Detector technologies for charm superfactories

The detector for a charm factory is a general-purpose high-hermiticity magnetic spectrometer optimized for precision studies of the production and decay properties of various particles. The tracking system consists of an inner tracker aimed at providing superior spatial resolution at the interaction point (IP) and a main tracker for precise momentum measurement. For the inner tracker micropattern gaseous detector, Complementary Metal-Oxide-Semiconductor(CMOS) maps and time projection chamber options are considered. The technology for the main tracker is a drift chamber in a 1.0 T axial magnetic field provided by a superconducting solenoid. The particle identification system is based on Cherenkov light detection using DIRC-like time-of-flight or Ring Imaging Cherenkov Detector (RICH) detectors. Photons are detected using an electromagnetic calorimeter, which is built using pure CsI crystals to cope with high backgrounds. Muons and K_L mesons are identified in the instrumented (resistive plate chambers or organic scintillator) flux-return yoke. A detailed description of the SCTF and STCF detector designs can be found elsewhere [3, 4]. Unless explicitly stated otherwise, the SCTF project paradigm is assumed throughout this study.

Particle identification in the SCTF detector

Particle identification at the SCTF is based on several subsystems, and their contributions to PID and performance have been previously estimated using a fast simulation approach [5]. The dE/dx measurements inside the drift chamber are efficient for separating kaons (below ~700 MeV/c) and protons (below ~1200 MeV/c) from pions and muons. A CsI crystal electromagnetic calorimeter (with a crystal transversal size of approximately 1 Molière radius and a longitudinal depth of 1 nuclear interaction length) was used to separate hadrons from photons and electrons. Its contribution to muon-hadron separation is negligible for momenta <2 GeV/c, where hadronic showers (if any) can hardly be distinguished from minimum ionizing particle tracks. The main task of the muon system is the efficient identification of hard muons (with momenta >700 MeV/c).

For the middle-momentum range from ~0.5 to ~1.5 GeV/c, a dedicated subsystem is proposed, namely the Focusing-Aerogel Ring-Imaging Cherenkov (FARICH) detector. The FARICH radiator is composed of a few layers of aerogel with slightly different refraction indices, resulting in the focusing of Cherenkov photons in the thinner ring at the photodetector plane compared to that from a homogeneous radiator. Silicon photomultiplier matrices are considered as an option for photon detection devices. A detailed description of the concept and test beam results for the prototype can be found in Ref. [6].

Simulation and digitisation of the FARICH subsystem

Dedicated software packages are being developed for charm factory detector simulations and data processing. As many other modern HEP projects, both Aurora package [7] for the SCTF and OSCAR package [8] for the STCF are based on the DD4hep framework [9]. Within the SCTF Geant4 [10] detector model, the FARICH system was placed between the tracker and electromagnetic calorimeter. Hereinafter, the simulations of the FARICH barrel part are discussed, which has the following layout: it is composed of 27 equivalent trapezoid blocks starting at 800 mm from the IP with a total thickness of 40 mm, and each block contains four aerogel layers (radiator). The layer of the sensitive detector material was separated from the radiator by a 200-mm air gap. The number of aerogel layers and their optical properties in the FARICH subdetector model were identical to those in Ref. [11]. Figure 1 shows a schematic view of the FARICH subsystem of the SCTF detector on the left and a sketch of the focusing effect from the multilayer aerogel in the middle.

Fig. 1Full-screen View

(Color online) Left: a schematic view of the FARICH subdetector at the SCTF. Middle: FARICH design with four aerogel layers and Cherenkov photon path up to the photodetector plane. Right: FARICH photodetector plane with the signal from a simulated 1.5-GeV charged pions. The square grid shows the SiPM matrices, and each point corresponds to the signal from a single SiPM in the matrix. See text for details

Optical photon transport simulations are known to be extremely time-consuming. There are two simulation modes within the Aurora package: with and without the Geant4 optical photon functionality implemented for the FARICH subdetector. In this study, the signal reconstruction and particle identification performance were investigated using particle propagation from the interaction point with a 1 T magnetic field up to the FARICH subdetector and subsequent full Geant4 simulation of optical photon transport through the FARICH components. The vector of the particle momentum at the track endpoint in the tracker was obtained from the generator-level information and projected to the entrance point of the FARICH radiator.

