Preamble

A track reconstruction algorithm for the EicC central detector Zulun Zhang, Guoming Liu, Yutie Liang, and Aiqiang Guo 3, 4, 1 Preparatory Office of Guang’an Institute of Technology, Guangan 638000, China.

Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China.

Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China University of Chinese Academy of Sciences, Beijing 100049, China This paper presents an algorithm that combines track finding and track fitting, designed for track reconstruc- tion in the Electron-ion Collider in China (EicC). The algorithm’s goal is to fulfill the criterion of high track reconstruction efficiency. The algorithm is modularly constructed, leveraging an advanced cellular automaton model and the Kalman filter method to implement its core functionality. We optimize the algorithm using fully simulated Monte Carlo events in the EicCRoot software framework. The performance of the method is vali- dated, demonstrating excellent track reconstruction efficiency that fully meets the physical requirements of the EicC experiment.

Keywords

Track finding, Electron-ion collider in China, Cellular automaton, Kalman filter

INTRODUCTION

Lepton scattering is an established ideal tool for studying the inner structure of nucleons [ ]. As a future high-energy nuclear physics project, EicC has been proposed [ ]. The primary objectives of the EicC include conducting precision measurements of the nucleon’s structure in the sea quark re- gion, performing 3D tomography of nucleons [ ], explor-

ing the partonic structure of nuclei [ 6 , 7 ], and investigat- 8

ing how partons interact with the nuclear environment [ ]. Additionally, the EicC will also focus on studying ex-

otic states [ 11 – 13 ], particularly those containing heavy flavor 11

quarks. The EicC will operate at a center-of-mass energy range of 15–20 GeV, achieving a peak luminosity exceeding

10 33 cm − 2 · s − 1 while maintaining polarization levels of ap- 15

proximately 80% for electrons and 70% for protons under collider conditions [ ]. Driven by the physics program of EicC, a conceptual design for a general-purpose spectrom- eter is proposed [ ], which has a cylindrical structure, built with different layers around the beam pipe.

Charged particles initially enter the tracking detector, 21

where they interact with sensitive electronics to produce de- 22

tectable signals (or ’hits’). These hits are then analyzed to reconstruct both the particles’ trajectories and their spatial origin. The layout of the vertex and tracking system is de- picted in Fig. . The magnetic field within the tracking detec- tor region is maintained at a strength of 1.5 Tesla, achieved by a superconducting solenoid positioned outside the central detector. This solenoid features a diameter of 3.36 meters and extends to a length of 4.0 meters. Its design ensures an optimal balance between field strength and coverage, provid- ing the necessary magnetic environment for accurate particle This work is supported by National Natural Science Foundation of China (NSFC) under Contracts Nos. 12375194; Guangdong Major Project of Basic and Applied Basic Research No. 2020B0301030008. chang Rd., Lanzhou 730000, China, Contact No.: 18693271981. trajectory measurements. The central tracking system is seg- mented into three distinct regions: the barrel region, the ion- going region (aligned with the positive Z direction), and the electron-going region (aligned with the negative Z direction).

This division reflects the directional motion of the beams: the ion beam progresses along the positive Z axis, while the elec- tron beam travels oppositely along the negative Z axis. The tracking detector in each region is described as follows.

The tracking detector in the barrel region consists of an in- ner silicon layer [ ] and an outer micropattern gaseous detectors (MPGD) layer [ ]. The inner silicon cylinder has three vertex layers and two tracking layers, occupying an area with a maximum radius of 15 cm and a total length of 28 cm. The vertex layer utilizes wafer-scale suture sensors that bend around a beam pipe made of a beryllium cylinder with a radius of 3.17 cm, and the tracking layers also use the same stitched sensors but with different support struc- tures. The outer MPGD has two closely-spaced 2-D layers of Micro-Mesh Gaseous Detector which are chosen to cover

], and technology (Tech.) for the barrel tracking system.

R (cm) Length (cm) Pitch size ( 150(r 150(z) 150(r 150(z) 150(r 150(z) 150(r 150(z) the outermost barrel region. Their mean radii are approxi- mately 48 cm and 77 cm, and their maximum total length of approximately 200 cm. The radii of each layer and their cor- In the forward (ion-going) direction, five silicon tracker disks span z from 25 cm to 134 cm from the interaction point.

