Interface between STCF offline software and ACTS

The offline software system of the Super Tau-Charm Facility (OSCAR) [33, 34] serves as the event-processing framework for STCF. It provides core services for data handling and a suite of application tools for event generation, simulation, reconstruction, and physics analysis. For simulation, τ-charm physics processes generated by KKMC [35] are incorporated into OSCAR, and particle decays are modeled with EvtGen, as used in the BESIII experiment [36] – both integrated into the framework.

The STCF detector geometry is defined using the Detector Description Toolkit (DD4hep) [37], with geometric parameters stored in compact XML [38] files. To comprehensively simulate particle interactions with the detector, Geant4 [39] is integrated into OSCAR for full simulation. A track-finding algorithm based on the Hough Transform was developed for use within OSCAR.

The interface between OSCAR and ACTS enables conversion of experimental geometry, measurements, and initial track estimates into ACTS-compatible representations. Geometry plugins in ACTS facilitate this conversion from DD4hep or TGeo [40] formats into ACTS’s internal geometry description. For the ITK, the readout units in each μ-RWELL layer are converted into sensitive cylindrical surfaces. For the MDC, each sense wire in a drift cell is transformed into a line surface.

Dedicated material mapping tools within ACTS are employed to project detailed material properties onto auxiliary internal surfaces of the ACTS geometry. Two ROOT [41]-based readers were developed to convert simulation data: one extracts simulated hits from the full simulation and converts them into ACTS measurements with detector resolution taken into account; the other converts the initial track parameter estimates from the Hough Transform into ACTS track parameters.

ACTS seed finding

The seeding algorithm in ACTS identifies a minimal set of measurements that provide the global (x, y, z) coordinates for a particle to initiate the track-finding process. Without a seed, a track cannot be reconstructed; hence, the goal is to identify at least one seed per particle within the detector acceptance.

In a uniform magnetic field along the global z-axis, the helical trajectory of a charged particle can be accurately defined using three measurements, forming a seed. At STCF, seeds are generated by combining one compatible measurement from each of the three ITK layers, as shown in Fig. 3. For each seed candidate, the curvature and center of the projected circle on the x-y plane are determined using the Conformal Transform [42, 43]. These parameters are then used to compute the transverse momentum and transverse impact parameter, which must meet criteria optimized for relevant physics processes.

Fig. 3Full-screen View

Illustration of ACTS seeding using measurements from the STCF ITK

Additionally, the bending of the seed in the r-z plane must remain below a threshold optimized based on the effects of the magnetic field and multiple scattering. For further details on ACTS seeding, see Ref. [44].

Track finding with Hough Transform

The principle of the Hough Transform for tracking is illustrated in Fig. 4. In the presence of a magnetic field along the global z axis, the projection of a track onto the transverse x-y plane forms a circle, while its projection onto the s-z plane (where s is the path length in the x-y plane) forms a straight line. The Conformal Transform converts the circular projection of a track that passes through the origin into a straight line in the conformal u-v space. A drift circle tangent to the projected track is also transformed into another circle tangent to the line in the u-v space.

Fig. 4Full-screen View

(Color online) Example mapping of detector measurements in the transverse x-y plane (left) onto the Conformal u-v space (middle), and then onto Hough curves in Hough space (right), for a proton p in a $J/\psi \to \text{Λ}\left(\to p{\pi }^{-}\right)\overline{\text{Λ}}\left(\to \overline{p}{\pi }^{+}\right)$ event. The proton decays between the first and second layers of the ITK, producing two hits in ITK. Yellow and purple indicate ITK and MDC hits, respectively

For displaced tracks with a small but nonzero transverse impact parameter d₀ (compared with the projected track radius in the x-y plane), the trajectory of the transformed measurements (points or drift circles) in the conformal space can be approximately represented by a straight line, as shown in the middle panel of Fig. 4.

The Hough Transform operates on the principle that a straight line in either the geometrical or conformal space can be described by two parameters: the angle θ of its normal and its algebraic distance ρ from the origin. A point with coordinates (u, v) on the line can be mapped to a sinusoidal curve in Hough space using: $\rho =u\cdot \cos \alpha +v\cdot \sin \alpha .$ (1) For a circle centered at (u, v) with radius r tangent to the line, this produces two sinusoidal curves: $\rho =u\cdot \cos \alpha +v\cdot \sin \alpha \pm r.$ (2) The process of identifying measurements or drift circles belonging to the same track involves finding curves in the Hough space that intersect, as shown in the right panel of Fig. 4. A 2D histogram with optimized binning (based on track parameter resolution) is filled whenever a curve passes through a bin, and peaks in the histogram are identified, as detailed in Ref. [21]. The parameters at the intersections correspond to track parameters projected in either the x-y or s-z planes.

