Study of the Clocking Effect in the TRT Alignmentjohnda/Papers/ClockingStudy.pdfApril 15, 2008 – 19:07 DRAFT 3 1 Introduction In 2007 the Atlas community held the Computer System

Draft version 2.0

Study of the Clocking Effect in the TRT Alignment

John AlisonAart HeijboerJoel Heinrich

Joe KrollUniversity of Pennsylvania

Andrea BocciDuke University

April 15, 2008

Abstract

This paper provides a brief discussion of the TRT alignment in the recent CSCalignment challange and describes several studies of the clocking effect, apT de-pendentpT biasing, in the TRT alignment algorithm.

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Contents

1 Introduction 3

2 Nominal Study 5

3 Summary of Other Studies 93.1 Effect of Initial Misalignments . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Different Degrees of freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3 Alignment by layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.4 More Statistics/Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.5 Global Vs Localχ2 method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.6 Radial Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Impact on Tracking 21

5 Conclusions 24

A Rotation Study 25

B Comparison of releases 13.0.30 and 13.x.0 27

C Study of the dependence of the alignment on radial misalignments 28

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1 Introduction

In 2007 the Atlas community held the Computer System Commissioning (CSC) challenge [1], aproject wide test of the software and computing infrastructure required by collisions data taking.Playing a central role in this challenge was the task of the inner detector community to test theiralignment algorithms and calibration procedures on realistic Monte Carlo event samples. Forthis purpose, commissioning events were generated with initial misalignments thought to be trueof a realistic detector installation. In the fall of 2007 the alignment community released an initialset of alignment constants to the collaboration for use in other CSC analyzes, derived from thesecommissioning samples. This study is an attempt to clarify and understand discrepancies seenin these initial alignment constants with the input misalignments known a priori. In particular,it was seen by the alignment monitoring group that when the alignment constants found for theTransition Radiation Tracker (TRT) were included with those of the silicon tracking devices(Pixels and SCT) a systematic biasing of the transverse momentum(pT) of reconstructed trackswith respect to the truepT of the simulated tracks was introduced. A possible explanation ofthe biasing seen is a misalignment effect known as clocking. This note describes a study of theclocking effect in the TRT alignment algorithm (TRTAlignAlg) [2].

In the CSC alignment challenge the alignment of the TRT was done with TRTAlignAlg,in two steps. First the TRT barrel was aligned internally, using tracks that were reconstructedusing only TRT information. Then the TRT barrel and two endcaps were globally aligned tothe rest of the Inner Detector, using tracks common to both the TRT and the silicon subsys-tems. Shortly after the first results of the alignment were released, validation of the alignmentconstants was preformed using the Atlas alignment monitoring package (InDetAlignmentMon-itoring). [3] During the monitoring, it was then seen that when the TRT alignment was includeda pT dependent biasing of trackpT was introduced. When compared to the truth informationnegatively charged tracks tended to be reconstructed with higherpT , whereas positively chargedtracks tended to be reconstructed with lowerpT . This biasing can be seen in the blue lines inFigure 1, where the ratio of reconstructedpT to truepT is plotted as a function of the the truetrack pT , in the TRT barrel, using the alignment constants found for the TRT.

As mentioned above, a possible explanation of this systematic bias is the clocking effect.This effect is part of a larger group of effects that arise when degrees of freedom in the detectoralignment are unconstrained or weakly determined. These so called weakly determined modesare misalignments introduced which change the parametrization of the track from its correcthelical representation to another, different helical representation by systematically altering thetrack parameters. In the case of clocking the detector misalignment is a relative rotation ofdetector layers with respect to others about an axis of symmetry, and the parameter that isbiased is the trackpT .

As a result of how the TRT is aligned, internally first and then with respect to the restof the inner detector, there are a few ways in which clocking can be introduced via the TRT.The first two are via internal or level 2 (L2) misalignments. The TRT barrel is composed ofthree layers of modules, each with fullφ coverage and at increasing radius. A rotation ofthe outer module layers with respect to the inner layers would result in a clocking effect. Inaddition to a rotation of the layers, rotations at the individual module level can also give rise toa clocking effect. Each TRT layer is composed of 32 modules which are aligned individually inthe alignment algorithm. It has been shown Appendix A, that a uniform rotation of all modules

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Figure 1: reconstructedpT over truepT vs truepT for tracks with: no TRT information (black),TRT globally aligned and internally in ideal position (red) and, TRT aligned globally and inter-nally (blue),

about their center of gravity also leads to clocking. The final means by which the TRT mayintroduce the clocking effect is by an overall, global or level 1 (L1) rotation with respect tothe silicon detectors. In this case the TRT may be perfectly aligned internally and give rise toclocking simply by a global misalignment (Appendix A). In principle a clocking type effect,systematically biasing trackpT which is a due to the TRT can come from any one, or anycombination, of these mechanisms.

