Abstract
We study the formalism of Kosower-Maybee-O’Connell (KMOC) to extract classical impulse from quantum amplitude in the context of the partial wave expansion of a 2-to-2 elastic scattering. We take two complementary approaches to establish the connection. The first one takes advantage of Clebsch-Gordan relations for the base amplitudes of the partial wave expansion. The second one is a novel adaptation of the traditional saddle point approximation in the semi-classical limit. In the former, an interference between the S-matrix and its conjugate leads to a large degree of cancellation such that the saddle point approximation to handle a rapidly oscillating integral is no longer needed. As an example with a non-orbital angular momentum, we apply our methods to the charge-monopole scattering problem in the probe limit and reproduce both of the two angles characterizing the classical scattering. A spinor basis for the partial wave expansion, a non-relativistic avatar of the spinor-helicity variables, plays a crucial role throughout our computations.
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Acknowledgments
This work was supported in part by the National Research Foundation of Korea grant NRF-2019R1A2C2084608. We are grateful to Joon-Hwi Kim, Jung-Wook Kim, Kanghoon Lee and Sungjay Lee for discussions and comments on the manuscript. S.M. would like to thank SINP, Kolkata; TIFR, Mumbai and the organizers of ‘QCD Meets Gravity’ conference for hospitality while this work was in progress.
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Lee, H., Lee, S. & Mazumdar, S. Classical observables from partial wave amplitudes. J. High Energ. Phys. 2023, 96 (2023). https://doi.org/10.1007/JHEP06(2023)096
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DOI: https://doi.org/10.1007/JHEP06(2023)096