Introduction

The Beijing Spectrometer (BESIII) [1] at the Beijing Electron-Positron (BEPCII) Collider has been a great success in producing promising physics results [2] in the τ-charm sector since 2009. However, after operating for approximately 15 years, the detectors at BESIII have been subjected to aging effects, which degrade their performance [3].

The tracking detector at BESIII is a multilayer drift chamber (MDC), which provides measurements of the momentum and position of the charged tracks and information of energy loss in unit path length, i.e. dE/dx [4], of the charged tracks for particle identification. As shown in Ref. [3, 5], due to the beam-induced background with a hit rate up to 2 kHz/cm², the gain of the MDC cells in the first ten layers has shown an obvious decrease, with a maximum decrease of approximately 39% for the innermost layer cells in 2017. This further reduces the spatial and momentum resolution of the charged tracks. Because BESIII is not expected to complete its mission in the foreseen years [2, 3], the track reconstruction performance must be preserved and enhanced to avoid compromising the physics goals of BESIII, along with a possible upgrade of the tracking system with state-of-the-art technologies for the detection of charged particles. To obtain good preparation for the potential malfunction of the MDC owing to the aforementioned aging problem, plans to upgrade the BESIII inner tracker based on different technologies have been proposed [3]. This includes the replacement of the inner tracker with a new inner drift chamber [6] or a cylindrical gas electron multiplier (CGEM) tracker [7], which has attractive features such as high counting rate tolerance and low sensitivity to aging.

Compared with gaseous detectors, silicon pixel detectors have excellent spatial resolution and good radiation resistance. Therefore, an additional option for the BESIII inner-tracker upgrade is to use a large-area thin complementary metal oxide semiconductor (CMOS) pixel sensor with good spatial resolution based on cutting-edge stitching technology, which has already been used to produce CMOS pixel sensors for medical imaging applications [8-10]. The design for a first wafer-scale stitched sensor prototype, known as the monolithic stitched sensor (MOSS) chip, is discussed in recent studies. These efforts aim to enhance the performance of the vertex detector, i.e. the ITS3, at the ALICE experiment, as detailed in Ref. [11].

A Common Tracking Software (acts) [12] is a common high-energy physics (HEP) software. It provides a set of detector-agnostic, high-performance, and modular tools for the track reconstruction in HEP. The software leverages modern software technologies to facilitate concurrency, usability, maintenance, and extendability, addressing the prospective tracking challenges in HEP. To date, acts has been used for track reconstruction at ATLAS [13], FASER [14], sPHENIX [15], and STCF [16] for different types of tracking detectors. In particular, the promising tracking performance of acts for a tracking system with a drift chamber was first presented in Ref. [16].

In this study, the tracking performance of the BESIII MDC with an additional one-layer stitched cylindrical CMOS pixel detector inserted between the beam pipe and the inner wall of the MDC was studied using acts as the tracking software. The performance was compared with that of the current BESIII tracking detector using only the MDC based on the BESIII Offline Software System (boss) [17]. The remainder of this paper is organized as follows. In Sect. 2, the BESIII MDC and the proposed pixel detector based on the cylindrical CMOS pixel sensor are presented. Section 3 introduces the tracking strategies in boss and acts. The improvement in the tracking performance at BESIII with an additional pixel detector is presented in Sect. 4. Finally, a brief conclusion is provided in Sect. 5.

BESIII tracking detector and stitched CMOS pixel detector

The BESIII MDC is a cylindrical chamber operating with a helium-based gas mixture (He/C₃H₈ = 60:40) and is immersed in a 1-T magnetic field. The inner and outer radii of the MDC are 64 mm and 819 mm, respectively. The lengths of the wires range from 774 mm for the innermost layer to 2400 mm for the outermost layer. The drift cells, which are almost square-shaped, are arranged in 43 circular layers and alternate between the stereo layers and axial layers, i.e. in the order of eight stereo layers, 12 axial layers, 16 stereo layers, and 7 axial layers. The cell dimensions are approximately 12 mm × 12 mm for the eight inner layers and 16.2 mm × 16.2 mm for the 35 outer layers. The inner chamber is composed of 8 inner layers, and the outer chamber is composed of 35 outer layers.