By referring back to Figure 1 we can get a handle on where the effect is appearing. Herethe lines refer to tracks reconstructed after running the alignment on, only silicon with no TRTinformation(black), the silicon and the TRT at L1 while using the ideal L2 positions for the TRT(red), the silicon and the TRT aligned at L1 and L2 (blue). We conclude from the figure thatlittle or no bias is introduced by a global misalignment of the TRT with respect to the rest of theinner detector, but rather by misalignments internal to the TRT. The remainder of this paper isdevoted to an investigation of the internal L2 TRT alignment towards an understanding of thenature and origin of thepT biasing discussed above and is organized as follows. Section 2 andSection 3 present the results of several studies examining a possible clocking effect in the TRTalignment algorithm. Section 4 places the relevance of the TRT clocking effect in the context oftracking and track performance. Finally, Section 5 presents our conclusions and provides somequestions that remain.

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2 Nominal Study

In order to definitively determine that thepT biasing seen in the CSC alignment is due toclocking in the TRT, and via which mechanism the effect is introduced, the TRT alignmentas done in the context of the CSC challenge was repeated here with a few simplifications.First of all, because it was suspected that the clocking was due to TRT misalignments at L2,the alignment done here was only on the TRT at L2. The silicon detectors were placed intheir ideal positions (ie: corrected for the initial misalignments) and the TRT was correctedfor its global misalignment with respect to the silicon for simplicity. Secondly, because L2misalignments of the TRT in the CSC Monte Carlo data are only included for the barrel, andbecause a significant bias of trackpT from the TRT endcaps was not seen, only the TRT barrelwas aligned in this study. Again with the two TRT endcaps in their ideal positions for simplicity.As mentioned above, when the alignment constants for the TRT were originally produced forthe CSC challenge the TRT was aligned internally using tracks reconstructed with no siliconinformation. In order to determine if the clocking effect is dependent on this use of TRT onlytracks or a more general feature of the algorithm or the TRT geometry, the internal alignment ofthe TRT was done with full, “extended” tracks. That is, the tracks used in the alignment containboth silicon and TRT information.

As in the case for the CSC challenge the alignment was done with the TRT alignmentalgorithm (TRTAlignAlg) using the localχ2 method and with events containing ten muonseach. These multi-muon events were generated from distributions flat inφ , η , and pT (from2 to 50 GeV), but for this study only tracks with an|η | of less than 0.8 were used for thealignment. The alignment was preformed in Athena release 13.0.30 and iterated nine times1)

with 5000 events each, minimizing five degrees of freedom per module (three rotations aboutthe center of gravity and two translations perpendicular to the beam axis). The entire alignmentprocedure was then repeated with nine disjoint event samples2). The initial misalignments of theTRT modules can be seen in Figure 2 where the initial displacements from the ideal, simulatedin the CSC Monte Carlo, are shown for the three TRT layers in the upper and bottom left panels,as well as the projections of these layers into theφ direction in the bottom right panel. It is inthis bottom right panel in which the first type of clocking effect described above would manifestitself. Indeed, here we see that the initial CSC misplacements contain a clocking effect. [4] Thearrows are color coded such that translations parallel toφ in the clockwise direction are red,whereas translations inφ in the counter clockwise direction appear blue. The predominance ofred to blue arrows in this panel indicates that an initial clocking effect is present.

Figure 3 displays the residual misalignments, after the nine alignment iterations for a typicalevent sample. We see that while on the whole the alignment algorithm converges to the correctpositions, that is the module displacements decrease as they approach their correct values, a relicof the original clocking remains in the bottom right panel. Examining this panel we find thatalthough the size of the initial clocking effect is reduced in magnitude the direction is preserved.It is also seen that most of the arrows that were previously misaligned in the counter clockwisedirection are now in the clockwise direction.

1)The number of iterations is dictated by requiring the change inχ2 per degree of freedom from the previousiteration to be below a certian threshold value, throughout this note that value has been taken to be 1

2)The joboptions used in the study described here can be found at/afs/cern.ch/user/j/johnda/public/ClockingStudy/joboptionsNominalStudy.py

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Figure 2: Initial TRT module displacements as simulated for the CSC alignment challenge.

In order to quantify this effect pull distributions inφ were made for each module and forall nine event samples. The pulls are defined as the displacement of the TRT module from theideal position projected intoφ direction divided by the error on that position provided by thealignment algorithm, with a sign depending on direction of the displacement, clockwise beingpositive and counter clockwise negative. The results of all events samples after the alignmentprocedure can be seen in Figure 4, the upper left plot shows the pulls of all layers fitted witha Gaussian, and the pulls layer by layer are seen in the other three plots. Figure 5 shows thecorresponding misalignments associated with the pulls in Figure 4.

The pull distributions show means significantly different from zero, indicating that the align-ment tends to result in a net displacement in clockwiseφ direction, which is identified as aclocking effect. The biasing of the pulls above zero, found when including the different eventsamples, suggests that the clocking seen in Figure 3 is not a result of a statistical fluctuation inthat particular event sample, but a more robust phenomena. Although we see an effect that can

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Figure 3: Residual TRT module displacements after alignment procedure from CSC initialdisplacements for a typical event sample.

be associated with thepT biasing seen above, it remains unclear whether this is purely a func-tion of the initial CSC misalignments, or something more closely associated with the algorithmitself. To gain further insight into this question a number of other studies were conducted, theresults of which are presented in the next section.

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Figure 4: φ pulls for TRT modules after alignment from CSC initial displacements. All layersare shown in the upper left, modules from layer 0 are shown in the upper right, and layers 1 and2 are shown on the bottom

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Figure 5: φ misalignments for TRT modules after alignment from CSC initial displacements.All layers are shown in the upper left, modules from layer 0 are shown in the upper right, andlayers 1 and 2 are shown on the bottom

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3 Summary of Other Studies

In order to better understand the problems described in preceding section, we repeated thealignment procedure described there under various different conditions. The present sectionaims at collecting and presenting all these various studies, in hope of gaining further insightinto how and where clocking arises.

3.1 Effect of Initial Misalignments

To judge the effect of the initial displacements on the residual misalignments, the study de-scribed above in Section 2 was repeated with the detector in different initial positions.

In the first such test that was done, the study presented in Section 2 was repeated with thesame event samples and under the same conditions, however this time the TRT barrel was alsoplaced in its ideal or perfect position, that is, the alignment algorithm was run starting withno initial inner detector misalignments. In order to quantitatively examine misalignments inφ ,pulls distributions for the TRT modules for all nine event samples were made in the same waydescribed above and are shown in Figure 6, with the corresponding misalignments shown inFigure 7. Again we find means differing from zero with errors that are seemingly underesti-mated. Comparing these systematic shifts of theφ pull distributions to those seen in Section 2,we can conclude two things. First, by comparing the magnitudes of the residual clocking foundin the two cases we determine that initial misalignments do play a role in the determining themagnitude of the residual clocking. When starting with a detector which is initially misalignedand contains initial clocking we find a larger residual effect than when beginning in the idealpositions. Secondly, although the size of systematic shifts of the pull distributions are some-what smaller than was seen in Section 2, the clocking effect is still introduced, and in the samedirection, indicating the presence of a component of the clocking effect which is independentof the initial misalignments.

As mentioned above, the CSC Monte Carlo used in these studies contain radial as well asazimuthal misalignments. To gain a deeper understanding of the nature of their role in deter-mining the resulting clocking, the alignment was repeated with the initial CSC misalignmentsprojected in both the ˆr and theφ direction. In the first case the initial displacements are purelyradial and thus no initial clocking is present. For theφ misalignments the opposite is true, asthe initial misalignments introduce the same amount of clocking as is inherent in the nominalCSC misalignments. The alignment procedure as described in Section 2 was then repeated onone of the event samples, using the two initial positions. The results, after nine iterations of thealignment algorithm, are collected in Figures 8 and 9 where the module pulls and misalign-ments alongφ of the resulting detector positions, beginning with different initial positions, areshown for the three layers separately. The circles indicate the mean of the distributions and theerror bars represent the statistical uncertainty on those means.

Figure 8 shows that when the initial alignments are radial theφ pulls resemble those foundwhen using the ideal starting positions, whereas the pulls found starting with the misalignmentsin φ are similar to those when beginning with the nominal misalignments. From this it isconcluded that only the initial misalignments inφ direction, that is only the initial amount ofclocking, plays a role in the determining the residual effect and whatever underlying mechanismis responsible for introducing the level of clocking seen when starting from the ideal position is

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Figure 6: φ pulls for TRT modules after alignment from perfect initial positions. All layers areshown in the upper left, layer 0 is shown in the upper right, and layers 1 and 2 are shown on thebottom

also the dominating mechanism at work when beginning with only radial misalignments.The conclusion that the amount of residual clocking present after running the alignment

algorithm is dependent on the amount of clocking in the initial misalignments was further stud-ied, exploring the relationship in more detail. The alignment procedure as described in Section2was again repeated3) using various initial misalignments. In this case the misalignments usedwere multiples of the nominal CSC misalignment, projected in to theφ direction. That is, theindividual module misalignments used in the CSC data were scaled by a factor, between minusfive and five, and then radial component of the resulting misalignment was removed. The initialmisalignments were projected intoφ direction in light of the conclusion that only misalign-ments in this direction play a role in determining the residual amount of clocking. Figures 10and 11 show the pulls inφ and ˆr as a function of the scale factor used.

The nonzero slopes of theφ pulls seen in Figure 10 indicate the sensitivity of the alignmentalgorithm on the initial module positions. As the amount of clocking varies from five times theinitial CSC clocking, through no clocking in the ideal positions, to five times the initial clockingin the opposite direction, the remnant effect decreases to near zero for all layers and then turnsover resulting in clocking of an opposite sign than was seen above. The horizontal displacementof the three lines above the origin corresponds to the component of the effect independent ofinitial misalignments, seen in the clocking found when starting from the perfect positions. Incontrast, the ˆr pulls seen in Figure 11 show an independence of a radial expansion or contractionon the initialφ misalignment4).

3)Here the alignment procedure was done in release 13.x.0, see Appendix B for a comparison of clocking foundthere to 13.0.30

4)Appendix C repeats the study just described using radial, rather thanφ , misalignments

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Figure 7: φ misalignments for TRT modules after alignment from perfect initial positions. Alllayers are shown in the upper left, modules from layer 0 are shown in the upper right, and layers1 and 2 are shown on the bottom

3.2 Different Degrees of freedom

Along with the initial misalignments, another aspect of the alignment which may provide aclue as to how clocking is being introduced is the number of degrees of freedom being aligned.Throughout the studies described thus far each module has been aligned using five degrees offreedom. To determine if the clocking seen is due solely to a particular degree of freedom, orwhether an interplay among them is responsible, the alignment was repeated using differentvariations on these degrees of freedom.

Figures 12 and 13 presents theφ pull distributions and the residual misalignments of sev-eral such studies. Each of these studies were done with the same event sample and using thealignment method of Section 2 starting with the nominal CSC misalignments, varying only thedegrees of freedom aligned. The first bin shows theφ pulls when all five degrees of freedom arefit.5) Due to the geometry of the TRT, translations along the z axis of the modules are basicallyunconstrained and for similar reasons small rotations of the TRT about the global x and y-axesare also poorly determined by the alignment algorithm, but normally fitted for when doing thealignment at L2. It could be imagined that the extra freedom in theχ2 fit provided by these twopoorly constrained rotations can produce or enhance a possible clocking effect. However in thesecond bin, which shows the result of the alignment using only the well constrained degreesof freedom, translations in x and y and rotations around the z-axis, we find that theφ pulls areessentially unchanged and conclude that the clocking seen here is independent of the poorly

5)The discrepancy in the magnitude of the mean of pull distributions shown in Figure 12 for all 5 dof and inFigure 8 for the nominal misalignments, is due to the discrepancy in Athena release used. The studies shown inthis graph were done in 13.x.0, whereas those presented in Figure 8 were with 13.0.30. See Appendix B

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CSC Nominal Misalignments Perfect Positions Only Radial Misalignments MisalignmentsφOnly

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constrained degrees of freedom.The appearance of the effect is further isolated by running the alignment using only trans-

lations. The third bin shows the results for this case. Here again, we find no major discrepancywith the φ pulls seen for the alignment of five degrees of freedom. This result indicates thatthere is almost no sensitivity of the magnitude of the clocking effect to aligning rotations aboutthe module z-axis. Appendix A shows that such rotations can indeed lead to a clocking effect,however from bin three of Figure 12 it is concluded that the effect studied in this note is notintroduced through this mechanism.

