Charged Particle Tracking in Real-Time Using a Full-Mesh Data Delivery Architecture and Associative Memory Techniques_2

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Charged Particle Tracking in Real-Time Using a

Full-Mesh Data Delivery Architecture and Associative

Memory Techniques

Sudha Ajuhaa, Ailton Akira Shinodaa, Lucas Arruda Ramalhoa, Guillaume Baulieub,

Gaelle Boudoulb, Massimo Casarsac, Andre Cascadana, Emyr Clementd, Thiago Costa

de Paivaa, Souvik Dase, Suchandra Duttaf, Ricardo Eusebig, Giacomo Fedih, Vitor

Finotti Ferreiraa, Kristian Hahni, Zhen Huj, Sergo Jindarianij*, Jacobo Konigsberge,

Tiehui Liuj, Jia Fu Lowe, Emily MacDonaldk, Jamieson Olsenj, Fabrizio Pallah, Nicola

Pozzobonl, Denis Rathjensg, Luciano Ristorij, Roberto Rossinl, Kevin Sungi, Nhan

Tranj, Marco Trovatoi, Keith Ulmerk, Mario Vaza, Sebastien Viretb, Jin-Yuan Wuj,

Zijun Xum, and Silvia Zorzettii

aUNESP - Sao Paulo State University, Sao Paulo, Brazil

bInstitut de Physique Nucleaire de Lyon (IPNL), Lyon, France

cINFN Sezione di Trieste, Trieste, Italy

dUniversity of Bristol, Bristol, United Kingdom

eUniversity of Florida, Gainesville, Florida, USA

fSaha Institute of Nuclear Physics, HBNI, Kolkata, India

gTexas A&M University, College Station, Texas, USA

hINFN Sezione di Pisa, Pisa, Italy

iNorthwestern University, Evanston, Illinois, USA

jFermi National Accelerator Laboratory, Batavia, Illinois, USA

kUniversity of Colorado Boulder, Boulder, Colorado, USA

lINFN Sezione di Padova, Universita‘ di Padova, Padova, Italy

mPeking University, Beijing, China

October 7, 2022

∗

Abstract

We present a ﬂexible and scalable approach to address the challenges of charged

particle track reconstruction in real-time event ﬁlters (Level-1 triggers) in collider

physics experiments. The method described here is based on a full-mesh architecture

for data distribution and relies on the Associative Memory approach to implement

a pattern recognition algorithm that quickly identiﬁes and organizes hits associated

to trajectories of particles originating from particle collisions. We describe a suc-

cessful implementation of a demonstration system composed of several innovative

hardware and algorithmic elements. The implementation of a full-size system relies

on the assumption that an Associative Memory device with the suﬃcient pattern

density becomes available in the future, either through a dedicated ASIC or a mod-

ern FPGA. We demonstrate excellent performance in terms of track reconstruction

eﬃciency, purity, momentum resolution, and processing time measured with data

from a simulated LHC-like tracking detector.

∗Corresponding author, sergo@fnal.gov

arXiv:2210.02489v1 [hep-ex] 5 Oct 2022

Contents

1 Introduction 2

2 Overview of the Approach 4

2.1 DataProcessingStages ............................ 4

2.2 Assumptions .................................. 5

3 Data Delivery 7

3.1 TriggerTowers ................................. 7

3.2 FullMeshArchitecture............................. 9

4 Pattern Recognition and Track Fitting 10

4.1 SuperstripDeﬁnition .............................. 11

4.2 Generation of the Pattern Bank . . . . . . . . . . . . . . . . . . . . . . . . 12

4.3 Pattern Bank Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.4 TrackFitting .................................. 16

4.5 DuplicateRemoval ............................... 17

5 Demonstration System 17

6 Results 20

6.1 SystemLatency................................. 20

6.2 TrackingPerformance.............................. 21

7 Additional Studies 25

7.1 AM+Hough Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 26

7.2 Using Local Bend Information in AM . . . . . . . . . . . . . . . . . . . . . 28

8 Summary 28

9 Acknowledgements 30

A Demonstration Hardware 31

1 Introduction

Most high-energy physics experiments, such as those carried out at hadron colliders,

are exposed to ever increasing luminosity. Due to the large size, complexity, and high

granularity of their various detector components, the amount of data acquired by these

experiments can be staggering. As a result, recording and processing every collision event

is practically impossible. It is also not necessary since most of the events are not of

interest to the physics program. Collider experiments have dealt with this diﬃculty by

implementing real-time event selection methods, called triggers, that reduce the amount

of data to levels manageable for storage and oﬄine processing while recording most of the

events relevant for physics analyses. These triggers are critical to the success of the physics

program of the experiments, as they allow selecting only events with which important

measurements or discoveries can be made. To this end, the real-time reconstruction

of all physics objects in each event has to be carried out as fast and as accurately as

possible. Triggers are typically designed so that decisions are made in sequential steps.