CMOS pixel sensors have been widely used for vertex detectors in HEP because of their excellent spatial resolution down to a few μm, tolerance of high hit rates up to 10⁸ Hz/cm², and good detection efficiency and radiation resistance. For example, the CMOS pixel sensor has been used as the inner tracker or vertex detector at STAR experiments [18], ALICE experiments [19] and sPHENIX experiments [20]. It is also considered as the primary choice for pixel sensor technology in the CEPC physics program [21]. Despite the advantages of the CMOS pixel sensor, the tracking resolution of a traditional CMOS pixel detector, particularly for low-momentum tracks, can be limited by the irreducible material budget of the support structure and cooling pipe. This was demonstrated in Ref. [22], in which a MAPS-based CMOS pixel sensor was proposed to upgrade the BESIII inner chamber. Therefore, tracking based on traditional CMOS pixel sensors can be challenging at BESIII, in which tracks with a transverse momentum as low as 150 MeV must be reconstructed with good resolution.

In recent years, innovative stitching technologies have emerged with the aim of producing large-area sensors on one wafer, which can be further thinned to approximately 50 μm. With this thickness, the wafer can be curved into a cylindrical shape, thereby vastly simplifying the support structure and reducing the material budget. Based on this stitching technology, it is possible to construct a vertex detector using large-area thin CMOS pixel sensors with cylindrical shapes and simplified support structures. As discussed in Ref. [11], the material budget per pixel layer is expected to be reduced to 0.05% X₀ to allow bending of the silicon. In this study, we considered a vertex detector comprising a single layer of a stitched cylindrical pixel sensor with a thickness of 50 μm (0.05% X₀), as proposed in Ref. [11], length of 220 mm (including an insensitive area within 7 mm of each end), and a resolution of 8.66 μm and 57.74 μm in the r-ϕ and z directions, respectively. This layer was inserted between the 63-mm diameter beam pipe [7] and the MDC inner wall. The stitching technology foresees cooling by airflow and no readout circuits in the active area. Therefore, the additional material budget from the cooling and readout infrastructure, as well as the support structure in the active region of the pixel layer, is expected to have a negligible impact on the tracking performance; hence, it was not considered in this study.

The geometry of the BESIII MDC and the pixel detector is shown in Fig. 1.

Fig. 1Full-screen View

(Color online) Clipped view of the geometry of the BESIII MDC (cell wires are shown in green colors) and the pixel detector (shown in orange color) outside of the beampipe.

Tracking with BESIII offline software and acts

The simulation study was based on samples generated using boss, an offline software framework for event generation, simulation, reconstruction, performance validation, physics analysis, and visualization [23] for the BESIII experiment.

In boss, the production of both charmonium resonances and the continuum process from e⁺e^- collisions is provided by the kkmc [24] generator, and the decays of particles were modelled using evtgen [25], which can also be used to generate single-particle samples. The detector description is based on the Geometry Description Markup Language (gdml) [26], and the interaction of the particles with the detectors is simulated using geant4 [27].

The performance of the BESIII MDC with the additional pixel detector was studied using the acts software and compared with the performance of the BESIII MDC studied using the BESIII tracking software within boss. The workflow for studies of the tracking performance is illustrated in Fig. 2.

Fig. 2Full-screen View

Workflow of tracking performance studies based on boss and acts.

Tracking performance studies

4.1

Monte-Carlo sample generation

The effect of the pixel detector on the resolution of the track parameters was studied using single μ^- and single π^- samples. The samples were generated with a fixed transverse momentum p_T, cosθ (θ is the polar angle) uniformly distributed between [-0.8, 0.8], and an azimuthal angle ϕ uniformly distributed in the range of [0, 2π]. The impact of the pixel detector on the tracking efficiency was studied using $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi \mathrm{,}J/\psi \to {\mu }^{+}{\mu }^{-}$ events generated at $\sqrt{s}$ = 3.686 GeV. The two-dimensional distributions of cosθ and p_T for μ and π during this process are shown in Fig. 3.

