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Faddeev equation for three-boson system in low-energy short-distance effective field theory
Received date: 2022-05-18
Online published: 2023-07-25
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.
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
1 | WEINBERG S. Phenomenological lagrangians. Physica A, 1979, 96 (1/2): 327- 340. |
2 | GEORGI H. Effective field theory. Annual Review of Nuclear and Particle Science, 1993, 43 (1): 209- 252. |
3 | GASSER J, SAINIO M E, SVARC A. Nucleons with chiral loops. Nuclear Physics B, 1988, 307 (4): 779- 853. |
4 | WEINBERG S. Nuclear forces from chiral lagrangians. Physics Letters B, 1990, 251 (2): 288- 292. |
5 | KAPLAN D B, SAVAGE M J, WISE M B. A new expansion for nucleon-nucleon interactions. Physics Letters B, 1998, 424 (3): 390- 396. |
6 | EPELBAUM E, GL?CKLE W, MEI?NER U. Nuclear forces from chiral lagrangians using the method of unitary transformation II: The two-nucleon system. Nuclear Physics A, 2000, 671 (1): 295- 331. |
7 | ENTEM D R, MACHLEIDT R. Chiral 2π exchange at fourth order and peripheral NN scattering. Physical Review C, 2002, 66 (1): 014002. |
8 | YANG J F, HUANG J H. Renormalization of NN scattering: Contact potential. Physical Review C, 2005, 71 (3): 034001. |
9 | YANG J F. A note on nonperturbative renormalization for effective field theory. Journal of Physics A, 2009, 42 (34): 345402. |
10 | YANG J F. Nonperturbative NN scattering in 3S1–3D1 channel of EFT $ \left(\not { \pi }\right) $ . Annals of Physics, 2013, 339, 160- 180. |
11 | Lü J J, YANG J F. Running under tight constraints in pionless effective field theory. International Journal of Modern Physics E, 2021, 30 (5): 2150026. |
12 | PAN T W, YANG J F. Closed-form Brückner G-matrix and nuclear matter in EFT $ \left(\not { \pi }\right) $ . Physics Letters B, 2021, 817 (10): 136302. |
13 | PHILLIPS D R, BEANE S R, COHEN T D. Nonperturbative regularization and renormalization: Simple examples from nonrelativistic quantum mechanics. Annals of Physics, 1998, 263 (2): 255- 275. |
14 | FONSECA A C, PENA M T. Faddeev-Born-Oppenheimer equations for molecular three-body systems: Adiabatic calculation of 9Be . Nuclear Physics A, 1988, 487 (1): 92- 132. |
15 | STADLER A, GL?CKLE W, Sauer P U. Faddeev equations with three-nucleon force in momentum space. Physical Review C, 1991, 44 (6): 2319- 2327. |
16 | BEDAQUE P F, HAMMER H W, VAN KOLCK U. Renormalization of the three-body system with short-range interactions. Physical Review Letters, 1999, 82 (3): 463- 467. |
17 | BEDAQUE P F, RUPAK G, GRIE?HAMMER H W. Low energy expansion in the three-body system to all orders and triton channel. Nuclear Physics A, 2003, 714 (3/4): 589- 610. |
18 | JI C, PHILLIPS D R, PLATTER L. The three-boson system at next-to-leading order in an effective field theory for systems with a large scattering length. Annals of Physics, 2012, 327 (7): 1803- 1824. |
19 | GL?CKLE W. The Quantum Mechanical Few-body Problem [M]. Berlin: Springer, 1983. |
20 | JOACHAIN C J. Quantum Collision Theory [M]. Amsterdam: North-Holland Publishing Company, 1975. |
21 | NEWTON R J. Scattering Theory of Waves and Particles [M]. Berlin: Springer, 1982. |
22 | BAKER G A. Essentials of Padé Approximants [M]. New York: Academic Press, 1975. |
23 | YANG J F, NI G J. Padé improvement of beta-function in perturbative λ?4 and QED . Communications in Theoretical Physics, 1994, 22 (2): 207- 212. |
24 | YANG J F, HUANG J H, LIU D. Padé expansion and the renormalization of nucleon-nucleon scattering. Chinese Physics Letters, 2006, 23 (10): 2688- 2690. |
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