Each successive step, or level, handles a signiﬁcantly reduced event rate with respect to

the previous one and has access to more detailed information.

For example, the trigger systems of the current Large Hadron Collider (LHC) experi-

ments will continue to face increasingly complex requirements. In order to vastly expand

the physics reach of the ATLAS and CMS experiments, the LHC and the experimental

collaborations are pursuing an immense upgrade program with an expected completion

date of 2029. This will usher the so-called HL-LHC era (for High-Luminosity LHC) during

which the luminosity will increase by a factor of ﬁve relative to the Run 2 instantaneous

luminosity, resulting in an average number of proton-proton collisions per bunch crossing,

referred to as pileup, of approximately 200. To contend with such a serious increase in

proton-proton collision rates, and the correspondingly high detector occupancy, several

components of the ATLAS and CMS experiments will have to be upgraded. In particular,

the trigger systems need to undergo a signiﬁcant redesign [1–3]. Looking even further into

the future, the anticipated detector complexity and beam background conditions at the

high-energy colliders proposed beyond the LHC (FCC-hh, SppC, muon collider) will be

orders of magnitude higher than those at the HL-LHC, further exacerbating the problem

of real-time reconstruction.

The ability to reconstruct trajectories of charged particles in the trigger system and

to measure their transverse momenta (pT) with high precision can be a powerful asset as

this signiﬁcantly improves the pTmeasurement of leptons and jets, which are otherwise

measured much less accurately. This in turn means that the set of collision events with

such objects required to pass a certain pTthreshold in the trigger will be selected more

accurately, providing control over the trigger selection rate. An alternative to this would

be to require higher pTthresholds, which would lead to a reduction of events relevant

to the experiment’s physics program. Therefore, the implementation of a track trigger

system at HL-LHC and future collider experiments is important to the preservation, and

even the expansion, of programs that include extensive explorations at the electroweak

scale and the study of new processes with potential for discoveries.

The implementation of a Level-1 (L1) track trigger system is extremely challenging

due to the high rate of collision events, the amount of data produced in each event,

and the requirement for few microsecond processing time. The expected data rates from

the detector to the trigger electronics at the HL-LHC experiments are of the order of

100 Terabits per second (Tb/s) [1]. Prior to the start of track reconstruction, the data

need to be organized and distributed so that all energy deposits from charged particles,

referred to as hits, from a particular region of the tracker and from the same bunch

crossing are located in the same electronics processor board at the same time. To solve

this complex problem, a massively parallel data distribution and processing architecture

is needed. Such an architecture has to have the capability to simultaneously handle events

originating from diﬀerent bunch crossings (time multiplexing) as well as diﬀerent physical

detector regions within the same bunch crossing (regional multiplexing). It also has to

be ﬂexible and scalable in order to accommodate possible future changes, upgrades, or

unforeseen operating conditions. The challenge is to reconstruct all tracks above a low pT

threshold (of about 2 GeV) with high eﬃciency, purity, and momentum resolution that

are as close as possible to the quality of the oﬄine reconstruction.

In what follows, we describe a platform to demonstrate track reconstruction at the

L1 trigger for experiments running in an environment similar to what is expected at

the HL-LHC. Section 2 provides a general description of the approach and the speciﬁc

assumptions made for the development of the presented solution. Sections 3 and 4 provide

an overview of the full-mesh data delivery scheme and the Associative Memory (AM)+

FPGA approach, and include the studies and novel algorithmic concepts tried in order to

optimize the performance of the system. Section 5 describes the hardware and ﬁrmware

used for the demonstration setup, with its results presented in Section 6. Additional

simulation studies to further improve the performance of such a system are presented in

Section 7, and the paper concludes with a summary in Section 8.

The approach presented in this paper is one of three approaches described in the

Technical Design Report of the Phase-2 upgrade of the CMS tracker [1]. However, the

focus of this paper is more on the conceptual features of the approach and its scalability,

which can serve as guiding principles for addressing L1 tracking needs of future high-energy

collider experiments. The studies presented here were performed with a demonstration

setup at Fermilab.

2 Overview of the Approach

2.1 Data Processing Stages

The approach described in this paper is directly applicable to a generic tracking detector

with silicon sensors; however, it could also be applicable to other pattern recognition

problems in which execution speed is paramount.