The track-finding workflow using the Hough Transform in OSCAR is illustrated in Fig. 5. First, measurements from the ITK and MDC axial wires are used to reconstruct 2D track projections in the x-y plane, followed by circle fitting to extract their parameters. These 2D tracks are then associated with candidate measurements from MDC stereo wires. The z-position and path length s at each stereo wire are simultaneously estimated. Since each stereo wire yields two possible z-position solutions and may include incorrectly assigned hits, a second application of the Hough Transform is used to identify tracks in the s-z plane. Further details can be found in Ref. [21].

Fig. 5Full-screen View

Workflow for track finding using the Hough Transform in OSCAR

Track finding with ACTS CKF

Beginning with a set of initial track parameters, the ACTS CKF uses the ACTS track propagator to search for compatible measurements on a given surface through KF track fitting, as illustrated in Fig. 6. This iterative process, also referred to as track-following, associates the best-matching measurement with the track and updates the track parameters accordingly for continued propagation.

Fig. 6Full-screen View

Illustration of track finding using ACTS CKF with STCF ITK and MDC. Only two MDC layers are depicted

Monte-Carlo samples

The decay process $J/\psi \left(\to p{\pi }^{-}\right)\overline{\text{Λ}}\left(\to \overline{p}{\pi }^{+}\right)$ serves as an important benchmark channel at STCF, enabling several key physics studies related to Λ baryons. Signal events were generated using the KKMC and EvtGen generators within the OSCAR framework, without considering bream-related backgrounds, to evaluate tracking performance.

Figure 7 shows the 2D distributions of cosθ versus p_T, vertex displacement in the x-y plane Vxy versus p_T, and transverse impact track parameter d₀ versus p_T, for protons (and anti-protons), denoted as $p(\overline{p})$, and π in $J/\psi \left(\to p{\pi }^{-}\right)\overline{\text{Λ}}\left(\to \overline{p}{\pi }^{+}\right)$ events. The π has relatively low transverse momentum, with p_T below 310 MeV/c, while $p(\overline{p})$ reach up to 1.1 GeV/c.

Fig. 7Full-screen View

(Color online) Distributions of particle $\text{cos}\theta$ versus p_T (top), vertex displacement in the x-y plane Vxy versus p_T (middle), and d₀ versus p_T (bottom) for $p(\overline{p})$ (left) and π (right) in $J/\psi \to \text{Λ}\left(\to p{\pi }^{-}\right)\overline{\text{Λ}}\left(\to \overline{p}{\pi }^{+}\right)$ events

A significant fraction of particles decay outside the first layer of the ITK. However, most reconstructed tracks have d₀ values smaller than the radius of the first ITk layer, especially for $p(\overline{p})$.

Following event generation, Geant4 was used to simulate hits from final-state particles, which originated from primary interactions and traversed the STCF tracking system under a uniform 1 T magnetic field. Detector measurements were then obtained by applying Gaussian smearing to the simulated hit positions, using zero mean and widths determined by the detector resolution.

Track-finding performance

The performance of track finding – comprising seed finding using either the ACTS seeding algorithm or the Hough Transform algorithm in the first stage, and track following using ACTS CKF in the second stage – was studied.

Considering the acceptance of the STCF tracking system, only truth particles with p_T above 50 MeV/c and |cosθ| below 0.94 were included in the performance evaluation. This evaluation involves identifying the primary particle [22] of a seed or a track, i.e., the simulated particle contributing the most hits to that seed or track.

The seeding process serves as the initial step in track finding using the CKF and ideally should provide seeds for all particles within the detector acceptance. The ACTS seeding efficiency is defined as the fraction of particles within the acceptance region whose seeds are matched to hits originating from the same particle in all three ITK layers. For the Hough Transform, seeding efficiency is defined as the fraction of seeds with at least 50% of hits originating from the same primary particle.