Fig. 3Full-screen View

(Color online) Distributions of cosθ versus p_T for μ (left) and π (right) generated in $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi$, $J/\psi \to {\mu }^{+}{\mu }^{-}$ events.

Random background hits in the MDC due to beam-related background or electronic noise were generated in the standard simulation sample production at BESIII. Because a dedicated background noise model for the pixel detector is not yet available, no background noise was considered for the inserted pixel layer in this study.

4.2

Track reconstruction performance

The resolution of the impact track parameters, d₀ and dz, and the relative resolution of the transverse momentum p_T as a function of p_T for the BESIII MDC with an additional pixel layer, which is placed with radius $r_{\text{pixel}}$ at three different values (i.e. 35 mm, 45 mm, or 55 mm) compared to those of BESIII MDC, are shown in Fig. 4. Although $r_{\text{pixel}}$ has little impact on the resolution of p_T, the spatial resolution is better with a smaller $r_{\text{pixel}}$. With $r_{\text{pixel}}$ = 35 mm, the resolution of d₀ and dz is 60 μm and 120 μm for μ^- and π^- with p_T = 1 GeV, respectively, and the relative resolution of 44% for p_T at p_T = 1 GeV was achieved. The resolutions of d₀, dz, p_T can be improved by up to 67%, 93%, and 32%, respectively, by adding the proposed pixel detector to the current BESIII tracking detector.

Fig. 4Full-screen View

The resolution of d₀ (left), z₀ (middle) and relative resolution of p_T (right) for single μ^- (top) and single π^- (bottom) as a function of particle pT for the BESIII MDC only (black circle), and BESIII MDC with an additional pixel layer (denoted as "Pixel") placed with $r_{\text{pixel}}$ = 35 mm (blue dot), 45 mm (purple triangle) and 55 mm (yellow triangle), respectively.

A comparison of the tracking efficiency, which is defined as the fraction of the generated charged particles which have the corresponding reconstructed tracks in the detector region (|cosθ| > 0.93), between the BESIII MDC with the additional pixel layer and the BESIII MDC alone is shown in Fig. 5. The additional pixel layer can significantly improve the tracking efficiency for tracks with a particularly low momentum or large |cosθ|. For μ with p_T below 0.6 GeV in the $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi \mathrm{,}J/\psi \to {\mu }^{+}{\mu }^{-}$ process, the improvement can reach 9%. The improvement can reach 10% for π with 0.85 > |cosθ| < 0.93. A pixel with $r_{\text{pixel}}$ = 35 mm provides better tracking efficiency than the other two choices.

Fig. 5Full-screen View

The tracking efficiency of μ (top), π (bottom) in the process of $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi \mathrm{,}J/\psi \to m{u}^{+}{\mu }^{-}$ as a function of particle p_T (left) and cosθ (right) for the BESIII MDC only (black circle), and BESIII MDC with an additional pixel layer (denoted as "Pixel") placed with $r_{\text{pixel}}$ = 35 mm (blue dot), 45 mm (purple triangle) and 55 mm (yellow triangle), respectively.

Conclusion

After operating for approximately 15 years, the tracking detector of BESIII experiment has suffered from aging effects and must be upgraded to preserve its tracking performance for BESIII to fullfill its remaining physics goals in the next few years. The possibility of inserting a one-layer pixel detector using a large-area thin cylindrical CMOS pixel sensor based on stitching technology between the beam pipe and the MDC was considered. The spatial and momentum resolutions were studied using acts and compared with the performance of the current BESIII tracking detector obtained using the BESIII offline software. The proposed method based on the stitched cylindrical CMOS pixel sensor was found to be promising, i.e. the resolution of d₀, dz, p_T can be improved by up to 67%, 93%, and 32%, respectively, and the tracking efficiency for particles in the $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi \mathrm{,}J/\psi \to {\mu }^{+}{\mu }^{-}$ events can be improved by up to 10% in the low p_T or large |cosθ| region, with the additional pixel layer placed at a radius of 35 mm. Meanwhile, this is the first time that acts has been used for track reconstruction for a drift chamber with calibrated measurements and realistic noise hits. In future studies, the noise model of this state-of-the-art pixel detector will be studied, and the tracking performance considering the noise of the pixel detector will be investigated.