A Level 1 Tracking Trigger for the CMS Experiment

The second decade of Large Hadron Collider operations, from about 2020 onwards, envisages a remarkable increase in collider instantaneous luminosity, one order of magnitude above the project one. This luminosity increase presents several challenges to the LHC experiments. The present Tracker of the Compact Muon Solenoid experiment must be replaced with a system providing excellent tracking quality at higher luminosities, as well as Tracking Trigger inputs to the existing "Level 0" CMS Trigger system at the full 40 MHz bunch-crossing rate. The minimal requirements for a Tracking Trigger would be the capability to confirm the presence of high-pT tracks associated with Calorimeter and/or Muon Level 0 Triggers. The ability to provide effective isolation criteria may also be required, and would in any case substantially improve the Trigger performance. 
Maintaining the data rates generated by Tracking Trigger inputs within a manageable bandwidth requires sensor modules able to locally sparsify the data. Measuring at detector module level the track direction in the transverse plane, and hence deriving its transverse momentum, is the most promising solution to provide such a detector-embedded data reduction feature. These so-called "pT-modules"' would only transmit to the Level 1 Trigger "stubs", pairs of correlated hits in two closely separated sensors, derived by tracks with pT above a given threshold. To exemplify, a 2 GeV/c threshold would cut data rate of more than a factor 10, hence providing a data rate well within the capabilities of present data links. 
The pT-modules design discussed in this work consists of two, closely spaced segmented silicon sensors, featuring both pattern hit correlation across the module and a single hit position resolution high enough to compute stubs with the required accuracy to resolve track directions despite a lever arm of about only 1 mm. A concept Tracker layout, the so-called "Long Barrel", consisting in an Outer Tracker completely built out of pT-modules, has been proposed. The Long Barrel Tracker is particularly flexible in simulation studies of Tracking Trigger as it allows for information from several layers of the Tracker to be combined in a projective geometry. For this reason, it is meant as a testing ground to compare the performance of different designs and configurations. The Long Barrel layout also allows the generation of even more structured Trigger Objects such as "tracklets", consisting of pairs of stubs in opportunely paired layers, which can in turn be used as seeds to generate "Level 1 tracks", including even more stubs. 
The choice of stacked sensors for pT-modules has been recently strengthened by test beam results obtained with novel prototypes of Monolithic Active Pixel Sensors and reported in this thesis. The developement of Tracking Trigger simulations is also presented as a major step towards the design of a realistic Trigger capable Tracker upgrade. A particular challenge for the Trigger system is given by tau leptons produced in many rare processes searched at the LHC. The performance of a Tracking Trigger on final states with tau leptons will be crucial at very high luminosities and is presented at the and of this document as the natural step forward in the work on the subject.


Introduction
A luminosity upgrade of the CERN Large Hadron Collider 1 is expected to take place in two phases. 2,3 The typical collider luminosity will then range from L ≃ 5 × 10 34 cm −2 s −1 to 10 35 cm −2 s −1 , instead of the design one of 10 34 cm −2 s −1 . The current CMS tracker 4 was not designed to operate in such an environment: radiation damage and data losses will necessitate the replacement of the Pixel Detector in about 5 years, while novel trigger strategies will be needed when the event rate starts exceeding the scale of GHz. As an example, the maximum allowed Level 1 (L1) muon trigger bandwidth, for nominal LHC conditions, is 12.5 kHz, a rate that can be kept under control at L ≃ 5 × 10 34 cm −2 s −1 using full Muon System information but which will become much larger at L ≃ 10 35 cm −2 s −1 , requiring also the use of information from the tracker to overcome this limitation. Without upgrading the L1 trigger, the 12.5 kHz rate will be obtained imposing muon 2 p T thresholds at values larger than 60 GeV/c, which will eventually reject all the interesting events. The main goals of the L1 tracking trigger are the reduction of the overall data rate and the completion of muon and calorimeter L1 triggers to identify relevant trigger objects such as leptons. The first one can be achieved building L1 trigger primitives, independent on the tracker layout, rejecting hits from low p T tracks, while the accomplishment of the second one will need dedicated online tracking and vertexing algorithms.

On-Detector Data Rate Reduction
One promising strategy to reject hits from low p T tracks relies on pattern hit correlation in closely placed sensors. 5 Simulations of pp collisions at √ s = 14 TeV show that the 95% of tracks leaving hits in silicon sensors at radius R ≃ 30 -50 cm from the beam have p T < 2 GeV/c. The lateral displacement of hits from a p T = 2 GeV/c track in sensors at R ≃ 50 cm separated by ∆R ≃ 1 mm is about 100-150 µm, corresponding to the typical pitch of current pixels and strips of the CMS tracking system. Silicon tracker modules capable of performing the necessary hit correlation to identify low p T tracks based on this concept, called "stacked modules" or "p T -modules", are currently being designed. Two experimental proofs-of-principle took place in 2010. Spare strip modules of the current CMS tracker were bonded together 2 mm apart from each other and used to record the passage of cosmic rays. The angle of incidence of tracks could then be clearly correlated to the separation between measured clusters up to 20 • , an angle analogous to the one of p T = 2 GeV/c tracks at R ≃ 108 cm in a 4 T magnetic field. Another interesting proof of this concept came from pp collision data at √ s = 7 TeV. An offline analysis of hits in stereo double-sided strip modules at R ≃ 70 cm showed that a cut on lateral displacement between clusters could be translated in a p T threshold of few GeV/c with a clear turn-on curve, as shown in Fig. 1. 6 The L1 tracking trigger primitives built by p T -modules are called track stubs. This functionality is being studied both in terms of design of the chip logic (FNAL proposal) and simulations within the framework of CMS analysis software (CMSSW). One of the major proposals within CMS makes use of well-established designs already used in advanced computing electronics. The main requirements for the pipelines used for data transfer are the capability to sustain input data every 25 ns and to be asynchronous in order to avoid the use of additional clocks. A submission of a test chip through MOSIS is expected for spring 2012. 7

