Two-particle wave function in four dimensional Ising model

Calculation of the scattering phase shift is important to understand scatterings and decays of hadrons. The phase shift in I = 2 ππ scattering system [3] was evaluated with the finite volume method [1,2] derived by Lüscher. In the finite volume method two-particle wave function plays an important role, because the phase shift is extracted by the wave function. Study of the wave function was carried out by Balog et al. [4]. Using two-dimensional statistical model they evaluated the phase shift from the wave function for several two-particle states. Recently Ishizuka et al. and CP-PACS collaboration studied the wave function in I = 2 ππ scattering system [5]. They extracted the scattering length and scattering effective potential from the wave function for the ground state. Here calculation of the wave function for the first excited and an unstable states is attempted with a four dimensional simple Ising model. It is also aimed to evaluate the phase shift from these wave functions.