Finally, the alignment was done using only one degree of freedom, translations inφ . Thelast bin shows theφ pulls when starting with the modules constrained to be in their correctradial positions, because the alignment in ˆr is not being done, but using the same amount ofmisalignment inφ , found the nominal case. The similarity, in the pull distributions when align-ing all with five degrees of freedom to what is seen in this fourth bin, shows that almost all ofthe clocking seen above stems from the alignment (or lack thereof) of module translations in theφ direction and that the effect of cooperation among other degrees of freedom plays a negligiblerole in introducing or enhancing the effect.

3.3 Alignment by layer

In the previous section we saw that the clocking effect seen was due to module translations inφ . In this section we examine another aspect of the TRT alignment through which this typeof clocking effect can be studied, the correlations between the module layers. The clockingdescribed thus far has been a collective effect of all three TRT module layers. Figures 14 and 15show theφ pulls and the residual misalignments of the modules resulting from aligning differentcombinations of the TRT barrel layers. The alignment was done beginning with the nominalmisalignments for the modules in the layers being aligned, and the modules layers which werenot aligned were restricted to their correct positions.

The conclusion drawn from Figure 14 is that the clocking effect described in this note is

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indeed a collaborative effect among all three layers. When the layers are aligned individually,the resulting misalignments inφ are much smaller than that seen when aligned in unison. Whenaligned in pairs the implication of theφ pull distributions is not as obvious. The explanationof the pulls given here is that the clocking effect tends to be larger when aligned in pairs,however the restriction of the third layer to be in the ideal position has an anchoring effect onthe resulting clocking. When only the first two layers are aligned the outer module layer andthe silicon detectors serve as fixed points, inhibiting clocking. Similarly when inner and outermodule layers are aligned, the fixed middle layer serves as a barrier to conspiring misalignmentswhich could preserve the helical form of the fitted tracks, and results in clocking similar tothat seen when aligning the layers individually. However, in the case when the outer modulelayers are aligned there is nothing fixing the module positions at larger radii or prohibitingcollaboration of the two modules, giving rise to a larger effect than when aligned individually.Adding the additional inner module layer further enhances the effect, bringing the magnitudeclocking effect up to which was has been presented above.

3.4 More Statistics/Iterations

All the studies described thus far have involved the same basic alignment procedure, using 5000multi-muon events and iterating the alignment algorithm nine times. Figures 16 and 17 showthe φ pulls and residual misalignments when more statistics or iterations are used. The firsttwo bins give the results of running the alignment from the nominal and ideal positions for nineiterations, whereas the following two bins show the results using twice the iterations. Whenstarting from the nominal misalignment doubling the number of iterations reduces the residualclocking effect to near the level seen when starting from the ideal case. However increasingthe number of iterations has no effect on the resulting clocking when the alignment is begunin the perfect positions. The final two bins show the result of increasing the number of eventsused in the alignment procedure by a factor of ten, to 50000. When using higher statistics the

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Figure 10: Mean of theφ pull distribution vs CSC scale factor. (Misalignment inφ only)

pull distributions are much larger than was seen before, however from looking at the modulemisalignments in Figure 17 we find that the actual displacements from the true positions aresmaller and can conclude that the high shifts seen in theφ pull distributions are driven by thedecrease in the errors.

3.5 Global Vs Localχ2 method

The TRT alignment algorithm TRTAlignAlg computes the alignment constants by minimizingthe χ2 function with respect to the parameters being aligned [2]. TRTAlignAlg supports twoways of doing this, the local and globalχ2 method. In the global method the minimumχ2

condition is linearized, first and second derivatives of theχ2 are calculated with respect to aninitial alignment position, and the second derivative matrix is inverted. The localχ2 approachsimplifies the problem by ignoring correlations between modules, thereby having only to invertmuch smaller matrices. However because the detector elements are not uncorrelated, iterationsare necessary in the local approach to solve for the minimum.

The studies described thus far were done using the localχ2 method. From Figures 18 and19 which compare the two approaches, we can see that running the global method, beginning inthe nominal positions improves the resulting clocking to the level seen when starting from theideal positions. Alternatively, if the global method is run from the ideal positions the results aresimilar to those found when using the local method.

