Accelerating dark matter search in emulsion SHiP detector by deep learning

We introduce a novel approach for the reconstruction of particle properties for the SHiP detector. The SHiP experiment significantly focuses on finding effects of dark matter particle interaction. A characteristic trace of such an interaction is an electromagnetic shower. Our algorithm aims to reconstruct the energy and origin of such showers using online Target Tracker subdetectors that do not suffer from pile-up. Thus, the online observation of the excess of events with proper energy can be a signal for a dark matter. Two different approaches were applied: classical, using Gaussian Mixtures and machine learning based on a convolutional neural network. We’ve refined the output of the previous step by clusterization techniques to improve transverse coordinate estimation. The obtained results are 25% for energy resolution, 0.8 cm for position resolution in the longitudinal direction and 1 mm in the transverse direction, without any usage of the emulsion.


Introduction
The SHiP experiment [1] is dedicated to the search for Beyond the Standard Model physics. In particular, one can search for Dark Matter (DM) scattering on electrons in the SHiP scattering detector. The detector consists of lead, an emulsion and target trackers (TT). In order to search for DM signatures, one must detect electromagnetic showers (EM) in either the emulsion or target trackers. The emulsion can only be analysed after half a year of exposure, thus making it sensitive to background pile up. Techniques for EM location and separation in the emulsion were studied in [2].
On the contrary, TT is an online detector and thus does not suffer from events pile up. Nonetheless, it is challenging to identify energy and position of the initial particle in a particular scattering event in TT since the sampling frequency of TT is much smaller than of the emulsion. We investigate the possibility of reconstructing energy and position of the initial particle, using only TT.

Problem statement 2.1. Data sample
The electromagnetic shower is a cone-like structure, consisting of particles (hits), detected in emulsion. Each hit in the emulsion has six initial features: X, Y, Z coordinates, XZ and YZ planes projection angles -θ x and θ y , which fully determine the direction of the hit and χ 2 , which determines the goodness of fit of the hit. When an electromagnetic shower passes through the target tracker, the transverse proportion of the shower is detected. The resulted response of the TT is a 2D map of hits.
The resulting 2D map has a resolution of 1500x1800 pixels. The relative shape of the pixels in the picture and their intensity can indicate the energy and the position(X, Y, Z) of the vertex of the initial particle. Precise knowledge of the position and the energy is very important, since it facilitates the discrimination of a lot of background hits, as stated in [2]. Moreover the collaboration is currently considering the possibility to identify events associated with Dark Matter, using target trackers, without emulsion. The above task is even more important for such a study.
We will work with approximately 450000 events generated by Monte Carlo simulation, with training set size being 90% of the above data and rest 10% being test set size. The events are determined by the energy of the initial particle and the vertex location. The vertex location will be determined by the distance d to the first TT plane. This distance will vary from 0 to -7.5 cm, and all events are uniformly distributed in it. The energy of the particle will be denoted by E, it varies from 1 to 100 GeV and all events are also uniformly distributed in that range. The response of the detector is described by the "picture of hits".

Performance metrics
The energy of the shower is proportional to the number of hits, thus the reconstructed energy is defined as where N h is the number of reconstructed hits in the detector. The quality of the algorithm is assessed by energy resolution, which is defined as where E reco is the predicted energy, E true is the true energy of the shower and σ(·) denote the standard deviation function. This metric, of course, assumes that the predicted values are unbiased. The same metrics are useful to measure the performance of the vertex prediction, namely, The ideal algorithm will be unbiased and has zero resolution.

Related work
Classical techniques to identify eletromagnetic shower energy and position are presented in [3,4,5]. There are also some recently discussed techniques [6,7] based on manually created features, describing electromagnetic showers. Unfortunately, none of these techniques can be applied to our scenario. The reason for this, is that in this study tracking detectors are used. These detectors by construction are not suitable for reconstruction of energy of the shower. To the best of our knowledge, there have been no attempts to estimate the parameters described above using tracking detectors. The most modern techniques, connecting calorimetry and machine learning were discussed in [8,9]. Still, both of these approaches utilise proper calorimeters and are dedicated to generating the detector response with GANs. For example, the authors of Ref. [9] also discuss the problem of sparsity and how to approach it.

