Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons

Koji Harada, Hirofumi Kubo, Issei Yoshimoto

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Low-energy effective field theory describing a nonrelativistic three-body system is analyzed in the Wilsonian renormalization group method. No effective auxiliary field (dimeron) that corresponds to two-body propagation is introduced. The Efimov effect is expected in the case of an infinite two-body scattering length and is believed to be related to the limit cycle behavior in the three-body renormalization group equations (RGEs). If the one-loop property of the RGEs for the nonrelativistic system without the dimeron field, which is essential in deriving RGEs in the two-body sector, persists in the three-body sector, it appears to prevent the emergence of limit cycle behavior. We explain how the multiloop diagrams contribute in the three-body sector without contradicting the one-loop property of the RGEs and derive the correct RGEs, which lead to the limit cycle behavior. The Efimov parameter, s0, is obtained within a few percent error in the leading orders. We also remark on the correct use of the dimeron formulation. We find rich renormalization group flow structure in the three-body sector. In particular, a novel nontrivial fixed point of the three-body couplings is found when the two-body interactions are absent. We also find, on the two-body nontrivial fixed point, the limit cycle is realized as a loop of finite size in the space of three-body coupling constants when terms with derivatives are included.

Original languageEnglish
Article number085006
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number8
Publication statusPublished - Apr 2 2013

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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