Their radial coverage (minimum defined by beam/tube diver- 59

gence, maximum 77 cm) ensures particle tracking. A MPGD

at z = 165 cm provides forward coverage with 8 cm to 150 cm 61

], and technology (Tech.) for the endcap tracking system (ion-going direction).

Rin (cm) Rout (cm) Z (cm) Pitch size ( 165.0 50(r 250(r) The backward (electron-going) direction has five silicon disks. These disks start at 25 cm along the z-axis from the

point of interaction and extend back to 145 cm. The mini- 67

mum radius of the disc is determined by the divergence of the beam tubes, which ensures that they do not interfere with the beam path. The maximum outer radius of the disc is about 77 cm, providing ample coverage to track particles in the reced- ing area. All the geometry parameters and position, as well as the material budget in the two endcap regions, are listed in ], and technology (Tech.) for the end- cap region tracking system (electron-going direction).

Rin (cm) Rout (cm) Z (cm) Pitch size ( The study of transverse momentum dependent (TMD) par- ton distribution functions (PDFs) at the EicC calls for detec- tor and algorithmic capabilities beyond conventional designs.

The central physics goal—to probe the non-perturbative structure of nucleons by measuring hadrons at low trans-

verse momentum ( P hT <

1 GeV

)—imposes stringent re- 82

quirements on track reconstruction performance. This in- volves efficiently reconstructing challenging final states, such as low-momentum leptons from sea quark processes, decay products of heavy-flavor hadrons, and particles at extreme pseudorapidities in exclusive reactions. These demands give rise to two intertwined algorithmic challenges. First, for low

transverse momentum tracks ( p < 0 .

5 GeV

), pattern recog- 89

nition robustness is significantly compromised by multiple 90

Coulomb scattering in the detector material and high cur- vature in the solenoidal magnetic field. This motivates the development of adaptive track fitting algorithms incorporat- ing impact parameter weighting, along with rigorous opti- mization of the detector material budget to reduce scattering- induced resolution degradation. Second, particles at very for- ward angles ( ), essential for reconstructing exclu- sive events, must be distinguished from a high background of beam-gas interactions and diffractive secondaries. To address this, Kalman filter(KF) [ ]-based methods can be employed, leveraging outer tracking information to suppress background noise in the inner detector regions without degrading recon- struction efficiency for true physical signals.

To achieve physics objectives under the EicC’s high-luminosity regime, the tracking software stack must simultaneously maximize re-

construction efficiency ( > 95% ) across a wide momentum 106

range, maintain wide polar angle coverage, and operate with sub-microsecond latency per event. The inherent parallelism of cellular automaton(CA) [ ]-based algorithms makes them well-suited to meet these stringent real-time processing de-

mands, ensuring efficient and fast pattern recognition under 111

high event rates. The CA algorithm is adopted for track reconstruction at the EicC due to its capability in resolving low-momentum and large-angle particles under high occupancy. By model- ing detector hits as spatially correlated cells, the CA naturally avoids combinatorial explosion inherent to KF-based meth- ods while allowing curvature-aware hit merging in solenoid

magnetic fields. This hybrid strategy combining physics- 119

informed cellular evolution enables robust pattern recognition 120

in the EicC’s beam-gas-background-dominated regimes.

The CA method is widely adopted as a track-finding al- gorithm in particle physics experiments. For instance, in the Belle II experiment, signals measured by the Central Drift Chamber are filtered, reconstructed using a CA algorithm,

and subsequently fitted to tracks via a deterministic anneal- 126

ing filter [ Similarly, the CMS experiment employs a parallelized CA-based track-seeding method in its Phase-1 upgraded pixel detector to efficiently resolve combinatorial complexity under extreme pile-up conditions [ Our tracking work for the EicC is contextualized by par- allel developments for the Electron-Ion Collider (EIC) at Brookhaven National Laboratory (BNL).

