Machine learning-based prediction of multi-muon events in the INO-ICAL prototype stack

The upcoming India-based Neutrino Observatory (INO) will host a 50 kton magnetized Iron Calorimeter (ICAL) to study atmospheric neutrinos. As part of its proposal, small-scale prototype detectors have been built and are in operation. The primary focus in these prototypes has been on detector characterization studies. At the same time, few physics analyses were also carried out with the cosmic muon data collected. However, due to the small size of the detectors, such analyses always relied on the assumption that the tracks were of single muons only. Consequently, multi-muon events were discarded as noisy events, reducing the physics potential. In this work, we report the development of a machine learning model to predict multi-muon events, study its efficiency and report the muon multiplicity distribution observed using cosmic muon events from the prototype detector.


Introduction
The India-based Neutrino Observatory (INO) is a proposed non-accelerator-based high-energy physics project for atmospheric neutrino studies.The proposed detector at INO is a 50 kt Iron Calorimeter (ICAL) which will be placed inside a cavern with a rock overburden of about 1 km.About 30 000 Resistive Plate Chambers (RPCs) of 2 m × 2 m in the area will be used as active detectors [1].To analyse the performance of the detectors, various R&D programmes were initiated, and prototype detector setups were developed.The data collected using the prototype stack was primarily used for characterizing the detector performance estimated using its parameters like efficiency, spatial/timing resolution, and noise rates.In these analyses, the first step is to fit a straight-line to the tracks from which all other quantities are deduced.In the straight-line fit, tracks with a large χ 2 are flagged as noisy events and are removed from the analysis of some of the parameters [2].As a consequence of this procedure, some interesting events, for instance, multi-muon events, were also flagged as noisy events, reducing the physics potential of the detector.This study aims to develop a machine learning algorithm to identify multimuon events in the cosmic muon datasets in one of the prototype detectors, study the efficiency of the algorithm, and to report the muon multiplicity distribution thus obtained using the algorithm.

Motivation
Above a certain energy threshold, the rate of cosmic muon multiplicity carry signatures of chemical composition and energy spectrum of the nuclei in primary cosmic rays.This is due to the fact that, heavy nuclei are more effective in producing multiple muons than light nuclei with the same total energy per nucleus [3].Underground detectors are, therefore, more suitable for such studies as the energy threshold conditions are automatically satisfied.Many experiments have studied cosmic muon multiplicity distributions, comparing them with montecarlo estimations with varying chemical compositions of the primaries.Studies with the MACRO detector at Gran Sasso National Laboratory and the ALICE detector at CERN LHC are prime examples in this context [3,4].
The MACRO detector has a rock overburden of 3200 mwe similar to INO-ICAL (3370 mwe) with an energy threshold at the surface of about 1.4 TeV [5,6].Results from muon multiplicity and lateral separation between muons in the MACRO favour a light composition model i.e, with an enhanced proton component [7].The size of the MACRO detector is 76 m × 12 m × 9 m whereas the proposed INO-ICAL detector will be underground, with a volume of about 48 m × 16 m × 14.4 m.Owing to the larger size of INO-ICAL and acceptance compared to MACRO, it will be possible to study high muon multiplicities and large separations to validate the composition.
Prototype detectors of INO-ICAL are setup on the surface and are small for any reasonable physics to be extracted from the multiplicity distributions.Nevertheless, in view of the evergrowing need and role of machine learning in high energy physics applications, it was deemed to be of considerable interest to us to exploit machine learning techniques to identify multi-muon events and to understand the advantages and limitations that they may offer.The results may also prove important for bookkeeping purposes as such studies can be extended when the full detector is constructed.In line with our previous works, these activities serve as a platform to develop machine learning algorithms for the INO-ICAL detector [2,8].

