrade.

The definition and general interpretation of the figures shown in the following are explained in more detail in reference [3. The coordinate systems, including the definition of the primed coordinates, used in the following figures are also defined in this reference.

## DMR validation

Distributions of medians of unbiased track-hit residuals. Each track is refitted using the alignment constants under consideration, and the hit prediction for each module is obtained from all of the other track hits. The median of the distribution of unbiased hit residuals is then taken for each module and is histogrammed. The width of this distribution of the medians of residuals (DMR) is a measure of the local precision of the alignment results; deviations from zero indicate biases.

# Alignment constants derived with cosmic tracks

Performance figures of the tracker alignment constants derived with cosmic tracks before the beginning of proton-proton (pp) operation in 2018 are shown. The results are compared with the final alignment constants derived using data taken during 2017.

The final alignment constants using data taken during 2017 were derived using cosmic tracks, minimum bias pp-collision events, pp-collision events with isolated muons and pp-collision events with Z$\rightarrow\mu\mu$ decays. The alignment constants derived before the beginning of pp operation in 2018 were obtained using cosmic tracks collected with the CMS magnet at 0T and cosmic tracks collected with the CMS magnet at 3.8T. To compute these constants the barrel pixel and forward pixel detectors were aligned at sensor-level, with the large scale structures of the silicon strip detector aligned.

### DMR

Figure in PNG format (click on plot to get PDF) Description
Distributions of medians of unbiased track-hit residuals. Each track is refitted using the alignment constants under consideration, and the hit prediction for each module is obtained from all of the other track hits. The median of the distribution of unbiased hit residuals is then taken for each module and is histogrammed. The width of this distribution of the medians of residuals (DMR) is a measure of the statistical precision of alignment results; deviations from zero indicate possible biases. The width also has an intrinsic component due to the limited number of tracks, meaning that distributions can only be compared if they are produced with the same number of tracks, as is the case within each set of plots here.
Distributions of medians of unbiased track-hit residuals. Each track is refitted using the alignment constants under consideration, and the hit prediction for each module is obtained from all of the other track hits. The median of the distribution of unbiased hit residuals is then taken for each module and is histogrammed. The width of this distribution of the medians of residuals (DMR) is a measure of the statistical precision of alignment results; deviations from zero indicate possible biases. The width also has an intrinsic component due to the limited number of tracks, meaning that distributions can only be compared if they are produced with the same number of tracks, as is the case within each set of plots here.

### Track-splitting

Figure in PNG format (click on plot to get PDF) Description
Difference in impact parameter in the transverse plane between the top and bottom halves of cosmic tracks recorded with the CMS magnet at 3.8T. A comparison is made between the alignment constants obtained in the final alignment using 2017 data, and the alignment constants obtained by aligning the tracker using cosmic tracks recorded with the CMS magnet at 0T and at 3.8T before the start of proton-proton collisions in 2018. The mean and width of the distribution are significantly improved after the alignment with cosmic tracks.
Difference in impact parameter in the longitudinal plane between the top and bottom halves of cosmic tracks recorded with the CMS magnet at 3.8T. A comparison is made between the alignment constants obtained in the final alignment using 2017 data, and the alignment constants obtained by aligning the tracker using cosmic tracks recorded with the CMS magnet at 0T and at 3.8T before the start of proton-proton collisions in 2018. The mean and width of the distribution are significantly improved after the alignment with cosmic tracks.

# Alignment constants derived with data collected until the beginning of August 2018

Performance figures of the tracker alignment for the first part of the 2018 data-taking period are presented. The alignment constants are compared with those used at the time of data taking.

The alignment constants used at the time of data taking were obtained with cosmic-ray data taken prior to pp operation and collision data at the beginning of the 2018 data taking period. Time- dependent movements of the large scale structures of the pixel detector are corrected by an automated "prompt calibration loop"-procedure, described in more detail in reference [2.

The alignment constants obtained using data taken during the 2018 data-taking period until the beginning of August 2018 were derived using cosmic tracks, minimum-bias pp collision events, pp collision events with isolated muons and pp collision events with Z$\rightarrow\mu\mu$ decays. Time-dependent effects are taken into account.

### Comparison of module positions

Figure in PNG format (click on plot to get PDF) Description
Difference in the positions of the modules between the alignment constants used during data taking and the alignment constants obtained after aligning the tracker. The change in the z coordinate between the constants obtained after aligning the tracker and the alignment constants used during data taking is shown as a function of the coordinate r in the alignment constants used during data taking. Each point represents a module. The colours correspond to the different sub-detectors of the tracker, and match the colours used in the tracker layout shown above. The alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The large spread in movements in the tracker endcaps is due to noise. This module position comparison shows that the alignment procedure shifts the position of the barrel pixel detector.