The EicC’s physics program — prioritizing low- hadron reconstruction and

forward coverage for TMD studies and exclusive reactions — imposes requirements distinct from those of the BNL EIC, which focuses more on high momentum and high-multiplicity tracking. Our CA+KF algorithm is explicitly optimized for these EicC-specific challenges, including robustness at low curvature and high background in forward regions.

has established a similar technical foundation, employing the 141

Acts toolkit with a Combinatorial Kalman Filter for recon- struction and DD4hep for simulation. Their design also pri- oritizes a high-granularity, low-mass silicon tracker for large acceptance, achieving benchmark performance that meets the physics requirements outlined in the EIC Yellow Report [

The ongoing EIC effort to develop realistic pattern recogni- 147

tion and seeding for high-multiplicity events underscores a common challenge for next-generation colliders.

TRACK RECONSTRUCTION FOR EICC

Track reconstruction involves determining the paths 151

of charged particles as they propagate through a particle detector. When particle beams collide, the resulting charged particles move through a gaseous or solid-state medium

under the influence of a uniform magnetic field. The Lorentz 155

force, , acts perpendicularly to both the particle velocity and the magnetic field, causing the particles to fol- low curved trajectories. In the central detector region, where

the magnetic field is typically uniform and perpendicular to 159

the transverse plane, these particles trace out helical paths, as illustrated in the Fig. . The trajectory of the particle’s motion is described by the following equation:

x ( s ) = x 0 + R � cos � ϕ 0 + hs cos λ R

y ( s ) = y 0 + R � sin � ϕ 0 + hs cos λ R

z ( s ) = z 0 + s sin λ

Among them, the parameter is the dip-angle and which is the sense of rotation of the helixis. The projection of this trajectory on the x-y plane is a circle, as shown in the right panel of Fig. . The parametric equation of this circle is:

( x − x 0 + Rcosϕ 0 ) 2 + ( y − y 0 + Rsinϕ 0 ) 2 = R 2 (2) 172

Here, the parameters x 0 and y 0 are the coordinates at s =0, 173

is also related to the slope of the tangent to the circle

at s = 0 . The quantity R represents the radius of the circle. 175

Moving charged particles, e.g. electrons, interact with the

material in a detector and leave behind signals (e.g. ioniza- 177

tion or light). These signals are recorded at specific hits in the detector, typically using layers of sensors arranged in a geometric pattern as shown in Fig . The trajectory recon- struction consists of two parts: track finding and track fitting.

Track finding refers to analyzing the spatial distribution of

these signals (hits) and determining candidate particle trajec- 183

tories. Track fitting involves applying a track model to fit the points associated with a single candidate trajectory in order to determine key particle properties such as momentum, charge, and vertex position.

The process of track reconstruction By leveraging the geometric structure of the EicC detector, we have implemented a tracking algorithm that integrates a CA-based track finding approach with the KF for track fit- ting. CA are computational models comprising discrete grid

cells, each adhering to finite states and evolving through lo- 194

calized rules based on their current state and neighborhood interactions. Their parallelism, ability to model spatial cor- relations via proximity-driven rules, and adaptability to hier- archical patterns make them suitable for high-energy physics track reconstruction [ ]. They efficiently resolve particle trajectories from detector hits by iteratively connect- ing adjacent signals while suppressing noise through local- ized decision-making. Compared to traditional track finding methods, e.g. Hough transform [ ], one of the most sig-

nificant advantages of CA is their inherent parallelism [ 26 ]. 204

In track finding, where large amounts of data from detectors need to be processed simultaneously, the ability to process

many elements in parallel significantly reduces the overall 207

computation time, and CA algorithms can be efficiently im- plemented on parallel hardware, such as Graphics Processing

Units or dedicated parallel computing clusters. 210

The KF is an optimal estimation algorithm used to predict and correct the state of a dynamic system over time, based on noisy or incomplete measurements. It operates recursively by

combining prior knowledge (predictions) with new data (ob- 214

servations) to improve accuracy in estimating unknown vari- ables [ ]. In tracking particles in detectors, its ability to han- dle noisy measurements, estimate the state of a system over time, and optimize trajectory reconstruction makes it highly effective in various experimental scenarios.

This algorithm processes tracks generated by Monte Carlo (MC) simulations [ ]. Utilizing the EicCRoot software framework, which is an object-oriented framework built upon FairRoot [ ], the algorithm reconstructs tracks based on the hits left by simulated tracks on the detector layers. The im- plementation process of the algorithm is shown as follows:

Read all the hits information from the simulation.