Detector setup
In this study, we have considered the prototype stack at TIFR, Mumbai, which consists of 12 layers of glass RPCs of dimension 1 m × 1 m stacked as shown in figure 1.The gap between the layers is about 16.8 cm, and the height of the stack is about 1.85 m [9].Each RPC has 32 strips of 3cm each, one set on the top surface (x plane) and another at the bottom (y plane), such that the strips on the x plane are orthogonal to those on the y plane enabling a 2D readout scheme.A VME-based data acquisition system continuously records cosmic muon events in response to a trigger [10].When a charged particle enters the detectors and the trigger condition is satisfied, the data acquisition system reads out the digitized positional information and the timing information from the 12 RPCs.The selection of the trigger condition for a certain run is determined based on the experimental requirements.A common trigger condition is the coincidence of the top and bottom layers in the stack.Ideally, with this trigger, a set of 12 x, y positional hit information and timing data is expected for every single muon event.For a multi-muon event, on the other hand, the number of hits depends on the muon multiplicity and the angle of arrival.Due to this factor and others like noise and detector inefficiencies, the number of hits in an event may not correlate with the muon multiplicity.
The prototype detector is much smaller than the actual detector which will host 30,000 RPCs with a total volume of 48 m × 16 m × 14.5 m.The prototype detector does not have any magnetic fields whereas the full detector will have a magnetic field of 1.5 T. The triggering scheme of the prototype is a simple coincidence of few layers in the stack whereas for the full detector, a FPGA-based logic has been proposed to trigger on neutrino events with high efficiency [11].
The work presented here is based on the data collected from this prototype which is typically used for studies of detector characterization and long-term performance.

Machine learning pipeline
The pipeline for this analysis consists of three independent stages: the data generation stage, the training and testing stage, and the prediction stage.These stages are explained in the following sections.

Data generation
To generate the dataset for training the machine learning models, a python-based algorithm was developed.Given a specific muon multiplicity, the algorithm generates a set of random events each of the same multiplicity.Further, for the events to be similar to realistic events, parameters like detector efficiency, strip hit multiplicity and noise multiplicity can also be tweaked.With the aid of this algorithm, the following datasets were generated for training: Each strip in a layer is represented by an element in the sparse matrix of dimension 12 × 64, which corresponds to 12 layers and 32 strips in the two projections for each event in the dataset.The matrix is initialised to zero and if a strip has a hit, the corresponding element is set to unity.To generate multi-muon events, multiple random slopes and the intercepts are generated and strip hits are added accordingly.

Dataset II: Tracks including detector efficiency (η)
The RPCs used in the prototype stack have an efficiency of more than 90%, depending on the operating voltage and other ambient parameters.The parameter η represents this effect.The dataset used in this study was generated for detector efficiency of 97%.For simplicity, we have assumed the efficiencies of the x-side and y-side to be similar.

Dataset III: Tracks including η and strip hit multiplicity (S m )
Another parameter that characterizes the RPC performance is the strip hit multiplicity.As a muon passes through a RPC, it produces an avalanche in the gas medium.The size of this avalanche depends on many parameters and decides the spatial resolution of the detector.In some cases if the avalanche is near the edge of a strip, the neighbouring strips may also generate a hit leading to multiple neighbouring hits for a single particle.Based on previous studies, the average strip hit multiplicity for cosmic ray muon data is estimated to be ∼1.5 [12].

Dataset IV: Tracks including η, S m and noise multiplicity (N m )
The parameter N m characterizes the influence of noise in a event possibly generated due to improper gas distribution and electronic noise.The effect of noise in RPCs in general results in uncorrelated hits.We have considered a nominal noise of 3 hits per layer in this study.This step is performed after the inclusion of efficiency and strip hit multiplicity effects.
In each class of dataset a total of 40 000 events were generated and the maximum multiplicity of 4 was considered in this study.All the four muon multiplicities are equally represented in all the datasets.It is possible that fully noisy events, not generated due to a muon, are wrongly identified as genuine events by the machine  learning model.In order to remove this bias, 10 000 noisy events with all uncorrelated hits were added to all the datasets described above.
A sample event of multiplicity 4 after every stage of adding detector parameters is shown in figure 2.

Training and testing
A XGBoost based model was trained using the datasets mentioned earlier with 80% of the samples, the rest being used for testing [13].There are 5 classes in this classification study with four of them representing the four multiplicities and one representing a noisy event.The strip hit patterns in both the projections were used as the features for training.The training parameters were optimized by a trial and error process.The training was done on a machine with an Intel Xeon CPU with 256GB physical memory and installed with a Tesla V-100 GPU with 16 GB RAM.The GPU processing feature was enabled in the XGBoost model while training.The hyperparameters were set as follows: maximum depth = 3, learning rate = 0.1 and number of estimators = 1000.For each dataset, the total time taken for training was about 3 minutes.The results of testing with the 20% samples in the dataset is shown in figure 3.As seen from the figure, the results from machine learning predictions are over 97% for all the cases, and as expected, the predictions from Dataset IV, in which all the detector effects are included, are marginally poor compared to the other cases.

