BESIII Drift Chamber Tracking with Machine Learning

The tracking efficiency and the quality for the drift chamber of the BESIII experiment is essential to the physics analysis. The tracking efficiency of the drift chamber of BESIII is high for the high momentum tracks but still have room to improve for the low momentum tracks, especially for the tracks with multiple turn. A novel way to use a convolutional network called U-Net network is represented to solve the identification of the first turn’s hits for the multiple-turn tracks.


The BESIII experiment
The Beijing Spectrometer III (BESIII [1], Fig.1) has been running at the Beijing Electron Positron Collider II (BEPCII) for Tau-Charm physics since 2008. The tracking detector of the BESIII is a Multilayer Drift Chamber (MDC) [2]. The tracking efficiency for the high transverse momentum is high but lower when the cos(where  is the dip angle of the track ) is small for the low transverse momentum tracks (Fig. 2).

Multi-turn track finding of the drift chamber
Some of the curling tracks with multiple turn which |cos|<0.2 have bad tracking efficiency and quality as Fig. 2 shows. For the multi-turn tracks, the hits from different turns will adjacent to each other and even overlap as Fig. 3 shows. The tracking efficiency is low due to the effect of the non-first turn's hits during tracking procedure. The solution to remove the non-first turn hits in traditional tracking algorithm is to apply a cut on the distance between the track and the MDC wires. The disadvantage of the traditional method is that the track should be reconstructed with the contamination of the non-first turn hits and worsen the track parameter which is used for the selection of the hits. In our work, the first turn hits can be identified without the knowledge the track. In our work, we use the technology of the supervised semantic segmentation of the deep learning to do the hit level classification for the single track. The aim of this work is to separate the first turn's hit from the non-first's turn hits for the multi-turn tracks.

Multi-turn hits separation with U-Net
The track finding of the tracking detector is a problem of pattern recognition which is very suitable for the utilization of the machine learning or deep learning technic. In the work of this paper, the hits from one event in drift chamber are mapped as the elements in a 2dimensional matrix which will be described in detail in the session 2.1. The problem of identification the hits between the first turn and non-first turn became a problem of training a convolutional neural network to do the pixelwise semantic segmentation for the matrix of each event.

The training sample
To learn the behavior of the multi-turn tracks, the training sample is the multi-turn curling tracks generated with Monte-Carlo which are at small dip angle and various transverse momentum. The particle type is single  − and single  + . The tracks with transverse momentum less than 120MeV/c will curling in the MDC is generated. Only the tracks of more than one turn have been selected for the training, validation and testing. The momentum, angle and turn number distribution of the training set show in the Fig. 4.

Fig. 4. Distributions of the training dataset
The MDC has 43 layers and the cell number of each layers range from 40 to 288. To make the shape fit between input and output, the rows and columns of the matrix are set to be the powers of 2. The cells of the drift chamber for each layers were top centered mapped into the corresponding row of a 64 x 256 matrix. The feature set to be the raw time of each hit after correction with the event start time. The feature of the cell without hits were set with a default value of 2000ns. The truth turn number from Monte-Carlo simulation used as target. The hits from the first turn were marked as one. The hits from non-first turns and cells without hit were set to be the default value of zero. And zero also treated to be the default value of the target. Dummy elements in the matrix were set to be the default values.  (1) Where, X is the target matrix and Y is the prediction matrix. In this work, |X| and |Y| are approximately equal with the number of the true first turn's hits and the predicted first turn's hits respectively,| ∩ | is approximately equal with the number of the hits marked as the first turn hits and predicted as the first turn hits.

Performance and conclusion
The efficiency and purity have been evaluated for the single track with validation sample. The definition of the efficiency and the purity show as following: = ′ (4) Where TP is the number of the predicted first turn and marked as first turn by Monte-Carlo truth, P is the number of the true first turn hits and ′ is the number of the hits predicted as first turn. The ROC curve of the average hit efficiency and purity in Fig. 7 shows that at the threshold of about 0.85 the prediction gives the efficiency and purity are about 91%. And more than half of the events have efficiency and purity greater than 95%. An event display in Fig. 8 shows most of the hits from first turn have been predicted correctly.