Perform the track-finding algorithm by the CA method.

Fit the found track candidates by the KF method to ob- tain the track information.

The application of CA to EicC track finding As previously mentioned, the tracking system of the EicC is divided into three regions: the barrel, the ion-going end- cap, and the electron-going endcap. As shown in Fig. , the

barrel consists of nine layers, the ion-going region has six 234

layers, and the electron-going region contains five layers. To facilitate the processing of hit information across these many

layers, we assign unique identifiers to each detector layer. 237

Specifically, layer IDs in the barrel are numbered from 0 to 8, in the ion-going region from 9 to 14, and in the electron- going region from 15 to 19. The detailed description of the full track finding procedure is presented below.

Silicon Vertex Silicon Tracker MPGD Tracker Support Barrel region Ion-going region E-going region R [m] Z [m] Graph list Frequency (%)

• Definition of graph 242

A graph is a data structure that encodes information about all detector layers, the pairs of adjacent layers, and the root layer through which the particle travels.

The root layer refers to the first detector layer a par- ticle traverses after the collision. The construction of

the graph is a crucial step in the algorithm’s initial- 248

ization process, with all subsequent algorithmic oper- ations building the necessary data structures based on the specific layer list of each graph.

Using the EicC software framework, we generated 10,000 MC single-muon events, where the track mo- mentum ranges from 0 to 5 GeV and the angular dis- tribution covers the full 0 to 360 degrees. We analyzed all track trajectories and recorded every possible com- bination of detector layers that a track can pass through layer combinations, while the right column displays the frequency of each specific combination’s occurrence.

These combinations, referred to as graphs, form the ba- sis for the subsequent track-finding algorithm.

Creation of cells After graph creation, we need to connect the hit points of adjacent layers to form a doublet, which serves as a cell in the graph. The core component of the algo-

rithm involves determining whether two hits from ad- 267

jacent layers can be linked to form a doublet. Given that a particle’s trajectory in the tracking system is he- lical, we decompose the trajectory into two planes: the x-y plane and the r-z plane. On these two planes, we evaluate whether the angle formed by connecting the two hit points to the coordinate origin meets a prede-

fined critical value, thereby determining if hits between 274

adjacent layers can be linked to form a doublet. We an- alyze 10,000 events generated by MC simulation and examine the angles formed by adjacent hit points on each real track. According to this study, as the cut- ting becomes more relaxed, the efficiency increases ac- cordingly. As illustrated in Fig. , the coverage effi- ciency of true hit pairs exhibits a strong dependence on the angular selection thresholds in both the transverse (x-y) and longitudinal (r-z) planes. On the x-y plane, relaxing the threshold beyond 2.5 mrad ensures that over 99% of true hit pairs are retained, with full effi- ciency (100%) achieved near 4 mrad. Similarly, on the r-z plane, a threshold exceeding 0.009 mrad recovers 98% of true hits, while full coverage is attained around 0.03 mrad. These thresholds define critical boundaries

for selection optimization, maximizing efficiency while

minimizing contamination from false hit pairs in mixed 291

samples. All adjacent layers in a graph are given to a function in turn, and the algorithm judges all hit pairs according to the geometrical requirement obtained from the simula- tion data shown above. Then all the hit pairs that satisfy the requirement are saved to a specific data structure for further processing.

Fraction(%) Fraction(%) Fraction(%) Fraction(%) Right: The fraction as a function of requirement on Cells connection The connection of cells is the key procedure for track finding with CA. The first step is to convert all doublet data structures into cell data structures. Starting from the root layer of each graph, a state variable, CAState,

is assigned to the each cell, initialized to zero. The 308

second step consists of finding neighbors for each cell.

Two cells are considered neighboring cells if all of the following conditions are satisfied: Firstly, they belong to different layer pairs. Secondly, they share a common hit, where the inner hit of one cell is the outer hit of the other. Finally, the corresponding constraints are satis- fied in both the x-y and r-z planes. The angle between two neighboring cells in plane is illustrated in To establish the criteria for selecting neighboring cells in the x-y and r-z planes, we simulated 10,000 events.

Fraction(%) Fraction(%) Fraction(%) Fraction(%) (mrad) (mrad) Right: The fraction as a function of requirement on As shown in Fig. , the coverage efficiency of ac-

tual cell connections depends significantly on the an- 321

gular selection thresholds in both the transverse (x- y) and longitudinal (r-z) planes.

On the x-y plane, a threshold exceeding approximately 0.6 mrad retains over 99% of true connections—nearly reaching full efficiency.

Meanwhile, on the r-z plane, a more le-

nient threshold beyond 0.0009 mrad ensures complete 327

(100%) coverage. These thresholds serve as approxi- mate boundaries for cut optimization when distinguish- ing true connections from background mixtures in later analyses. For each graph, the algorithm evaluates adja- cent cells based on these criteria derived from the sim- ulation. The IDs of matched cells are stored to ensure that matched adjacent cells can be accurately identified in subsequent stages of the algorithm.

Evolution and track candidate creation After establishing the graph, including all cells and their relationships, the final step in track finding is to select the longest path from a root cell within the graph.

A root cell is characterized as a node with no incoming

connections, meaning it has no neighboring cells pre- 342

ceding it in the graph structure. This is accomplished by evolving the graph over several generations accord- ing to a specific rule, allowing the longest path to be

identified based on the state values of the cells. Ini- 346

tially, the state of each cell in the graph is set to zero.

During the evolution process, the state values of all cells are updated based on the state value of the cell un- der investigation and its neighbors. A cell’s state value is incremented by one if it matches the state value of any of its neighbors. The algorithm begins at the root layer of each graph and iterates over all the layer pairs within it. The total number of cycles is determined by the number of layers minus two in the graph. Figure illustrates the state values of all cells for a four-layer graph after two cycles of evolution.

After the evolution process, the algorithm conducts a depth-first search starting from a root cell to generate track candidates. The entire graph is then traversed, and sequential cells with descending state values are selected as track candidates. These candidates are sub- sequently stored for further analysis and the track find-

ing procedure is completed. Kalman filter in EicC track reconstruction With the track candidates, which represents subsequently stored hits information detected by the tracking detector, the track information can be extracted by fitting the track candi- dates with KF method. The KF represents an iterative process designed to estimate the states of dynamic systems. It can be employed in track reconstruction on the assumption that the track can be regarded as a discrete dynamic system. In the fitting, the state of the track at each detector surface i is char- acterized by the state vector . The state is parametrized with 5 coordinates in a local plane coordinate system, as al- ready shown in Fig. . The cartesian position and direction translate into plane coordinates according to the following equations:

⃗P = ( q p, µ ′ , ν ′ , µ, ν ) T (3) 382

Here, are the directions of the state.

µ = ( ⃗x − ⃗o ) · ⃗µ and ν = ( ⃗x − ⃗o ) · ⃗ν represent the coordi- 384

nates of the state in the local frame. Given the state vector , which delineates the state of the track at surface the system equation defines the propagated state vector the subsequent surface k. As shown in Fig. , the KF uti- lizes both previous and current measurements to estimate the current state.

When implementing KF for the trajectory fitting algorithm of EicC, a measurement plane is first constructed for each hit

in the candidate trajectory. For the initial evolution, we need 394

to estimate the initial state parameters, including the momen- 395

tum direction and magnitude. We use the direction of the hit 396

point closest to the origin as the initial direction of the trajec- 397

tory. The first three measurements are fitted by a helical track

model using the least-squares method to obtain the initial mo- 399

mentum. The track fitting involves iterating in two opposite direc- tions, a process known as the smoothing procedure, to obtain the best estimation of track parameters. This bidirectional fit- ting helps refine the track estimate by incorporating informa- tion from both forward and backward passes, thus improving accuracy.

In the track fitting approach for EicC, it’s common for the same root cell to have multiple candidate tracks, particularly when hit points from different tracks are in close proximity.

To address this, the algorithm selects the best track candidate based on the smallest chi-square value obtained during the KF fitting procedure. The chi-square value serves as a mea- sure of fit quality, allowing the algorithm to identify the track candidate that best represents the observed hits with the least statistical deviation, ensuring the most accurate track recon- struction.

Algorithm optimization for track finding The geometric criteria for hit-pair formation and CA cell connections were optimized using simulated events. To eval- uate performance, we generated 10,000 simulated events with

tracks spanning a momentum range of [0–1] GeV and polar 421

angles between [20–160] degree. Each event contained five tracks to benchmark the algorithm’s efficiency under moder- ate track multiplicity conditions.

The criteria in the optimization include: are the angles between two vectors formed by the hit and the collision point in different planes in constructing a doublet; are the angles between two cells in different planes when connecting two cells as illustrated Fig. . The Figure-of-Merit (FOM) quantifies the purity of reconstructed doublets and connections: for the transverse and longitudinal angles ( ), it is defined as the ratio of correctly identified doublets to all reconstructed doublets, while for the orientation angles ( ), it measures the fraction

of topologically valid connections relative to all found con- nections. The optimized results are shown below:

Purity(%) Purity(%) Purity(%) Purity(%) (mrad) Purity(%) Purity(%) Purity(%) Purity(%) (mrad) parameter for the cell creation. (b) FOM as a function of requirement on parameter for the cell creation. (c) FOM as a function of requirement parameter. (d) FOM as a function of requirement on parameter. lar requirements for doublet and connection reconstruction.

Panel (a) shows the FOM dependence on , with an op- timal value of 0.8727 mrad. Similarly, panel (b) evaluates , yielding an optimal threshold of 0.0122 mrad. For con-

nection angles, panel (c) reveals that α x − y = 0 . 4537 mrad 442

maximizes the FOM, while panel (d) identifies 0.00014 mrad as the ideal value for ALGORITHM PERFORMANCE A large number of collision scenarios are generated using MC simulation to validate the performance of the track recon- struction algorithm within the EicC simulation framework.

The angular range in the simulation is uniformly set from 0° 449

to 360°, with muons selected as the reference particle type.

A total of 100,000 events are produced, covering track multi- plicities of 2, 4, and 6. Momentum values are sampled within the range [0–3] GeV. These simulated datasets are then pro- cessed by the algorithm, and the results are used to evaluate its performance.

The main criteria for assessing track reconstruction quality include:

Hit efficiency Hit efficiency is calculated as

ϵ hit = N hit rec N hit gen , (4) 460

where denotes the number of hits successfully re- constructed, and represents the number of hits originally generated in a given track. This metric pro- vides an indication of how well the reconstruction al- gorithm identifies individual hits along particle trajec- tories.

Tracking efficiency The tracking efficiency, defined as

ϵ track = N track rec N track gen , (5) 469

represents the ratio of reconstructed tracks ( track generated tracks ( track ). A track is considered suc- cessfully reconstructed if over 89% of the hits in its re- constructed trajectory originate from the same particle track.

Fake efficiency The fake efficiency, defined as

ϵ fake = N fake rec N all rec , (6) 477

represents the ratio of reconstructed fake tracks ( to all reconstructed tracks ( ). A track is defined as a fake track if the hit efficiency is less than 70%. This metric is used to assess the contamination of incorrectly reconstructed tracks in the tracking output.

Execution time The execution time is defined as the central processing

unit (CPU) time consumed during the track reconstruc- 485

tion process. The hit, tracking and fake efficiencies are evaluated across different momentum ranges and track multiplicities as well as these performance at different pseudorapidity using sim- ulated events. The results of these studies are presented in The hit efficiency demonstrates excellent perfor- mance, consistently approaching 100% over a wide range of momenta. Furthermore, the trajectory reconstruction effi-

ciency increases significantly with momentum, rising sharply 494

between 0.4 GeV and 1.4 GeV. This characteristic is primarily dictated by the detector’s acceptance and magnetic field con- figuration. Consequently, this low-momentum threshold must be considered in physics analyses sensitive to this region, such as the measurement of TMD PDFs. When momentum surpasses 1.5 GeV, the efficiency nears perfection, approach- ing 100%. In the lower momentum range, the fake efficiency does not exceed 5%, slightly increases with the increase of the multiple number of the trajectory, and the fake efficiency basically tends to zero at medium and high momentum. The hit efficiency is relatively high in both the central and forward regions, with a slight drop in the transition region. The fake rate is lowest in the forward region and increases gradually toward lower pseudorapidity. Overall, the tracking efficiency shows a strong dependence on pseudorapidity.