April 15, 2008 – 19 : 07 DRAFT 15

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Figure 11: Mean of the radial pull distribution vs CSC scale factor. (Misalignment inφ only)

3.6 Radial Comments

Throughout this section, and indeed the entire paper, we have been concerned primarily withthe module pulls inφ and have paid little or no attention to the pull distributions in the radialdirection, however referring to Figure 20 we can see that they are fairly insensitive to changesmade to the alignment procedure discussed in this section. It seems that on average the align-ment algorithm tends to move the modules out radially with almost no variation due to the initialmisalignment or the degrees of freedom involved.

April 15, 2008 – 19 : 07 DRAFT 16

All five Dof Only well constrained Dof Only translations) φOnly translations in

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Figure 12: Resultingφ pulls after running the alignment with various degrees of freedom

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Figure 13: Resultingφ misalignments after running the alignment with various degrees offreedom

April 15, 2008 – 19 : 07 DRAFT 17

All three layers Layer 0 Layer 1 Layer 2 Layers 0 and 1 Layers 1 and 2 Layers 0 and 2

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Figure 14: Resultingφ pulls after aligning different combinations of the module layers

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Figure 15: Resultingφ misalignments after aligning different combinations of the module layers

April 15, 2008 – 19 : 07 DRAFT 18

9 Iterations (Nominal) 9 Iterations (Perfect) 18 Iterations (Nominal) 18 Iterations (Perfect) High statistics (Nominal) High statistics (Perfect)

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Figure 16: Resultingφ pulls after aligning for more iterations and with more statistics

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Figure 17: Resultingφ misalignments after aligning for more iterations and with more statistics

April 15, 2008 – 19 : 07 DRAFT 19

Local method (Nominal) Local method (Perfect) Global method (Nominal) Global method (Perfect)

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Figure 18: Comparison of theφ pulls after aligning using the local and globalχ2 methods

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Figure 19: Comparison of theφ misalignments after aligning using the local and globalχ2

methods

April 15, 2008 – 19 : 07 DRAFT 20

13.0.x CSC Nominal misalignments

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Figure 20: Survey of Clocking Study: ˆr pulls

April 15, 2008 – 19 : 07 DRAFT 21

4 Impact on Tracking

In order to address the significance of the size of the clocking effect seen in the studies describedabove, this section examines their impact on tracking. Apart from Figure 1, another way inwhich the clocking effect manifests itself is through its impact on the trackpT pull distributions.Clocking biases positively and negatively charged tracks in opposite ways, causing their pulldistributions to shift apart or separate. Figure 21, shows thepT pull distributions for tracksreconstructed with the ideal geometry(upper left), using the residual misalignments resultingfrom aligning from the perfect positions (upper right), and using the residual misalignments ofnominal study as shown in Figure 3(lower left). ThepT pull distributions shown are defined asthe difference between the true Monte CarlopT and the reconstructedpT , divided by the errorassociated with the reconstructedpT . The plots each contain the same 5000 events and havetracks with an|η | of less than 0.5, insuring that they are reconstructed in the TRT barrel. Pullsfor all tracks(black), and for positive(blue) and negative(red) tracks individually, are shown foreach detector geometry. Indeed, we find in Figure 21 the separation of the means of the pulls forpositive and negative tracks growing from 0.027 in the ideal case, to 0.277 after aligning fromthe perfect situation, further still to 0.494 when beginning the alignment with a realisticallymisaligned detector.

Entries 9245Mean 0.04831RMS 1.299

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Figure 21: pT pulls for: all tracks(black), positive tracks(blue) and negative tracks(red) areshown reconstructed with various detector geometries

As was mentioned above and can be seen in Figure 1, the impact of the clocking effecton the momentum bias varies with the trackpT . What makes the clocking effect particularly

April 15, 2008 – 19 : 07 DRAFT 22

bothersome is that the biasing is worse in tracks with largepT , the ones most interesting froma physics point of view. To see this born out in our studies we have reproduced the trackpT

pull distributions in Figure 21 for tracks at the higher and lower end of our spectrum. Figure 22show the pulls distributions for tracks withpT from 2 to 20 GeV on the left hand side andfor tracks with 40 to 50 GeV on the right. The upper two plots are for tracks reconstructedwith the perfect detector geometry, followed by tracks found using the residual misalignmentin the perfect case, and finally the bottom two plots show the pull distributions for the high andlow pT tracks using the detector after the alignment is run with the CSC misalignments. Asadvertised the separation between tracks with opposite charge grows with theirpT , providingfurther evidence of clocking.