### DMR validation

Figure in PNG format (click on plot to get PDF) Description
The distribution of median residuals is plotted for the local x’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.
The distribution of median residuals is plotted for the local y’ -direction in the barrel pixel detector (BPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.
The distribution of median residuals is plotted for the local x’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.
The distribution of median residuals is plotted for the local y’ -direction in the forward pixel detector (FPIX). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.
The distribution of median residuals is plotted for the local x’ -direction in the tracker inner barrel (TIB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.
The distribution of median residuals is plotted for the local x’ -direction in the tracker outer barrel (TOB). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.
The distribution of median residuals is plotted for the local x’ -direction in the tracker inner disks (TID). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.
The distribution of median residuals is plotted for the local x’ -direction in the tracker endcaps (TEC). The red line shows the results using the alignment constants used in data taking. The blue line shows the results using the alignment constants obtained after aligning the tracker. The exact alignment constants are time-dependent, those used here were obtained for data taken from 18-19 May 2018. The quoted means $\mu$ and standard deviations σ are the parameters of Gaussian fits to the distributions. Aligning the tracker improves the standard deviation.

### Primary vertex validation

Figure in PNG format (click on plot to get PDF) Description
Mean track-vertex impact parameter in the transverse plane as a function of track azimuth $\phi$. The impact parameters are obtained by recalculating the vertex position after removing the track being studied from it, and considering the impact parameter of this removed track. The red points show the results with the alignment constants as used during data taking, the blue points show the results using the alignment constants obtained in the alignment procedure. The alignment constants are time-dependent, those used here were obtained for data taken during 30-31 May 2018. Modulations visible in this distribution with the alignment constants considered during data-taking are improved with the aligned tracker.
The mean of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker improves the mean of this distribution.
The RMS of the average impact parameter in the longitudinal plane versus track azimuth $\phi$, as a function of integrated luminosity. The vertical black lines indicate changes in the calibration of the local hit reconstruction in the pixel tracker. The blue points show the results with the alignment constants used during data taking, the red points show the results with the alignment constants as obtained in the alignment procedure. Aligning the tracker reduces the RMS.

### Cosmic-ray data at 0T

Figure in PNG format (click on plot to get PDF) Description
Unbiased track-hit residuals for 0T tracks in BPIX x'. After the first alignment of the barrel pixel high-level structures (cyan triangles) both the bias and the width of the distribution are strongly reduced with respect to the geometry assumed before performing any alignment (black circles). The width of the distribution is further reduced after aligning the full pixel tracker down to the level of single modules (red squares). The mentioned alignments have been performed using 0T cosmic-ray tracks.
Unbiased track-hit residuals for 0T tracks in BPIX y'. After the first alignment of the barrel pixel high-level structures (cyan triangles) both the bias and the width of the distribution are strongly reduced with respect to the geometry assumed before performing any alignment (black circles). The width of the distribution is further reduced after aligning the full pixel tracker down to the level of single modules (red squares). The mentioned alignments have been performed using 0T cosmic-ray tracks.
Unbiased track-hit residuals for 0T tracks in FPIX x'. After the first alignment of the forward pixel high-level structures (blue triangles) both the bias and the width of the distribution are strongly reduced with respect to the geometry assumed before performing any alignment (black circles). The width of the distribution is further reduced after aligning the full pixel tracker down to the level of single modules (red squares). The mentioned alignments have been performed using 0T cosmic-ray tracks.
Unbiased track-hit residuals for 0T tracks in FPIX y'. After the first alignment of the forward pixel high-level structures (blue triangles) both the bias and the width of the distribution are strongly reduced with respect to the geometry assumed before performing any alignment (black circles). The width of the distribution is further reduced after aligning the full pixel tracker down to the level of single modules (red squares). The mentioned alignments have been performed using 0T cosmic-ray tracks.

# References

1. CMS Collaboration "The CMS experiment at the CERN LHC" JINST 3 (2018) doi:10.1088/1748-0221/3/08/S08004
2. G. Cerminara, B. van Besien "Automated workflows for critical time-dependent calibrations at the CMS experiment" J.Phys.Conf.Ser. 664 (2015) no. 7, 072009 doi:10.1088/1742-6596/664/7/072009
3. CMS Collaboration "Alignment of the CMS tracker with LHC and cosmic ray data " 2014 JINST 9 P06009 doi:10.1088/1748-0221/9/06/P06009

-- AdeWit - 2018-10-25

• Zmm_ReReco.png:

• Zmm_Prompt.png:

• mgr_r_vs_dz_tracker_1_customised.png: