«STUDENT RESEARCH PAPERS SUMMER 2011 VOLUME 22 REU DIRECTOR UMESH GARG, PH.D. REU Student Research Papers – Summer 2011 University of Notre Dame – ...»
Since this is done with the HLT, the algorithm can be relatively involved and, indeed, is a 5 step process. By ﬁrst starting with the clusters of hits from the pixel and strip detectors, seeds, or two closely spaced hits, are generated from the innermost layer. By projecting the trajectory of the seed outwards, the tracker moves through a pattern recognition phase. After sorting out fake and duplicate tracks with combined data from the other layers, the tracker
To Table of Contentsﬁnally assigns a ﬁt to the track. The pattern recognition requires that a variety of possible paths through the hits be processed. The possible paths can be computed because the solenoid maintains an almost constant, well known magnetic ﬁeld over the tracker volume.
This whole process is eﬀective, but its complexity necessitates that it be implemented in the HLT. For more information on the tracking process, see section 6.4 of the CMS TDR 2006 (p.240) .
3 LHC Upgrade in 2020: SLHC After an extended period of continual operation, the LHC will be shutdown in order to upgrade the machine and its detectors. From 2010 to 2020, known as Phase 1, the LHC will work towards achieving design energy and luminosity. Two long shutdowns will occur in 2013 and 2017 to prepare the machine to reach full 14TeV energy and 2 ∗ 1034 cm−2 /s luminosity. A more substantial upgrade to the machine and detectors will come around 2020, termed Phase 2, in which the machine will have another long shutdown to prepare the LHC and its detectors for a factor of 10 increase in luminosity.  This upgrade in 2020 will move the LHC to the SuperLHC (SLHC). The upgrade will seek to increase luminosity from 1034 cm−2 /s to 1035 cm−2 /s. This will signiﬁcantly increase the number of particle collisions per bunch crossing, mainly by increasing the number of protons per bunch. Currently, CMS is operating at around 8 interactions per bunch crossing.
At SLHC luminosities, there will be on average 200 interactions per bunch crossing, assuming bunch crossings will occur every 25 ns. CMS is not currently outﬁtted to handle such high collision rates. The L1 trigger rate as it is now at CMS ﬂattens out with pT threshold, due to a poor momentum measurement in the current L1 muon system. The detector components are not robust enough to distinguish so many particles at such high occupancy. At luminosities around 1035 cm−2 /s, the current trigger ﬁres at a rate well over 20 kHz for muons, which is hoped to be reduced by a factor of 100 .
After ten years of operation, the inner components of the detector, speciﬁcally the pixel detector and the silicon tracker, will have to be replaced anyway. At this time, these components will have been so signiﬁcantly radiation bombarded that most of the electronics will no longer be fully operational. This is in part due to the fact that the radiation from the collisions will destroy the crystal lattice of the silicon, and thereby fry some of the electronics permanently. The shutdown will provide an excellent opportunity to replace the tracking layers.
As stated previously, the current trigger at CMS uses a two level triggering system, but the new tracking detector will require a new trigger. With SLHC luminosities, the L1
To Table of Contentstrigger would trigger on muons much more often, thus overloading the HLT in its ability to select the important events in which to save. To reduce the load placed on the HLT, there is signiﬁcant interest in implementing track reconstruction in the L1 trigger for the upgrade.
This presents a signiﬁcant challenge, as the hardware necessary would have to be incredibly precise and fast to process the extremely high occupancies in the silicon trackers created by such large amounts of pileup, or additional interactions created per crossing.
Hardware is signiﬁcantly faster than software in analyzing and computing transverse momentum given a set of hits, which gives a motivation for providing tracking information to the L1 Trigger. Once a collection of hits from each event is found, this information can be immediately passed to the L1 trigger composed of high-speed electronics. Through the use of ﬁeld programmable gate arrays (FPGAs), the hardware could quickly sort out matched tracks from fake or incomplete tracks. FPGAs consist of an integrated circuit whose logic can be conﬁgured after production and any time after implementation. Depending on the physics that is being investigated, certain cuts can be placed on the trigger, in which many events can be rejected based on acceptance in pT and location in φ and η of the actual hits by changing the logic in the FPGA.
4 CMS Upgrade Geometry For the purpose of the upgrade, diﬀerent geometries are being investigated for the silicon tracker than the one currently in place at CMS. The silicon tracker geometry that was investigated for this study was long barrel straw-man.  The long barrel extends the full length in the beam direction. In order to cover a complete circle around the beam, the cylinder is divided into alternating sliced layers. The full geometry is shown below.
In this geometry, there are no forward end caps. In order to catch near parallel tracks, four other forward barrel stack layers are added at 180cm in the z direction. The stacks are spaced radially at 32cm, 35cm, 48cm, 52cm, 98cm, 102cm, and with the forward barrel stacks at 64cm, 68cm, 80cm, 84cm. The tracker extends to 275cm in the z direction. Each layer in the above diagrams has two sides of sensors, together that layer makes a stack. A pair of connected hits in a stack is known as a stub. In the upgrade to CMS, there will not be silicon strip detectors, as all layers will use only silicon pixel detectors. The sensors to be used are silicon pixels that are 100µm by 1mm.
4.1 Path Computation Using software release CMSSW 3 3 6, Monte Carlo simulation studies done in Fast Simulation were ﬁrst performed as to how well this geometry could match actual hits with simulation truth information. This was ﬁrst performed with single track events without pileup. For the sake of simplifying the study, η was restricted to 1.2 to exclude the forward barrels. The eﬃciency of ﬁnding all the stubs created for single track 5 GeV/c muons was very close to one hundred percent. Charged pions and electrons at 5 GeV/c were fairly similar to each other, staying around 97 to 93 percent per stub layer. Upon moving to real events, such as high pT QCD events and Higgs to four lepton events, the eﬃciency remained exceptionally high. After this initial testing was completed, conﬁrming the usefulness of the new geometry, a new algorithm was developed based on intersecting concentric circles.
Charged particles in the detector are assumed to travel in perfect circles in the transverse direction due to the magnetic ﬁeld of the solenoid. Due to the symmetry of the cylinders, it is possible to reconstruct the path of the particle in φ given a hit in any layer. For the purposes of this algorithm, it was assumed that tracks that were worth saving made it all the way to the furthest layer in radius, at 102cm, shown in the ﬁgure as r6, and high η events that left stubs in the forward barrel were ignored. From this, a position in φ is calculated per layer by projecting the track back to the vertex. See Figure 4 and Equations 1 and 2 for an example.
Figure 5: Calculating Stub pT
4.2 Stub pT Stub pT is measured by taking the two closely spaced hits in a given stub, and by projecting a circular curve back to the vertex, the curvature from the magnetic ﬁeld gives a transverse momentum. At higher momentum, tracks bend less, and the angle between the hits on a stub becomes signiﬁcantly smaller, reducing the precision in the momentum measurement. At momenta above 50 GeV/c, the diﬀerence between angles becomes so small, the sign of the curvature actually becomes ambiguous, as positive and negative curvatures can no longer be accurately determined. Figure 5 shows how stub pT is visualized.
As shown in Figure 6 (See online for color), momentum resolution quickly falls oﬀ towards higher momentum tracks, around 5 GeV/c, often considered the cutoﬀ for high momentum. If cuts were to be placed on tracks, it is guaranteed that true 2 GeV/c tracks
To Table of Contentswill not be measured above 5 GeV/c, and true 5 GeV/c tracks will not be measured below 2 GeV/c. For the purposes of designing a tracking algorithm, using stub pT measurement as a cut can greatly reduce both the possibilities of stubs for building tracks and thus reducing the chances of ﬁnding fake tracks. Additionally, although not shown, tracks that are 100 GeV/c, will never be measured lower than 10 GeV/c, which can be useful in placing cuts on tracks associated with high momentum used for track ﬁnding to reduce fake tracks.
Figure 6: Range of stub measurements of pT for diﬀerent incident muon energies.
5 CMS Upgrade Tracking Due to the increased luminosity (both instantaneous and absolute), the triggering system needs to improved to handle the increase in detector occupation. The method which was investigated for this is an upgrade to the L1 triggering system which incorporates tracking, and, through this, pT estimation. By incorporating track information into the L1 trigger, the rejection rate for the L1 trigger can be increased signiﬁcantly, which would allow the amount of data being sent to the HLT to remain constant with the increased event rate entering the L1 trigger.
To Table of Contents
5.1 First attempt: Stub pT Matching The ﬁrst method of track ﬁnding we attempted was matching stub pT s from the sixth layer based on a computed uncertainty function in the measurement. For the purposes of this investigation, we are focusing only on the barrel portion of the long barrel, and so the sixth layer refers to the outermost layer. This attempt was not successful, as the momentum uncertainty was very large (and asymmetric) when measured, and so many of the stubs contained overlapping momenta. The uncertainty was so large because the layers forming the stubs are so close together, and so there is little ability to see the eﬀects of the curvature of the particle in a magnetic ﬁeld. This resulted in the algorithm being overwhelmed by the number of matches, and therefore producing little to no interesting information. The number of matches can be decreased substantially by requiring that the stubs lie, with some degree of uncertainty, on a straight line from where they were produced. This is a straight line in the r-z plane, and starts at a z value between -10cm and 10cm, narrowong to a point at the sixth layer. The SLHC interaction point is expected to have an error of 5cm in z.
5.2 Final Approach: Curvature Bins Even using this z cut, matching stub measured pT was unsuccessful in singling out tracks, so we decided to ignore the reported pT at ﬁrst and only use the location of the stubs for information. So instead we started from the assumption that any stub in the sixth layer was formed by a particle starting at the center which passed through all six layers and left stubs.
We then set out to invesigate what pT it might have had. This was done by creating ranges in pT which, when converted to their corresponding curvature and intersected with the lower layers, corresponded to speciﬁc ranges in φ. These ranges in φ are refered to as φ bins. The cut in the z axis was left in, as it still is an eﬀective way to shrink the stub space. We started by creating 100 bins spaced in momentum such that they subtended equal φ ranges.
This caused the momentum resolution to decrease as momentum increased, but this was not unexpected, as particles tend to take paths that approach a straight line as momentum tends toward inﬁnity. When these bins were implemented with no overlap, the eﬃciency vs pT plot contained oscillations due to the fact that some particles with a momentum near the bin boundaries would fail to have all hits in one bin or the other, and so there would not be a hit on each layer in the bin. To ﬁx this problem, we had to deﬁne overlapping bins, which was done by deﬁning the bin centers with a given amount of slop. Slop is a quantity which scales the bin widths linearly in curvature. The lowest and highest curvature bins presented were exceptions, as 0.5 slop corresponds to bins, which completely ﬁll momentum/curvature space, but have zero overlap, while 1.0 slop means that a bin will extend from the center of
To Table of Contentsthe bin before it to the center of the bin after it. This slop value is a parameter which we adjust based on binning. Higher slop values will lead to a higher eﬃciency of track ﬁnding at the expense of a higher fake rate. This method of binning tended to slice the lower part of the momentum spectrum much too ﬁnely, to the point that eﬃciency was lost below 5 GeV/c depending on the exact parameters. If slop was increased to bring this eﬃciency up, then the resolution on the higher end of the pT spectrum was decreased by too large of a factor to be useful.
Our ﬁrst attempt to resolve this issue was to allocate a set number of bins for diﬀerent parts of the momentum spectrum (while still keeping a total of 100 bins), but this merely resulted in the spectrum being sliced too ﬁnely in two spaces instead of one. As this indicated that 100 bins was too many, we decided to merge the lower bins until a speciﬁc threshold was met, but this either did not ﬁx the problem, or created too few bins. Another tack we took was to plateau the pT ranges of the smaller bins, or dynamically increase the slop such that these bin widths never got smaller than a given pT or φ range, but this tended to result in absurdly wide bins at low momenta (the same φ point being covered by 10+ bins). Finally we came to the conclusion that we needed to decrease the number of bins to get eﬃcient φ coverage. We used linear pT steps (of varying size) on the low momentum end of the spectrum and switch over to the equal curvature slicing starting at 10 GeV/c.
In the ﬁnal iteration of this custom binning, there was one bin from 0.1 GeV/c to 2 GeV/c, followed by linear steps of size
0.2 GeV/c from 2 GeV/c to 4 GeV/c, then linear steps from 4 GeV/c to 6 GeV/c of size