The simulated response of the FARICH subsystem was produced by Cherenkov photons generated and propagated to sensitive detectors using Geant4. To obtain realistic hits, the quantum and geometrical efficiencies of photosensors were implemented as a digitization procedure of the photon detection: the Geant4-generated Cherenkov photon spectrum was convolved with the quantum efficiency curve and an additional factor to account for an effective geometrical efficiency. The energy dependence of the quantum efficiency was obtained from Ref. [12] for the KETEK 8×8 SiPM matrix (SiPM: silicon photomultiplier) proposed as one of the photosensor options. These photodetectors have pixel (SiPM) sizes of 3.36 mm×3.36 mm and geometrical fill factors of ~88%. Subsequently, the photon arrival points in the detector plane were placed on a square grid with a size corresponding to the aforementioned pixel size. One or more photons registered in a single pixel forced the pixel to produce one hit. An example of a Cherenkov ring in the FARICH subdetector from a simulated pion is shown in Fig. 1 (right).

The noise hits corresponding to various assumptions about the SiPM dark count rates (DCR) were also superimposed at the digitization step. The number of noise hits for each event was sampled from a Poisson distribution with a mean corresponding to the expected noise level in a pixel area. Two spatial coordinates of each noise hit at the photodetector plane were generated uniformly, and the times of hits were uniformly distributed over the event time frame of 7 ns.

Ring reconstruction algorithm

The typical reconstructed hit image from a single particle in the FARICH is not a regular ring but a distorted elliptical figure because of the inclination of the particle trajectory with respect to the photodetector plane and the additional air gap between the radiator and photosensors. The distortion effect depends on the incident angle of the particle. Moreover, the restricted efficiency of photon detection results in stochastic fluctuations in the number of hits for the same particle velocity β.

To account for these peculiarities, a dedicated algorithm for ring reconstruction was developed and tested on simulated events in the FARICH prototype [11]. The value of β is extracted using the incident particle momentum and direction at the photodetector plane, the relative number of hits per ring around the projected particle momentum, and the photon arrival times. The intersection of the track projection from the tracker with the FARICH photosensor plane serves as a “seed” for Cherenkov ring reconstruction.

The analyzed value is the ratio S = N(R,T)/R, where N is the number of hits calculated in bins at the (R, T) plane, where R is the hit radius w.r.t. the “seed” point defined above and T is the hit time. The outputs of the algorithm are the reconstructed radius, R_reco, which corresponds to the maximum value of the ratio, S_max, and the signal z-score parameter, Z_DCR, which is defined as follows:(2)where S_DCR and V_DCR are the mean and standard deviation of the ratio S estimated from the pure noise events for a given DCR value, respectively. The parameter Z_DCR characterizes the signal significance over the given photosensor dark count rate and is used for identification. An alternative ring reconstruction approach based on machine learning was presented in Ref. [13] and demonstrated comparable performance.

Boosted Decision Trees classifier

The particle identification landscape at charm superfactory energies is expected to contain several species: electrons, muons, pions, kaons, and protons. In the tracker with a radius of 800 mm positioned inside the 1 T magnetic field, only particles with momenta above ~310 MeV/c will reach the FARICH subdetector at incident angles smaller than 45°. Tracks with larger incident angles were not considered for analysis owing to the poor performance of the ring reconstruction algorithm. To produce Cherenkov light in the radiator with given parameters (see Sect. 2.3), the particle momentum should exceed approximately 350 MeV/c for muons, 500 MeV/c for pions, and 1800 MeV/c for kaons. Electrons and protons were excluded from the analysis because electrons always produce a maximal Cherenkov ring, whereas protons do not produce any rings. Moreover, electrons are expected to be reconstructed in the electromagnetic calorimeter with high efficiency. A particle species is identified using the Boosted Decision Tree (BDT) technique. For the current study, the classifier is considered.

2.5.1

BDT training and optimisation

The classifiers were constructed and trained using the XGBoost library version 2.1.2 [14] for several noise levels. Four variables serve as BDT inputs: particle momentum and incident angle at the photodetector plane, reconstructed ring radius (R_reco), and signal z-score parameter defined in Eq. 2 and dependent on the chosen photosensor dark count rate (see Sect. 2.4). The particle momentum and incident angle in the real detector are reconstructed in the tracker and extrapolated to the radiator plane closer to the tracker.

The reconstruction of the particle velocity is an intermediate step in BDT-based classification. Figure 2 shows the results of the preliminary stage of the algorithm tuning, that is, the accuracy of velocity reconstruction by the FARICH subsystem for single pions simulated in the SCTF detector for different DCR values of photosensors. The BDT-based approach implemented in the full-scale detector model provides uncertainties of velocity reconstruction by a factor of ~1.5 smaller than the previous results from Ref. [11] obtained without BDT for a standalone FARICH prototype.

