Journal of East China Normal University(Natural Science) >

2023 , Vol. 2023 >Issue 4: 137 - 150

DOI: https://doi.org/10.3969/j.issn.1000-5641.2023.04.015

Physics and Electronics

Faddeev equation for three-boson system in low-energy short-distance effective field theory

  • Kai WANG ,
  • Jifeng YANG
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  • School of Physics and Electronic Science, East China Normal University, Shanghai　200241, China

Received date: 2022-05-18

  Online published: 2023-07-25

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Abstract

Based on the closed-form t matrix of a two-body system in low-energy short-distance effective field theory, the approximate closed-form three-body T matrix for a zero-spin three-boson system is obtained using the Faddeev equation under two-body contact interactions. In momentum representation, the contact potentials are polynomials, and the Lippmann-Schwinger equation can be simplified to algebraic equations using a factorization trick, facilitating nonperturbative renormalization. However, it is impossible to apply such a factorization trick directly to the Faddeev equation. Therefore, the momenta dependence of the T matrix is “split” such that the factorization trick can still be applied. The closed-form T matrices are then obtained as nonperturbative approximate solutions of the Faddeev equation under the leading and next-to-leading order contact potentials with verified consistency. As in a two-body case, such a closed-form T matrix also facilitates the convenient implementation of the nonperturbative renormalization.

Key words： effective field theory; Faddeev equations; nonperturbative approximation; general parametrization

Cite this article

Kai WANG , Jifeng YANG . Faddeev equation for three-boson system in low-energy short-distance effective field theory[J]. Journal of East China Normal University(Natural Science), 2023 , 2023(4) : 137 -150 . DOI: 10.3969/j.issn.1000-5641.2023.04.015

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