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