Our approach utilizes a full-mesh architecture for eﬃcient data distribution and relies

on AM, implemented in fast electronics chips [4], to handle pattern recognition and the

rapid growth of pattern complexity with hit occupancy. In this paper, we refer to this

approach as AM+FPGA; however, it should be noted that the full-mesh architecture is

generally compatible with other (non-AM) pattern recognition schemes.

An approach based on AM was implemented successfully in the CDF experiment [5]

during Run 2 of the Tevatron in a real-time trigger that selected tracks originating from

secondary vertices produced by the decay of bottom and charm hadrons [6, 7]. The

challenge is that real-time track reconstruction at the HL-LHC is much more complex

than what the CDF experiment had to contend with: not only is the collision rate much

higher, but also the number of electronic channels is orders of magnitude larger.

The AM+FPGA approach can be described as a sequence of three processing stages:

data delivery, pattern recognition, and track ﬁtting. In the data delivery stage, the data

from the tracker back-end electronics are formatted and distributed so that all hits that

originate in a certain geometric region of the detector and belong to the same bunch cross-

ing, are brought simultaneously to a Data Organizer (DO) unit for common processing.

The pattern recognition stage involves selecting those hits that were potentially created by

the same charged particle. To do that, each layer of the tracking detector is subdivided

into coarse groupings of silicon strips (superstrips) which are then linked across layers

into patterns that correspond to probable trajectories of charged particles through the

detector. The set of all most likely patterns produced by charged tracks is obtained from

simulation and loaded into the Associative Memory, implemented in an ASIC or FPGA.

The AM provides a very fast way to simultaneously recognize all those patterns that were

produced by the tracks created in the collisions and reject all hits that do not belong to

any of those patterns. Each pattern recognized by the Associative Memory is grouped

together with all the hits that fall within that pattern to form a road. The roads are sent

Figure 1: One quadrant of the CMS tracker geometry used for the demonstration. Only

the Outer Tracker modules shown in red and blue are providing data for L1 track recon-

struction.

to the track ﬁtting stage, where the hits are used to extract track parameters from the

coordinates of the stubs [7].

Track ﬁtting is implemented in FGPAs [8] downstream from the pattern recognition

stage. The Combination Builder (CB) generates all possible combinations of hits within

each road. The hits from each combination are then input to a number of linearized χ2

track ﬁtters (TF). The coeﬃcients used in the linearized ﬁts are pre-determined from a

principal component analysis (PCA) of simulated tracks. Mis-reconstructed tracks that

do not correspond to particles are referred to as fake tracks and suppressed by requiring

good quality of the ﬁt. Some tracks may be reconstructed multiple times in this procedure.

Such duplicate tracks are removed by selecting the track with the best χ2probability from

sets of tracks that contain hits in common.

2.2 Assumptions

In this section, we describe the detector conﬁguration and provide key speciﬁcations for

the demonstration. While it is important to state them here, we stress that the presented

approach is largely independent of the speciﬁcs of the tracker geometry and of the data

formatting schemes in the detector front-end electronics.

We use a right-handed coordinate system, with the origin at the nominal collision

point, the x-axis pointing to the center of the collider ring, the y-axis pointing up (perpen-

dicular to the collider plane), and the z-axis along the counterclockwise beam direction.

The polar angle θis measured from the positive z-axis and the azimuthal angle (φ) is

measured from the positive x-axis in the x-yplane. The radius (r) denotes the distance

from the z-axis and the pseudorapidity ηis deﬁned as η=−ln[tan(θ/2)].

For the purpose of the speciﬁc study presented here, we consider a geometry consist-

ing of six cylindrical barrel layers in the central region, with modules aligned along the

beam direction, and ﬁve endcap discs on each side of the barrel, with modules aligned

perpendicular to the beam direction. This geometry is shown in Fig. 1 and was initially

proposed for the HL-LHC upgrade of the CMS tracker and was later modiﬁed [1]. This

paper focuses primarily on track reconstruction in the barrel part of such a detector, cor-

responding to the pseudorapidity region |η|<1.0. However the techniques can be easily

extended into the endcap region.

The vast majority of hits in hadron collisions originate from particles with low trans-

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ChargedParticleTrackinginReal-TimeUsingaFull-MeshDataDeliveryArchitectureandAssociativeMemoryTechniquesSudhaAjuhaa,AiltonAkiraShinodaa,LucasArrudaRamalhoa,GuillaumeBaulieub,GaelleBoudoulb,MassimoCasarsac,AndreCascadana,EmyrClementd,ThiagoCostadePaivaa,SouvikDase,SuchandraDuttaf,RicardoEusebig,Giacom...

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Charged Particle Tracking in Real-Time Using a Full-Mesh Data Delivery Architecture and Associative Memory Techniques_2

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