Title:

On Machine Learning and the Phase of the S-Matrix

The Scattering Matrix (S-Matrix) is a matrix representation of the probability amplitudes of how particles can scatter off each other. In the 1970s, D. Atkinson found families of solutions to the equations governing this scattering with phase-shift ambiguities. In Atkinson’s work, he solved for a parameter called sinμ, which governs if the scattering angle for two particles has a unique solution. The lowest value of sinμ that Atkinson was able to solve for was 2.15. After Atkinson’s work, research in the field went quiet for many decades until 2023. A. Dersy, M. Schwartz, and A. Zhiboedov used machine learning to solve for a new lowest sinμ value of 1.67. Dersy et al. published the S-Matrix Bootstrap program used to solve for this new lowest sinμ value in their paper, which we have modified for this project. In the S-Matrix Bootstrap program, we added additional points to the integral equation used to solve for the value of sinμ and added an Adaptive Fourier layer to the network. Both these additions to the program have been able to reproduce the results of Dersy et al. and have possibly led to a new lowest sinμ value of 1.447, though more analysis is needed to confirm this result.

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