The commissioning samples used throughout the studies presented in this paper containtracks with pT reaching up to 50 GeV, but presumably in similar distributions produced fortracks with higherpT the impact of the effect would be seen to grow further still. At thelevel of the misalignments seen in the studies of Section 2 and 3 we see a clear impact on thereconstructed trackpT ’s and thus in the physics in which one is interested.

April 15, 2008 – 19 : 07 DRAFT 23


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Figure 22: pT pulls for: all tracks(black), positive tracks(blue) and negative tracks(red) areshown reconstructed with various detector geometries and for high and lowpT seperately

April 15, 2008 – 19 : 07 DRAFT 24

5 Conclusions

The internal TRT alignments reached in the recent CSC challenge were shown to give rise toa pT dependentpT biasing. In this note we have seen that this biasing is brought about bysystematic misalignments of modules in the TRT barrel. It was seen that the effect is enhancedby the collaborative effort among modules in different layers and is insensitive to including otherdegrees of freedom in the alignment. Both of the TRTAlignAlg’s methods ofχ2 minimization(local and global) were studied and shown to result in residual clocking when the alignment wasrun beginning with an ideal inner detector geometry. This suggests the presence of an aspectof the TRT alignment problem which is dependent on the inherent detector geometry or eventtopology which leads to clocking.

Throughout this paper we have run the alignment using the highly idealized multi-muonevent samples with negligible noise or background. The clocking effect seen in the TRT align-ment in these simple situations must be viewed as a lower limit to what we can expect usingmore realistic event samples. If improvements are to be made they must come from exploit-ing fundamentally different event topologies or imposing other independent constraints on thealignment problem. Can cosmic events from recent and future milestone runs control or elimi-nate this effect? If so how many tracks are needed to bring the clocking down to an acceptablelevel?

The TRT plays a crucial role in determining the momenta of tracks in the Inner Detector. Inthis note we have attempted to convey how misalignment, both internal to the TRT and relativeto other sub-detectors, can disrupt this determination, and have hopefully provided some insightinto how and why this can happen.

April 15, 2008 – 19 : 07 DRAFT 25

A Rotation Study

As mentioned in Section 1 there are a number of different sources of the clocking effect in theTRT, appearing both as a result of global misalignments and due to misalignments internal tothe detector. In this appendix we examine two of these mechanisms, a L1 rotation of the entireTRT with respect to the rest of the inner detector and rotations of the individual phi modulesabout their center of gravity, in order to determine the size of the induced effect as a function ofthe corresponding misalignments.

Although the entire Inner Detector is insensitive to a global rotation about the beam axis,a relative angle between subdetectors does have a noticeable effect. In particular a rotation ofthe TRT barrel with respect to the other silicon detectors can result in a systematic biasing oftrack pT , the clocking effect. To study the magnitude of this effect the track reconstruction waspreformed with the TRT barrel misaligned with various such a rotations. The results can beseen in Figure 23, where the mean of thepT pull distributions for negative and positive tracksare plotted separately, as a function of the magnitude of the level 1 rotation given to the TRT.The tracks in the pull distributions shown here were required to go through the TRT barrel, andare from 5000 of the CSC muon events described in the main text.

rad)µTRT L1 Rotation (0 20 40 60 80 100 120

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Figure 23: means of thepT pull distributions for positively and negatively charged tracks areshown versus angle of L1 TRT rotation ,

In this context, the size of the clocking effect is identified with the splitting of the means ofthe positive and negative tracks’ pull distributions. Here we see that a L1 rotation introducesclocking and is, in fact, quite sensitive to small angles. With a misalignment of only 80µrad,the separation between positive and negative tracks is already of order oneσ . Although notaddressed further in this paper, the clocking effect is seen to be sensitive to a small relativeangular misalignment of the TRT and silicon trackers and will continue to pose a significantchallenge to eliminatingpT biases in future alignments procedures.

Another means in which the clocking effect is expected to manifest itself is through rotations

April 15, 2008 – 19 : 07 DRAFT 26

of the TRT modules themselves. To study clocking under this guise, the TRT was placed in itsideal position with respect to the silicon, and then varying rotations were given the individualmodules that compose the TRT Barrel. The modules were all rotated by the same angle andabout the axis parallel to the beam pipe and through their center of gravity.

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Figure 24: means of thepT pull distributions for positively and negatively charged tracks areshown versus angle of L2 rotation of TRT modules ,

Figure 24 shows results very similar to those seen in the case of the Level 1 rotations justdiscussed. Here again the clocking effect is seen, and with a large dependence on the Level 2rotation angle. The similarity of the magnitude of the effect in these two cases along with thesmall size of the angles involved, leads us to conclude that to a close approximation that theactual physical movements of the straws associated with the modules is the same for both typesof rotations.