For tracks

with very low transverse momentum ( P t < 300 MeV), the 510

Hit Efficiency(%) Hit Efficiency(%) dp/p(%) multiple_2 multiple_4 multiple_6

0.0<|η|<1.0 1.0<|η|<2.0 2.0<|η|<3.0

(GeV) (GeV) Tracking Efficiency(%) Tracking Efficiency(%) dφ(mrad)

0.0<|η|<1.0 2.0<|η|<3.0 1.0<|η|<2.0

multiple_2 multiple_4 multiple_6 (GeV) (GeV) multiple_2 multiple_4 multiple_6

2.0<|η|<3.0 1.0<|η|<2.0 0.0<|η|<1.0 (f)

Fake Efficiency(%) Fake Efficiency(%) (GeV) (GeV)

tracking efficiency remains high (>72%) across much of the 511

pseudorapidity range. The efficiency decreases for tracks at small pseudorapidity (central region), primarily due to shorter track lengths. These soft, spiraling tracks traverse fewer de- tector layers, limiting the number of available hits for pattern

recognition. 516

It is important to note that this study does not account for beam-related background. This kind of background would dramatically increase the number of hits in the detectors, many of which are uncorrelated with the primary vertex or the tracks of interest and substantially increase the fake track rate.

To mitigate these anticipated challenges, we envision imple-

menting advanced clustering and noise rejection techniques at 523

the hit level to filter out isolated, low-energy, or geometrically

inconsistent deposits before the track pattern recognition even 525

begins. Furthermore, we will employ a suite of quality selec- tion criteria based on the kinematic and topological properties of the tracks.

We also assessed the quality of the trajectory reconstruc- tion by evaluating the momentum and angular resolutions. increases approximately linearly with particle transverse mo- mentum. This trend is well understood, as higher-momentum tracks produce a smaller curvature, reducing the measured sagitta and consequently degrading the momentum resolu- (GeV) (GeV) Multiplicity (GeV) (b): The polar angle resolution of all reconstructed tracks. (c): The azimuth angle resolution of all reconstructed tracks. (d): The execu- tion time of CPU with different multiplicity. tion. Particularly in the low-momentum regime, the resolu- tion curve bends upward. In the low-momentum regime, mo- mentum resolution is primarily dominated by multiple scat-

tering. The lower the momentum, the more significant the 539

impact of multiple scattering, leading to poorer resolution. As momentum increases, the effect of multiple scattering gradu-

ally diminishes, and the spatial resolution of the detector be- 542

comes the dominant factor. At higher momenta, the trajec- tory becomes increasingly straight, and the sagitta decreases, resulting in progressively worse resolution. Superior momen- tum resolution is critical for TMD measurements, as shown

in Ref.[ 35 ], as it minimizes the smearing of low-transverse- 547

momentum hadrons to ensure clean extraction of spin asym- metries. Furthermore, high tracking efficiency and vertex res- olution are essential for reducing combinatorial background in heavy-flavor tagging, which tightens constraints on gluon PDFs [ ]. The angular resolution deteriorates as particle transverse momentum increases, as evidenced in the top right and bottom left panels. This trend is attributed to the reduc- tion of multiple scattering effects at higher momenta.

The computational performance is measured on an Intel Xeon Gold 6248R processor (24 cores, 3.0 GHz base fre- quency). The execution time of the CPU will increase with the increase of the number of tracks as shown in the bottom right pannel of Fig . The increase in track multiplicity can also lead to an increase in multi-threading overhead, thereby

resulting in a significant increase in execution time. 562

This study establishes the high tracking efficiency and pre- cision momentum resolution that form the essential founda- tion for robust vertex reconstruction at the EicC. While a full characterization of the vertexing algorithm is beyond the scope of this paper, its performance is a direct consequence of the track quality demonstrated here. Excellent vertex reso- lution is paramount for the EicC’s flagship physics programs,

such as gluon PDF extraction via open charm measurements, where the precise identification of displaced secondary ver- tices is required to suppress combinatorial background. A dedicated analysis of primary and secondary vertex finding efficiency and resolution, building upon this tracking founda- tion, is the immediate next step in our software development chain and will be presented in a forthcoming publication.

SUMMARY

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