O(2,1) decomposition of the equal-mass multipheripheral equation at t=0
We extend the results of a group-theoretical analysis of the t=0 multiperipheral equation to the case t<0 for pairwise equal masses. Using variables discussed in a previous paper, we diagonalize the equation in the Bali-Chew-Pignotti (BCP) model with respect to the 0(2, 1) group and relate the solutions to the equation so obtained with the solutions obtained after diagonalization with respect to the 0(3, 1) group. Poles in the 0(3, 1) partial-wave amplitude give rise to the expected sequence of daughter poles in the 0(2, 1) partial-wave amplitude. At general momentum transfer, we establish factorization at the 0(1, 1) poles in the decomposition of the BCP amplitude, and present further simplifications to the diagonalized equations based upon this model.