3
Simple clustering algorithms are needed to reduce the number of combinatory hit pairs to be matched in order to build stubs. To have them implemented in fast boolean logic, all the strips or pixels over threshold count as a logic "1". The simplest of these algorithms compares the signals from adjacent strips or pixels in the plane transverse to the beam line, requiring that no more than three consecutive positive signals are found between two cells with null content. Other algorithms under preliminary study may be eligible for ∼ 1 mm long pixels and try to include in the cluster also signals from adjacent rows in the sensor. The production of track stubs, according to the FNAL proposal, is based on the comparison between position of clusters in sensors with different length: the outer sensor has longer pixels or strips which are used to give the actual p T discrimination while the shorter ones in the inner sensor are used to locate the stubs in the direction of the beam. The size of search windows are defined by look-up tables (LUT's) depending mainly on the distance from the beam line. LUT-based algorithms, even if easy to implement, are not currently being used within CMSSW in favor of procedures based on p T threshold and backprojection to the luminous region, until the final tracker layout is chosen and LUT's can be optimized. 8 Fig. 1. Proof-of-principle of low p T track rejection with stacked sensors. The correlation between lateral separation of Si strip clusters in the two sides of the second layer of the current CMS Tracker Outer Barrel, and track p T , is shown on the left. The efficiency in selecting tracks as a function of track p T is shown on the right for lateral separations smaller than 1.5 mm. 6

Off-Detector Online Tracking and Vertexing
The track stubs are the actual L1 tracking trigger primitives wich can be combined in a projective geometry to produce objects that can be used in lepton triggers to improve muon system or calorimeter resolutions or to isolate trigger objects from the same detectors. The concept tracker layout used to study this aspect is the so called "long barrel", which consists of the Phase 1 Pixel Detector and of an Outer Tracker composed of 6 barrel-like layers of p T modules. Barrels of stacks are mounted on ladders featuring a lever arm between stacks of ∼ 4 cm and arranged in a hermetic fashion so that data flow to combine stubs together into consecutive stacks is mantained within each ladder, allowing also for redundancy in overlap regions. If the stub production corresponds to the current local trigger, the matching of pairs of stubs together within a ladder into tracklets is analogous to the regional trigger while the full tracking at L1 corresponds to the global trigger idea. There are also other layouts under evaluation and a variety of tools are being developed to help in the decision of the final design. Tracking algorithms at L1 for the long barrel tracker are currently being studied both in the context of the FNAL proposal and CMSSW. In both cases, stubs are used as inputs for track finders and tracklets seed the search. To guarantee a parallel approach, the FNAL proposal requires that the tracker is divided into 15 • sectors so that the bending radius of a track spanning also an adjacent sector (maximizing the search window) corresponds to p T ≃ 2.4 GeV/c, which then becomes a sort of "intrinsic" threshold within the tracking algorithm, as shown in Fig. 2. Straight line approximation of tracklet projection is used to program a cluster of about 20 FPGA's per sector which actually will compose the hardware of the online tracking. On the CMSSW simulations side, the collaboration is 5 currently facing some of the relevant problems in the development of L1 tracking trigger tools, such as optimizing the tracklet builder, defining the seed propagation and the matching windows, handling and removing duplicate tracks, defining the required vertex resolution, assigning momentum information to a track minimizing the number of encoding bits. 9 Moreover, once these simulation tools are realistic in their implementation, an accurate evaluation of fake rates will be needed in order to rely on the candidate physical objects which the L1 trigger will output.

Summary
The effort in developing a L1 tracking trigger for the CMS experiment at the LHC Phase 2 luminosities is dealing with many challenging aspects of the final task to be accomplished. The rejection of low p T tracks by means of pattern hit correlation in closely placed sensors has already undergone proof-of-principle also with collision data. Different options for the trigger modules and the front-end electronics are being designed for test and evaluation. Also the design of an online tracking algorithm to be implemented in FPGA's and coping with a 40 MHz bunch crossing is in progress and based on sound ideas which can be realized with commercial electronics. Different ongoing studies aim at the definition of physical objects to trigger on, and eventually this will be of major interest for the L1 tracking trigger because of its impact on CMS scientific production.