Fig. 2Full-screen View

Uncertainty of β_reco from the simulations of single pion response in the FARICH subdetector of the SCTF at different DCR levels. See text for details about nσ separation

The reconstruction accuracy achieved by the BDT-based algorithm is better than 0.001 for β < 0.999 at incident angles up to 45° and photodetector dark count rates of to 10⁵ Hz/mm². The performance slightly worsens at higher dark count rates, which is expected due to the damage of SiPMs by irradiation under SCTF conditions. The “nσ” separation between the pion and muon mass distributions is shown in Fig. 2 in terms of the requirements for β reconstruction accuracy, as it gives the dominant contribution compared to the momentum reconstruction accuracy in the drift chamber². Assuming the same accuracy for pions and muons, the difference between means of pion and muon reconstructed mass distributions is larger than 5 standard deviations (5σ separation) up to β=0.985 even for the worst case of DCR = 1 MHz/mm². For DCR ≤ 100 kHz/mm², the 5σ FARICH-based separation is available up to β=0.995.

As shown in Fig. 2, the reconstruction algorithm shows very similar performance for dark count rates from 100 kHz/mm² and below. Therefore, two separate classifiers were trained for noise levels of 100 kHz/mm² and 1 MHz/mm² and used for further analysis. For training, 450,000 events were generated, 150,000 for each muon, charged pion, and charged kaon sample. The particle momentum for each particle type was uniformly distributed from 310 MeV/c (the minimum momentum detected in the FARICH subsystem) to 2500 MeV/c. Figure 3 shows the loss function behavior during training. For both noise levels, approximately 250 boosting rounds were sufficient to achieve good performance without overtraining. A study of feature importance using the standard tool from the XGBOOST package showed that the importance scores were quite similar for all four input variables; the difference between the highest (for ring radius) and lowest (for incident angle) scores did not exceed 15%.

Fig. 3Full-screen View

Multiclass logistic loss function dependence on the number of boosting rounds for training (blue) and validation (orange) samples for DCR = 100 kHz/mm² (left) and DCR = 1 MHz/mm² (right)

The classifier hyperparameters were optimized on the grid by maximizing the performance characteristic ROC-AUC using the tool provided in the XGBoost library. An additional 50,000 events per particle species (150,000 events in total) were generated for the test samples, which were used to demonstrate the classifier quality. Both the training and test samples of the single particles had the same fractions of the three particle species.

2.5.2

BDT performance for single particles

The single BDT classifier was trained for the entire momentum range. However, the PID performance differs significantly from the momentum. Therefore, the confusion matrices for the test sample are presented in six momentum ranges in Figs. 4 and 5 for the two DCR values. At low momenta, the reconstruction efficiency suffers from the low number of detected Cherenkov photons, which is further reduced by the implementation of realistic photon detection and geometrical efficiencies in digitization. As a result, the first momentum bin with 300 ≤ p ≤ 600 MeV/c is the one where kaon misidentification has a noticeable probability, the pion-kaon separation being more affected than muon-kaon because pions have higher Cherenkov threshold than muons.

Fig. 4Full-screen View

(Color online) Confusion matrices (fraction of predicted type for a given true type) for the test sample of simulated single particles in the SCTF for DCR = 100 kHz/mm² in six momentum ranges

Fig. 5Full-screen View

(Color online) Confusion matrices (fraction of predicted type for a given true type) for the test sample of simulated single particles in the SCTF for DCR = 1 MHz/mm² in six momentum ranges

The assumed SiPM geometrical resolution makes it impossible to distinguish between muons and pions with momenta above ~1800 MeV/c, which leads to an inevitable drop in classification quality in this range with FARICH as the only PID subsystem. Therefore, the last bin covers the momentum range above 1800 MeV/c, although the information on the number of signal hits in each event, which is incorporated into the z-score value, allows a certain level of identification above this threshold.

The muon identification efficiency and misidentification probability of pions as muons are shown for the test sample in Fig. 6 for two DCR levels in several momentum bins. For a DCR level of 1 MHz/mm² the drop in identification performance can be observed in all momentum ranges. The worsening of the PID quality in the momentum range below 600 MeV/c is related to the significant confusion of both pions and muons with kaons.

Fig. 6Full-screen View

(Color online) Muon identification efficiency versus pion-as-muon misidentification probability (π-as-μ MisID) for the test sample of simulated single particles in the SCTF for DCR = 100 kHz/mm² (left) and DCR = 1 MHz/mm² (right) in six momentum ranges

Signal and background simulation and event selection

To estimate the performance of the developed PID algorithm for the physics analysis discussed above, 550,000 events with decays at the center-of-mass energy of e⁺e^- beams MeV have been generated and propagated through the tracker and FARICH subsystem of the SCTF detector. The produced was simulated to decay into invisible particles and was ignored. The D⁰ meson is forced to decay as either (signal) or (background). The propagation of particles in a drift chamber volume in a 1 T magnetic field, as well as the generation of Cherenkov photons in the FARICH subsystem and hits detection, were simulated within the Aurora framework.

