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

作者：Aoki Sinya^*; Ishii Noriyoshi; Doi Takumi; Ikeda Yoichi; Inoue Takashi

来源：PHYSICAL REVIEW D, 2013, 88(1): 014036.

DOI：10.1103/PhysRevD.88.014036

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 %26quot;potential%26apos;%26apos; 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%26apos;s definition of potentials for three or more nucleons (or baryons) in terms of the NBS wave functions.

• 出版日期2013-7-24
• 单位RIKEN