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Volume 363 - 37th International Symposium on Lattice Field Theory (LATTICE2019) - Main session
Two-pion scattering amplitude from Bethe-Salpeter wave function at the interaction boundary
T. Yamazaki,* Y. Namekawa
*corresponding author
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Pre-published on: 2020 January 17
Published on:
Abstract
We observe that the ratio of the on-shell scattering amplitude to the Bethe-Salpeter (BS) wave function outside the interaction range is almost independent of time in our quenched calculation of the $I=2$ two-pion scattering with almost zero momentum. In order to discuss the time independence, we present a relation between the two-pion scattering amplitude and the surface term of the BS wave function at the boundary. Using the relation under some assumptions, we show that the ratio is independent of time if the two-pion four-point function in early time is dominated by scattering states with almost zero momentum in addition to the ground state of the two-pion scattering.
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