Line shape analysis of $\Lambda(1405)$ in $\gamma p \rightarrow K^+\Sigma^-\pi^+$ reaction using convolutional neural network

Interpreting peaks or dips that appear in an invariant mass distribution is a recurring challenge in hadron physics. These enhancements can be ambiguous, especially near a two-hadron threshold since kinematical and dynamical effects play an important role in their nature. One such enhancement is an exotic baryon $\Lambda(1405)$ which was first observed in 1973. Despite the few available experimental data, the statistics of the measurements of $\Lambda(1405)$ have improved for line shape analysis. The present consensus is that it is a structure of two poles both on the second Riemann sheet. However, there are still investigations of other pole structures corresponding to $\Lambda(1405)$. Lately, the use of a deep neural network in analyzing these line shapes has been proven to be effective, especially in distinguishing pole structures. Thus, in this study, we develop a convolutional neural network, a type of DNN, to determine the general pole structure that corresponds to $\Lambda(1405)$ found in the $\Sigma^-\pi^+$ invariant mass distribution measured by CLAS in their experiment involving the $\gamma p \rightarrow K^+\Sigma\pi$ reaction. The CNN is trained using a two-channel uniformized $S$-matrix allowing us to control the position and the corresponding Riemann sheet of the poles. Our preliminary results show that the trained CNN can accurately distinguish pole structures in the $\Sigma^-\pi^+$ invariant mass distribution and agrees with the present consensus of a two-pole structure. This supports the preceding works on the $\Lambda(1405)$ and requires a thorough analysis of $\Sigma^+\pi^-$ and $\Sigma^0\pi^0$ invariant mass spectra.