April 15, 2008 – 19 : 07 DRAFT 27

B Comparison of releases 13.0.30 and 13.x.0

13.0.x CSC Nominal Misalignments 13.0.x Perfect Positions 13.x.0 CSC Nominal Misalignments 13.x.0 Perfect Positions

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Figure 25: Survey of Clocking Studies:φ pulls.

Clocking in the TRT was first studied by the present authors in Athena release 13.0.30.Shortly after release 13.0.30, significant changes to the tracking regarding TRT informationwere implemented in Athena versions 13.x.0 and above. These changes included updatingthe errors associated to TRT hits, improving how ambiguities in tracks found in the TRT areresolved, and allowing the left-right assignment of the TRT driftcircles to occur at a later stagein the tracking. To determine what effect these changes had on the TRT alignment, the studiesdescribed in Sections 2 and in the begining of section 3, were repeated on the same events usingthe two different releases. Again, the alignment was done with 5000 CSC multimuon events andfor nine iterations, aligning five degrees of freedom. The results are shown in Figure 25. Thefirst two bins in the figure show the pulls of the resulting module positions after aligning usingrelease 13.0.30 and starting from the nominal CSC misalignments(Figure 2) and the perfectpositions, respectively. The following two bins show the results using the updated tracking inAthena release 13.x.0. Although the improvements made to the tracking seem to reduce theφ

pulls, and hence the resulting clocking, the effect as seen in 13.0.30 is still present with clockingsignificantly different from zero.

April 15, 2008 – 19 : 07 DRAFT 28

C Study of the dependence of the alignment on radial mis-alignments

The impact of the initial misalignments on the residual clocking effect was explored in Sec-tion 3. There the initial misalignments used were multiples of the nominal CSC misalignmentsprojected in theφ direction. This appendix presents the results of a similar study using insteadthe initial misalignments projected in the radial direction.

The results are summarized in Figures 26 and 27. The means of the pull distributions of theφ

and ˆr misalignments are shown as a function of the scale factor used in the initial misalignments.In contrast to the previous findings, using theφ misalignments, in the figures we see almost nodependence of the resulting misalignments on the initial radial positions of the modules. Thisprovides further support to our conclusion that the residual clocking effect is only sensitive toinitial misalignments inφ .

It may have been suspected that the residual misalignments in a particular direction are onlysensitive to initial misalignments in that direction, as was the case in Section 3. However wesee here that along with the misalignments inφ , the ˆr module positions have little reliance onthe initial misalignments.

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Figure 26: Meanφ pull vs CSC scale factor.

April 15, 2008 – 19 : 07 DRAFT 29

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Figure 27: Mean ˆr pull vs CSC scale factor.

April 15, 2008 – 19 : 07 DRAFT 30

References

[1] D. Barberis, ATLAS plans for 2006:Computing System Commissioning and Service Chal-lenge 4, 2006,hep.phys.sfu.ca/~rwalker/ATLAS_SC4_Mumbai.pdf.

[2] A. Bocci and W. Hulsbergen, TRT Alignment for SR1 Cosmics and Beyond, 2007, atl-indet-pub-2007-009.

[3] B. Cooper, T. Golling, B. Heinemann, S. Strandberg, and J. Alison, First lookat Pavel + TRT Alignment,https://hypernews.cern.ch/HyperNews/Atlas/get/IDAlignment/318.html.

[4] A. Bocci and C. Schmitt, TRT Alignment, 2007,http://indico.cern.ch/contributionDisplay.py?contribId=13&sessionId=14&confId=9662.

hep.phys.sfu.ca/~rwalker/ATLAS_SC4_Mumbai.pdf

https://hypernews.cern.ch/HyperNews/Atlas/get/IDAlignment/318.html

https://hypernews.cern.ch/HyperNews/Atlas/get/IDAlignment/318.html

http://indico.cern.ch/contributionDisplay.py?contribId=13&sessionId=14&confId=9662

http://indico.cern.ch/contributionDisplay.py?contribId=13&sessionId=14&confId=9662

Documents

Study of the Clocking Effect in the TRT Alignmentjohnda/Papers/ClockingStudy.pdfApril 15, 2008 – 19:07 DRAFT 3 1 Introduction In 2007 the Atlas community held the Computer System