ACTS seeding is only possible for tracks from particles that produce hits in all three ITK layers, which corresponds to a vertex displacement below 66.5 mm. A comparison of the efficiencies of ACTS seeding and the Hough Transform as a function of vertex displacement in the x-y plane (Vxy) is shown in Fig. 8 (top panels). ACTS seeding efficiency approaches 100% when there are at least three ITK measurements. In particular, ACTS seeding provides higher efficiency than the Hough Transform for π with small Vxy. However, ACTS efficiency drops sharply to zero if fewer than three ITK hits are present, highlighting a key limitation for long-lived particles. In contrast, the Hough Transform, functioning as a global tracking algorithm, shows reduced sensitivity to the number of ITK layers traversed.

Fig. 8Full-screen View

Seeding efficiency vs. particle Vxy (top) and p_T (bottom) for $p(\overline{p})$ (left) and π (right) in 200k $J/\psi \to \text{Λ}\left(\to p{\pi }^{-}\right)\overline{\text{Λ}}\left(\to \overline{p}{\pi }^{+}\right)$ events. Solid purple squares and yellow dots represent the ACTS seeding for negative and positive particles, respectively. Hollow red squares and green circles represent the Hough Transform for negative and positive particles, respectively

Figure 8 (bottom panels) shows seeding efficiency as a function of particle p_T. The Hough Transform achieves over 90% efficiency for $p(\overline{p})$ with p_T above 350 MeV/c, and over 80% for π with p_T above 85 MeV/c – an improvement over ACTS seeding.

Reconstructed tracks are required to have at least five measurements and reconstructed |cosθ| < 0.94. A track is matched to its primary particle if at least 50% of its hits originate from that particle (track purity). A track not matched to its primary particle is labeled as fake. If multiple tracks match the same simulated particle, the one with the highest purity is considered the true track, and others are labeled as duplicates.

Track reconstruction efficiency is defined as the fraction of simulated particles (with at least five hits in the detector acceptance) that are matched to reconstructed tracks. The fake rate is the fraction of fake tracks among all reconstructed tracks. The duplication rate is the fraction of particles with at least one duplicate track among those with five or more simulated hits.

Figure 9 shows the tracking efficiency as a function of particle Vxy and p_T. As expected, tracking efficiency using ACTS seeding with CKF drops to zero when Vxy exceeds 66.5 mm. In contrast, tracking with the Hough Transform and CKF shows weaker dependence on Vxy, achieving above 80% for $p(\overline{p})$ with p_T above 350 MeV/c and above 70% for π with p_T above 85 MeV/c.

Fig. 9Full-screen View

Tracking efficiency vs. particle Vxy (top) and p_T (bottom) for $p(\overline{p})$ (left) and π (right) in 200k $J/\psi \to \text{Λ}\left(\to p{\pi }^{-}\right)\overline{\text{Λ}}\left(\to \overline{p}{\pi }^{+}\right)$ events. Same color and marker conventions as in Figure 8

Figure 10 presents the fake and duplicate rates for the two seeding strategies. The fake rate remains below 0.4%. A non-negligible number of duplicate tracks appear for particles with pT below 150 MeV/c due to looping trajectories in the magnetic field. ACTS seeding yields lower fake and duplicate rates compared to Hough Transform seeding.

Fig. 10Full-screen View

Fake rate vs. track p_T (top) and duplicate rate vs. particle pT (bottom) for $p(\overline{p})$ (left) and π (right) in 200k $J/\psi \to \text{Λ}\left(\to p{\pi }^{-}\right)\overline{\text{Λ}}\left(\to \overline{p}{\pi }^{+}\right)$ events. Same color and marker conventions as in Figure 8

The tracking performance of an alternative MAPS-based ITK was compared to that of a μ-RWELL-based ITK for long-lived particles. Figure 11 shows the tracking efficiency, fake rate, and duplication rate using the combined Hough Transform and ACTS CKF for both designs. Due to its smaller radii in the first two layers, the MAPS-based ITK is less effective for long-lived particles and shows slightly lower tracking efficiency than the μ-RWELL-based ITK. However, fake and duplicate rates are similar between the two designs.

Fig. 11Full-screen View

Tracking efficiency (top), fake rate (middle), and duplicate rate (bottom) as a function of Vxy and p_T for $p(\overline{p})$ (left) and π (right) in 200k $J/\psi \to \text{Λ}\left(\to p{\pi }^{-}\right)\overline{\text{Λ}}\left(\to \overline{p}{\pi }^{+}\right)$ events, using the combined Hough Transform and ACTS CKF. Yellow dots and purple squares represent results for the μ-RWELL-based ITK (ITKW) and MAPS-based ITK (ITKM), respectively