Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for multiparticles in quantum field theories

Sinya Aoki, Noriyoshi Ishii, Takumi Doi, Yoichi Ikeda, Takashi Inoue

研究成果: Contribution to journalArticle査読

23 被引用数 (Scopus)


We derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than two particles in quantum field theories. To deal with n particles in the center-of-mass frame coherently, we introduce the Jacobi coordinates of n particles and then combine their 3(n-1) coordinates into the one spherical coordinate in D=3(n-1) dimensions. We parametrize the on-shell T matrix for n scalar particles at low energy using the unitarity constraint of the S matrix. We then express asymptotic behaviors of the NBS wave function for n particles at low energy in terms of parameters of the T matrix and show that the NBS wave function carries information of the T matrix such as phase shifts and mixing angles of the n-particle system in its own asymptotic behavior, so that the NBS wave function can be considered as the scattering wave of n particles in quantum mechanics. This property is one of the essential ingredients of the HAL QCD scheme to define "potential" from the NBS wave function in quantum field theories such as QCD. Our results, together with an extension to systems with spin 1/2 particles, justify the HAL QCD's definition of potentials for three or more nucleons (or baryons) in terms of the NBS wave functions.

ジャーナルPhysical Review D - Particles, Fields, Gravitation and Cosmology
出版ステータス出版済み - 7 24 2013

All Science Journal Classification (ASJC) codes

  • 核物理学および高エネルギー物理学
  • 物理学および天文学(その他)


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