Analysis using machine learning predictions
Using the trained model from Dataset IV, which includes all detector parameters, cosmic muon events were labelled according to their multiplicity.About 25 × 10 6 cosmic muon events recorded over a 213-hour time period were used in this analysis.A sample of multi-muon events predicted from cosmic muon data is presented in figure 4. The multiplicity distribution is also shown in figure 5.As is seen from this distribution, the single muon events dominate over all other multiplicities (98%), with a very small fraction of events falling into the other multiplicity classes.It is to be noted here that noisy events shown as class 0 in the figure need not necessarily indicate a genuine noisy track as higher multiplicity events might also be included in this class.Since the time of occurrence of multi-muon events is considered to be random, it is expected that the distribution of time difference between consecutive events to follow an exponential distribution [14,15].The same is demonstrated in figure 6 and the average rate as estimated from the plot is 0.07 s −1 .The average trigger rate seen in the detector is about 10Hz [9].The ratio of two-multiplicity events to single muons events is about 5 × 10 −3 .Assuming that the two-multiplicity rates scales according to this ratio, the rate of two-multiplicity events is about 0.05 s −1 .Similarly, the three-multiplicity and four multiplicity rates are found to be, 0.02 s −1 and 0.01 s −1 .The weighted average of multi-muon rates is found to be 0.6 s −1 , very close to the mean rate.

Conclusion
In this work, we have demonstrated the development and application of a machine learning algorithm to predict multi-muon events in the cosmic muon data collected using the INO-ICAL prototype TIFR stack at TIFR Mumbai.A machine learning model was trained with different datasets to quantify the impact of various detector parameters on the labelling efficiency.It was seen that all the models yielded an efficiency of more than 97%.In a cosmic muon dataset of about 25 × 10 6 events, the trained model was able to identify multi-muon events upto a maximum multiplicity of 4. It was seen from the multiplicity distribution that the single muon events dominated over all other multiplicities.Further, a polynomial fit to the logarithm of the time difference distribution indicated that the multi-muon events were uncorrelated and that the mean rate is about 0.07 s −1 .The datasets collected over a period of more than 10 years were until now used for studying detector performance.This study has helped extend the physics potential of the detector adding a level of event labelling thus providing a handle for other possible physics studies with multi-muon events.The study was performed using a Linux system with Intel Xeon processor, 256 GB of physical memory, hosting a a Tesla V-100 GPU with 16 GB of RAM.The GPU parallel processing feature for training was enabled for the XGBoost model used in this study.The average prediction time is about 760 μs, and therefore the model can be integrated in the existing data acquisition system to predict multi-muon events in real-time and to write the labels directly.

Figure 1 .
Figure 1.A schematic of the prototype detector stack at TIFR consisting of 12 layers of RPCs.Reproduced from [9].© IOP Publishing Ltd.All rights reserved.
Dataset I: Clean tracks • Dataset II: Tracks including detector efficiency (η) • Dataset III: Tracks including η and strip hit multiplicity (S m ) • Dataset IV: Tracks including η, S m , and noise multiplicity (N m )These datasets help benchmark and quantify the effects of the detector parameters on the performance of the machine learning models.4.1.1.Dataset I: Clean tracksThis dataset contains clean tracks ignoring the effects of efficiency, strip hit multiplicity, or noise.

Figure 2 .
Figure 2. Sample simulated events of multiplicity 4 in each stage a) Clean track, b) After adding detector efficiency factor, c) Detector efficiency and strip hit multiplicity added, and d) All effects and noise multiplicity added.Here x-axis represents the strips, and the yaxis, the layers.

Figure 3 .
Figure 3. Prediction efficiency plot as a function of multiplicity for all four datasets.Noisy events fall in the class of −1.

Figure 4 .
Figure 4. Predicted multi-muon events from cosmic muon data collected from TIFR INO-ICAL prototype stack.Top: a multiplicity 2 event; Middle: a multiplicity 3 event; Bottom: a multiplicity 4 event.

Figure 5 .
Figure 5. Multiplicity distribution of cosmic muons collected from the TIFR prototype stack.About 25 × 10 6 events were used in this analysis.The noisy events are labelled as 0.