Journal of East China Normal University(Natural Science) ›› 2023, Vol. 2023 ›› Issue (4): 137-150.doi: 10.3969/j.issn.1000-5641.2023.04.015

• Physics and Electronics • Previous Articles     Next Articles

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

Kai WANG, Jifeng YANG*()   

  1. School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
  • Received:2022-05-18 Online:2023-07-25 Published:2023-07-25
  • Contact: Jifeng YANG


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

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