Deep Neural Network for Detecting Nucleon-Nucleon Bound State

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Introduction

We oftentimes associate the peak position and width of a distribution to the real and imaginary part of an energy pole, respectively. However, the presence of a branch point distorts the lineshape, making it difficult to specify whether the pole is located above or below the threshold. It turns out that this problem can be solved using the machine learning approach. In this work, we designed a deep neural network to classify the enhancement near a twobody threshold. That is, given the scattering amplitude as an input, our neural network will give the nature of nearthreshold pole. To fully describe our approach, we consider only the single-channel scattering of the nucleon-nucleon system.

Materials and Methods

A sizable training dataset is generated using a generic S-matrix model satisfying both analyticity and unitarity. Six deep neural networks with different architectures and different optimizers are prepared. During the training, we monitor any possible overfitting of the model using a separate testing set. To ensure that our deep neural networks can generalize beyond the training dataset, we prepared an independent set of validation data. The validation data is generated using two separable potential models. Finally, we use the Nijmegen data analysis and models for nucleon-nucleon scattering amplitude as a final test of our approach.

Results and Discussion

Figure 1 shows the performance of our models against the validation dataset. We only expect accurate predictions within the shaded region since some parameters of training dataset overlaps with the validation set. However, the result shows that the neural network can generalize beyond the training dataset. We then used our models on the nucleon-nucleon low energy scattering data and obtained correct predictions.

Conclusions

We demonstrated the deep learning can help probe the nature of scattering enhancement using only the data. Our approach will be useful in understanding the already established and recently discovered hadron exotic resonances.