Relativistic partial-wave analysis for three-meson systems. I

In previous Faddeev-type treatments of three-meson resonant systems, the Galilean two-body relative momentum has been employed in relativistic partial-wave analyses carried out in the three-body center-of-mass frame. However, this leads to difficulties in the interpretation of the Galilean form as the proper relativistic two-body relative momentum. We show that these difficulties are overcome if the two-body internal momentum is defined so as to have both its magnitude and direction independent of the Lorentz frame in which it is evaluated, analogous to the identical property of the Galilean relative momentum for various Galilean frames. Using such a relativistic version of the internal momentum, we carry out, as an example, a partial-wave analysis of the minimal-dynamics K-matrix equations by using the Omnes coupling scheme. Finally we apply our results to the I = 0 channel of the three-pion system