Gaussian fit approach
Since we are basically solving a regression problem, we can use some simple methods, like linear regression or SVM and simple features, describing the signal. For example, one can fit a Gaussian function in the middle of the TT response picture and use its variance and covariance as descriptors for the response. The idea behind this is that the two variables we want to predict, energy and Z coordinate, are correlated and the shape of the response depends on both of them.
If we now independently fit three 2D Gaussians to each of the target tracker planes, we will get 3x3 features and the number of hits in each of the tracker -a total of 12 features.

Convolutional Neural Network approach
Since our response is basically an image, we can represent it by stacking detectors as "color" maps. Then, we can devise an architecture of the network and a loss function, that will perform well. With the basic Convolutional Neural Network(CNN) architecture we get 7 GeV RMSE for the energy and ∼ 0.87 cm for the distance. With minimising the Huber loss as the objective, we were able to achieve better performance. The Huber loss is defined as Due to faster convergence and better robustness, the CoordConv [10] layers have been used in the final architecture. The benefit of such a convolution is that it can learn local aware features, but unlike locally-connected convolution, it adds only O(K) additional parameters, where K is the size of the kernel. The net was trained with Loss Huber , where targets were initially scaled to the same range. The training process with gradual L 2 weight regularisation removal was applied. The initial regularisation constant is set to 0.01 and decreased by half every ten epochs. The training loss and validation metrics for the training process are presented in Fig. 3   In the Fig. 5a and Fig. 5a the final physics metrics are shown. As determined by physical laws, the energy resolution should follow ∼ 1/ √ E dependency. The same rule applies to the position resolution due to common ideas. As one can see, the fit of both metrics lies within the uncertainty error of the bins. This verifies that the predictions of the regressor follows the above physical laws.
The comparison of the algorithms described above is presented in table 1.

Transverse shower origin position reconstruction
As discussed in the problem statement, one more task was to reconstruct the (X,Y) coordinates of the vertex. This task is much simpler, since the response of the detectors explicitly contains information about the (X,Y) coordinates.  We have applied the (H)DBSCAN algorithm [11,12] to each map of the response picture. The algorithm is presented in alg. 1. if len(cluster centers) > 0 then SelectBestCluster(cluster centers); else reject event; where F indCenter(cluster) x,y = i∈cluster (x, y) * I i i∈cluster I i , with I i being the intensity of the hit. SelectBestCluster algorithm works as follows: It performs a linear fit between all possible combinations of the cluster centers in all the TT stations. It selects those cluster centers in each TT station, which minimises MSE error of the fit. Nevertheless we perform a combinatorial number of operations to perform this fit, this is feasable in pracite, since the number of clusters is of order 2 to 3 in each TT station. As a FindClusters function we have tested DBSCAN, HDBSCAN and GaussianMixtures and selected DBSCAN as the best option. The obtained position resolution is ∼ 0.1 cm, whereas the baseline solution (locating center of the cluster just as a weighted mean of all the hits the TT station) provides only ∼ 0.3 cm resolution. Results are shown in Fig. 6a, 6b. (a) (b) Figure 6: (a) XY resolution with clustering. (b) XY resolution without clustering.

Conclusion
We provide particle energy and position reconstruction algorithms for the SHiP experiment given only online detector output. Our approach shows comparable resolution in energy and position to classical emulsion algorithms [13] for high energy events. A Shallow convolutional neural network with special (CoordConv) convolutional layers, trained with gradual regularisation, was used. A resolution of 24% in energy and 0.8 cm in longitudinal direction was obtained. The (H)DBSCAN was used for the prediction of the transverse coordinates. A resolution of ∼ 0.1 cm in the transverse direction was obtained.