For the performance analysis, events were selected using generator-level information about the particle momenta. The selection efficiencies listed below affect the signal-to-background ratio and do not depend on the PID performance.

The numbers of signal and background events, N_sel(Kμν) and N_sel(Kππ⁰), selected before identification, can be calculated from the efficiencies listed above as(3)(4)where is the number of generated signal events (about 100,000) and . As can be seen from Eq. (3) and (4), in addition to particle identification characteristics, the efficiency of π⁰ reconstruction also affects the background admixture to the signal sample under study.

Two constraints on the minimal photon energy detected in the calorimeter were investigated, representing the baseline and the most conservative assumptions about calorimeter performance, 50 MeV and 200 MeV for E_γcut values, respectively. The first value is widely used in Belle analyses³ [17]. Although the SCTF calorimeter is designed to detect photons starting from 20 MeV, the expected number of background clusters increases drastically with a decrease in the cluster energy cutoff, which, in combination with increased luminosity, results in a large combinatorial background and degradation of the reconstruction efficiency [18]. And the fact that the current analysis suffers from the signal impurity rather than from the lack of statistics justifies the choice of such a tight energy cut for the most conservative estimate. The efficiencies of signal and background event reconstruction and numbers of selected events for the four probabilities of lost π⁰ are summarised in Table 1.

The normalized momentum distributions of the final-state particles for both the signal and background channels are shown in Fig. 7. For the background, the two most different options are shown: the baseline and the most conservative one. The sharp low-momentum edge of the after-cut distributions is due to the sensitivity limit of the FARICH subsystem, as stated in the last item of the aforementioned list of constraints.

Fig. 7Full-screen View

(Color online) Distributions of particle momentum for signal channel kaons (a) and muons (b) and background channel kaons (c) and charged pions (d): before selections (blue), after signal selections (orange at a, b) and after background selections (c, d) with conservative (orange) and baseline (green) assumptions about π⁰ reconstruction efficiency. Histograms are normalised to generated number of signal (a, b) or background (c, d) events

Estimate of PID performance

The ring reconstruction algorithm described above and the BDT inference to identify a particle species are applied to selected events, and the number of identified signals and misidentified background events are calculated. The efficiency of kaon identification, ϵ_K, is considered: negatively charged tracks are required to be identified as kaons. The numbers of selected and reconstructed signal events identified as signals can be represented as follows:(5)where ϵμ is the efficiency of muon identification in the FARICH subsystem. The number of background events misidentified as signals can be calculated as follows:(6)where τπ/μ is the misidentification probability of pion as muon. From Eq. (5) and (6), the pairs of ϵ_PID and τ_PID values can be obtained for various BDT working points defined by the classifier threshold at different assumptions about the probabilities of lost π⁰. The efficiency of signal identification ϵ_PID versus the probability of background misidentification τ_PID is shown in Fig. 8 for the two noise levels. The belts shown represent the maximal variation between the results obtained with different assumptions about ϵ_2γ and from Table 1. As shown in Fig. 8, significant differences between π⁰ reconstruction efficiencies result in a similar π / μ separation performance.

Fig. 8Full-screen View

(Color online) Signal identification efficiency versus background misidentification probability for the expected mixture of signal () and background () events for DCR = 100 kHz/mm² (blue) and DCR = 1 MHz/mm² (orange). The width of the belt corresponds to the maximal differences between the background admixture options from Table 1. See text for details

The unprecedented expected luminosity of charm superfactories, together with the achieved performance of particle identification, leads to a negligible statistical uncertainty for the branching ratio measurements at a level well below 0.1%. Figure 9 shows the percentage of background admixture in the reconstructed signal sample, f_bgd, for various assumptions regarding the π⁰ reconstruction efficiencies and for two noise levels. With the possibility of moving the background contribution below 0.5%, the systematic uncertainty can also be reduced, opening the opportunity to achieve a new level of LFU measurement precision at charm superfactories.

Fig. 9Full-screen View

Expected background fraction in the reconstructed signal sample versus the background misidentification probability for different efficiencies of π⁰ reconstruction at DCR = 100 kHz/mm² (solid lines, open markers) and DCR = 1 MHz/mm² (dashed lines, filled markers). The lines are shown to guide the eye